View in EDS HTML Full Text PDF Full Text

Building Concept Maps by Adapting Semantic Distance Metrics to Wikipedia

Saved in:
Bibliographic Details
Title: Building Concept Maps by Adapting Semantic Distance Metrics to Wikipedia
Language: English
Authors: Fuentes-Lorenzo, Damaris, Morato, Jorge, Sanchez-Cuadrado, Sonia, Sanchez, Luis
Source: Education for Information. 2019 35(3):209-240.
Availability: IOS Press. Nieuwe Hemweg 6B, Amsterdam, 1013 BG, The Netherlands. Tel: +31-20-688-3355; Fax: +31-20-687-0039; e-mail: info@iospress.nl; Web site: http://www.iospress.nl
Peer Reviewed: Y
Page Count: 32
Publication Date: 2019
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Concept Mapping, Web Sites, Collaborative Writing, Information Sources, Taxonomy, Computational Linguistics, Nouns, Vocabulary, Natural Language Processing, Comparative Analysis, Measurement, Semantics, Visual Learning
DOI: 10.3233/EFI-190279
ISSN: 0167-8329
Abstract: Building and checking concept maps is an active research topic in visual learning. Concept maps are intended to show visual representations of interrelated concepts in educational and professional settings. For the last decades, numerous formulas have been proposed to compute the semantic proximity between any pair of concepts in the map. A review of the employment of semantic distances in concept map construction shows the lack of a clear criterion to select a suitable formula. Traditional metrics can be basically grouped depending on the representation of their knowledge source: statistic approaches based on co-occurrence of words in big corpora; path-based methods using lexical structures, like taxonomies; and multi-source methods which combine statistic approaches and path-based methods. On the one hand, path-based measures give better results than corpora-based metrics, but they cannot be used to process specific concepts or proper nouns due to the limited vocabulary of the taxonomies used. On the other side, information obtained from big corpora -- including the World Wide Web -- is not organized in a specific way and natural language processing techniques are usually needed in order to obtain acceptable results. In this research Wikipedia is proposed since it does not have such limitations. This article defines an approach to adapt path-based semantic similarity measures to Wikipedia for building concept maps. Experimental evaluation with a well-known set of human similarity judgments shows that the Wikipedia adapted metrics obtains equal or even better results when compared with the non-adapted approaches.
Abstractor: As Provided
Entry Date: 2019
Accession Number: EJ1228204
Database: ERIC
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
    Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwEm04zHK3i2GVXimd6RnnTaAAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDCABrBW_ovItu6KYsgIBEICBm6l2zHRkmeqR2OS2kK1K-0ymy2tlyhGObNHYdYX6B0ZfZHYi37HxrLpIeZA9anoz6npndrr5SLmjHjkPc1EQaCGbQSLPpEUuR-Ul9342Vmm9BfcwzgZ0ZC_qUUgZ87bllJ7d-gVyMSXMJ7S3i4lvhYkNAiMinwrNIQ2gnlzqThgeA9gcJb5XTMbYKJ22Q9ULGu5fpf42FlfuMDZP
Text:
  Availability: 1
  Value: <anid>AN0138480701;efi01jul.19;2019Sep09.02:44;v2.2.500</anid> <title id="AN0138480701-1">Building concept maps by adapting semantic distance metrics to Wikipedia </title> <p>Building and checking concept maps is an active research topic in visual learning. Concept maps are intended to show visual representations of interrelated concepts in educational and professional settings. For the last decades, numerous formulas have been proposed to compute the semantic proximity between any pair of concepts in the map. A review of the employment of semantic distances in concept map construction shows the lack of a clear criterion to select a suitable formula. Traditional metrics can be basically grouped depending on the representation of their knowledge source: statistic approaches based on co-occurrence of words in big corpora; path-based methods using lexical structures, like taxonomies; and multi-source methods which combine statistic approaches and path-based methods. On the one hand, path-based measures give better results than corpora-based metrics, but they cannot be used to process specific concepts or proper nouns due to the limited vocabulary of the taxonomies used. On the other side, information obtained from big corpora – including the World Wide Web – is not organized in a specific way and natural language processing techniques are usually needed in order to obtain acceptable results. In this research Wikipedia is proposed since it does not have such limitations. This article defines an approach to adapt path-based semantic similarity measures to Wikipedia for building concept maps. Experimental evaluation with a well-known set of human similarity judgments shows that the Wikipedia adapted metrics obtains equal or even better results when compared with the non-adapted approaches.</p> <p>Keywords: Visual learning; concept maps; semantic similarity; semantic distance; path-based measures; similarity judgments</p> <hd id="AN0138480701-2">1. Introduction</hd> <p>Building concept map is an active research topic in visual learning. These maps are intended to show visual representations of interrelated concepts in educational and professional settings (Morato et al., 2014). Concept maps are not only a knowledge representation tool for teaching, but an evaluation tool as well. In 1970, Novak proposed its use to assess students' understanding of a subject (Kumar et al., 2012). Checking by hand the adequacy of these representations may be a tedious work. It is in this context that semantic similarity metrics are employed. Although, a review of the employment of the different semantic distances in concept map construction shows the lack of a clear criterion to select a suitable formula.</p> <p>Semantic similarity indicates how much two words are related in meaning, and it is different from semantic relatedness, which evaluates how much two words are associated in general (Resnik, 1995). Numerous models have been proposed to calculate semantic similarity between words. These traditional approaches can be grouped depending on the representation of their knowledge source: (<reflink idref="bib1" id="ref1">1</reflink>) Statistic approaches based on co-occurrence of words, using big corpora; (<reflink idref="bib2" id="ref2">2</reflink>) path-based methods using lexical structures; and (<reflink idref="bib3" id="ref3">3</reflink>) multi-source methods, which combine statistic approaches with path-based methods. Measures using big unstructured corpora take advantage of their great coverage. One specific case are the methods using web search engines, which take the updated indexed documents of the World Wide Web as input; however, they cannot take benefit from path-based features of well-structured sources and results obtained are worse than taxonomy (path)-based approaches. Most of the path-based and multi-source methods have been developed and evaluated for WordNet taxonomy (Miller & Charles, 1991), and they have proved to yield good results, mainly because a taxonomically structured resource is best suited to estimate taxonomic similarity. However, path-based and multi-source methods using taxonomies or dictionaries suffer from several drawbacks that make their use difficult for building concept maps:</p> <p></p> <ulist> <item> • They cannot be used for scenarios that require a great coverage of the real world; for example, words such as some proper nouns (<emph>Angela Merkel</emph>) or specific terminology (<emph>hyperpolarization</emph>) are not defined in WordNet.</item> <p></p> <item> • New words or modifications in existing traditional corpora are managed slowly in time.</item> <p></p> <item> • Most of these sources are built just in English, and metrics that perform well cannot be used in other languages.</item> </ulist> <p>Wikipedia solves these drawbacks by providing a vast knowledge for computing semantic similarity between word senses. It is a free online site where the information of each real world concept is represented in single pages or articles. It is built upon a more defined structure than web search engines and has more information than WordNet or specific taxonomies. Since 2006, there are many works that confirm Wikipedia as a complete source in a wide variety of applications in areas of Computational Linguistics and Intelligence, like disambiguation of words (Li et al., 2011), text annotation (Fernandez et al., 2011; Makris et al., 2013), text classification (Jiang et al., 2013) or semantic search in web engines (Fuentes-Lorenzo et al., 2013). Among its facilities to build concept maps, we can find the following:</p> <p></p> <ulist> <item> • It offers concepts from a great variety of domains, such as science, geography, etc.</item> <p></p> <item> • Its information is constantly updated by a large community.</item> <p></p> <item> • Its contents have been translated to numerous languages.</item> <p></p> <item> • Concepts belonging to different parts of speech are located under the same structure, whereas in many vocabularies, like WordNet, they are separated (nouns with nouns, verbs with verbs), what makes difficult to analyze their similarity.</item> </ulist> <p>The strength of Wikipedia lies in its size; however, despite its advantages, the size is also a disadvantage. As explained in Strube and Ponzetto (2006), the search space in the Wikipedia category graph is very large in terms of depth, branching factor and multiple inheritance relations, which create problems related to finding efficient mining methods. Besides, the category relations cannot be only interpreted as hyponym associations (is-a relations) of well-formed taxonomies.</p> <p>The article review previous works to employ semantic distances to build and check concept maps. We consider that Wikipedia is a valid semantic source to compute semantic similarity. Our work considers the drawbacks in order to adapt path-based and multi-source metrics to use information from the Wikipedia categorization structure. Our approach shows that existing metrics can be adapted to use Wikipedia, obtaining as good results as those yielded by traditional sources like WordNet, but without their limitations.</p> <p>This article is structured as follows. In Section 2 there is a review of some works that apply semantic distances for building and checking concept maps in visual learning. In the next section, we review relevant work on semantic similarity techniques exposed so far in the literature. Section 4 gives a brief review on the reported results of these techniques and how Wikipedia can be used to also achieve good values. In Section 5 we look at the characteristics of the Wikipedia categorization structure. Section 6 defines the elements involved in our approach. Section 7 explains the adaptation of the main traditional semantic similarity techniques seen in Section 3 to the special features of Wikipedia. The evaluation of these new modified measures is exposed in Section 8, along with a discussion of these outcomes compared to other related works. Finally, in Section 9 we expose some concluding remarks.</p> <hd id="AN0138480701-3">2. Concept maps in visual learning</hd> <p>Imran, Mansoor and Islam (2014) observe that visual learners are prevalent among students. This is one of the reasons that explains why images improve learning dramatically. In their work pedagogical text documents are converted to visual learning objects. Even in software engineering there is a need to diagram the projects, with the graph language UML, in order to improve the problem-solution understanding. Also, Dewan (2015) emphasizes the need to use visual learning objects to improve communication. Specifically, this author mentions the usefulness of infodoodles, infographics and concept maps. A more detailed survey about these resources is presented in Davies (2011). The author notes that meaningful learning often implies adding and rejecting some concepts to the concept map. Imran et al. (2014) convert a text into a word cloud by the following procedure: 1) to extract the terms with NLP techniques; 2) compute the semantic distance of the concepts to avoid natural language ambiguities; and 3) query the Internet to retrieve a semantic visual representation of the word (Morato et al., 2014).</p> <p>Kardan et al. (2016) proposed assessing learners by a combination of tagging technologies and semantic distances from Wordnet. A set of experts' tags and automatic extracted tags were offered to the learners to tag learning objects. Results showed that the accuracy between the text and the tags, computed by the semantic distance, was correlated with the results in multiple choice questions tests. A similar approach with Wordnet was carried out by Imran et al. (2012) in order to tag lecture videos from the transcripts. In this case semantic distance was computed to perform sense disambiguation process. Kumaran and Sankar (2013) automatically computed the semantic distance between the concepts shown in the student's concept map and an expert's ontology in order to assess the student and identify learning difficulties. As Eiman Aeiad (2017) suggested developing personalized and adaptable learning environments are currently a major challenge. Learning objects should be adapted to the learner's background and learning style. Aeiad, in his thesis (2017), points out that similarity measures should be employed for matching the extracted material from the Web to the domain concepts and preferences explicated by the user.</p> <hd id="AN0138480701-4">3. Previous works on semantic similarity measures</hd> <p>Traditional approaches to calculate semantic similarity can be divided in three main groups, based on: (<reflink idref="bib1" id="ref4">1</reflink>) co-occurrence of words in big corpora; (<reflink idref="bib2" id="ref5">2</reflink>) paths in lexical structures; and (<reflink idref="bib3" id="ref6">3</reflink>) multi-sources, combining co-occurrence approaches with path-based methods. Next, these three groups are analyzed.</p> <hd id="AN0138480701-5">3.1 Co-occurrence-based Measures</hd> <p>These metrics use statistical approaches or vector-based methods in text corpora, focusing on the co-occurrence of words. They are usually applied to situations where there is not a well-formed lexical structure- taxonomies or thesauri – to process.</p> <p>The first important group is represented by gloss-based measures, which use word-sense glosses of machine-readable dictionaries to compute similarity and relatedness in general. One example is Lesk's algorithm (Lesk, 1986) which uses dictionary-gloss overlapping to disambiguate the words in a phrase. For instance, in choosing the disambiguation of the word <emph>bank</emph> in the sentence <emph>I sat on the bank of the lake</emph>, two possible definitions of <emph>bank</emph> are:</p> <p>def(bank) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="normal">=</mo></math> </ephtml> "financial institution that accepts deposits and channels the money into lending activities";</p> <p>def(bank) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">2</mn></msub></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math> </ephtml><emph> "sloping land especially beside a body of water</emph>".</p> <p>And the definition of lake is:</p> <p>def(lake) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="normal">=</mo></math> </ephtml> a body of water surrounded by land.</p> <p>There is no overlap between <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext mathvariant="italic">def(bank)</mtext><mn>1</mn></msub></math> </ephtml> and def(lake), but there exists overlap between <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext mathvariant="italic">def(bank)</mtext><mn>2</mn></msub></math> </ephtml> and def(lake), with the words body and water. The problem with this simple method is that dictionary entries are short and may not provide enough information about the relation between two words.</p> <p>Another group of techniques uses vector-based methods which also focus on the co-occurrence distribution of words in dictionaries (Wilks et al., 1990) or large corpora (Church & Hanks, 1990). In these measures, the authors define a vocabulary from the words in the corpora or the dictionary glosses. Using this vocabulary, a co-occurrence matrix is built. This matrix indicates how often each word occurs with each other in the vocabulary. Thus, each word is represented by a vector, where each dimension shows how often the word occurs with another word in the vocabulary. Finally, to measure the similarity of two words, these techniques compute the similarity (i.e., cosine similarity) between their respective vectors.</p> <p>A variant of measures in this group is the web-based metrics, those where the knowledge source used is the World Wide Web. Using indexed documents from web search engines to compute semantic similarity has a clear advantage: almost any possible word or sense can be indexed, and a potential measure does not have to depend on limited sources which sometimes do not have concepts. One simple technique in this group consists on obtaining the hits (page counts) of two words (separately and together) from a search engine and applying similarity coefficients or overlapping metrics from statistics. Cilibrasi and Vitanyi (2007) calculated a distance metric based on hits and an overlapping metric, which was called Normalized Google Distance (NGD):</p> <p>(<reflink idref="bib1" id="ref7">1</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mrow><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>|</mo><msub><mi>c</mi><mn>1</mn></msub><mo>|</mo></mrow></mrow><mo>,</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>|</mo><msub><mi>c</mi><mn>2</mn></msub><mo>|</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow><mo>-</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>|</mo><mrow><msub><mi>c</mi><mn>1</mn></msub><mo>∩</mo><msub><mi>c</mi><mn>2</mn></msub></mrow><mo>|</mo></mrow></mrow></mrow><mrow><mrow><mi>log</mi><mo>⁡</mo><mi>N</mi></mrow><mo>-</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>|</mo><msub><mi>c</mi><mn>1</mn></msub><mo>|</mo></mrow></mrow><mo>,</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>|</mo><msub><mi>c</mi><mn>2</mn></msub><mo>|</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></mfrac></mstyle></mrow></math> </ephtml></p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> </ephtml> is the number of estimated indexed pages in Google engine, and <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>c</mi><mn>1</mn></msub><mo>∩</mo><msub><mi>c</mi><mn>2</mn></msub></mrow></math> </ephtml> are the set of pages where the term [ <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> ] AND [ <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> ] appears. Trillo et al. (2007) transformed the NGD into an exponential, monotonically increasing similarity measure:</p> <p>(<reflink idref="bib2" id="ref8">2</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>trillo</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mrow><mtext>2NGD</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></msup></mrow></math> </ephtml></p> <p>However, page counts ignore the position of a word in a document; even though two words may appear in a same document, one may be far away from the other, and may not be related at all. Besides, polysemous words can also be a problem for the results: searching for apple can yield pages about the fruit or about the company. In Bollegala et al. (2007), authors propose a model with a Support Vector Machine algorithm, combining four different coefficients based on hits (Jaccard, Dice, Overlap and Pointwise mutual information) and one Natural Language Processing (NLP) technique based on the extraction of syntactic patterns from text snippets. This last approach makes this measure more computationally expensive than the previous approaches.</p> <p>In general, co-occurrence measures are used to compute semantic relatedness; they are not focused on measuring semantic similarity. Besides, the election of an appropriate corpus is crucial to obtain acceptable results, especially important when working with specific domains.</p> <hd id="AN0138480701-6">3.2 Path-based measures</hd> <p>These measures are based on graphs of lexical taxonomies and usually focus on the paths between concepts of the hierarchy to calculate their similarity.</p> <p>One of the taxonomies most frequently used in the literature is WordNet (Miller, 1995), due mainly to its extensive scope and its free availability. Wordnet is an English lexical database where nouns, verbs, adjectives and adverbs are grouped separately into sets of cognitive synonyms, called synsets, each expressing a distinct concept. The most frequently encoded association among synsets is the hyponymy (also known as is-a relation) and represents the semantic relation of belonging to a generic term (e.g., a girl is a female person). Figure 1 shows an extract of the taxonomy for nouns in WordNet 3.1.</p> <p>Graph: Figure 1.Extract of the WordNet 3.1 taxonomy.</p> <p>A simple approach considers the minimal path length between two concepts, by counting the edges (or nodes) that separate them. This idea of edge or node counting goes back to Quillian's model of semantic memory (Quillian, 1967), where concepts were represented by nodes and relationships by links. Rada et al. (1989) demonstrated that counting the edges or nodes of the shortest path between two concepts in a net can be used as a measure of conceptual distance if just the hyponym relations are considered: the more similar two concepts are, the smaller the conceptual distance between them. If a word is polysemous (multiple senses represented in the net), multiple paths might exist, and the shortest path of all of them is considered. Rada et al. (1989), or other works such as Lee et al. (1993), used this metric as the basis for ranking documents by their similarity to a query.</p> <p>As conceptual distance is a decreasing function of similarity, distance metric is usually transformed into a similarity measure by subtracting the shortest path between two concepts (henceforth, shortest ( <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> )) to the longest possible path in a hierarchy (twice the maximum depth of the net, D):</p> <p>(<reflink idref="bib3" id="ref9">3</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>������</mtext><mtext>��������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>;</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mn>2</mn><mo>⁢</mo><mtext mathvariant="italic">D shortest</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>;</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></math> </ephtml></p> <p>Leacock and Chodorow (1994) also transform the conceptual distance into a similarity measure, but through a logarithm. Besides, they normalize the shortest path, dividing its length by the length of the longest path in the taxonomy:</p> <p>(<reflink idref="bib4" id="ref10">4</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi></mrow></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mo>-</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mrow><mtext>shortest</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>/</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⋅</mo><mi>D</mi></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></math> </ephtml></p> <p>The basic problem with the approaches based on shortest path is that they rely on the assumption that all relations in the hierarchy represent a uniform distance, and this is not usually true. Going back to Fig. 1, car <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo>←</mo></math> </ephtml> taxi seems to have a closer similarity than whole <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo>←</mo></math> </ephtml> artifact, but both relations are represented by the same distance. This problem is clearer when using broad-coverage sources. To avoid this, shortest-path technique is usually combined with some other taxonomic features:</p> <p> <bold>Local density:</bold> The density of a node in a hyponym relation is the number of its incoming links. It is considered that the greater the density, the closer the distance between the nodes involved in the association. <bold>Depth of a node:</bold> The depth of a node is the path of that node to the root of the taxonomy. Semantic distance is lower as we go down the hierarchy, because the differentiation among concepts is based on fine-grained details. Therefore, nodes in the upper levels of a hierarchy have less semantic similarity. <bold>Relation type:</bold> When not only semantic similarity is required, other hierarchical relations are used: meronymy-holonymy (also known as <emph>part-of</emph>, <emph>substance-of</emph>, etc.), associative (cause-effect), etc.</p> <p>In Sussna (1993), computation of semantic relatedness is calculated by these features. He states that links are not semantically uniform, so a different weight is assigned to each of them. In Wu and Palmer (1994), authors avoid using just the length of the shortest path. For that, they consider both the distance of two concepts in the hierarchy and the depth of the first common node upwards that subsumes these two concepts (see Fig. 2). This node is called least common subsumer (henceforth, <emph>lcs</emph>):</p> <p>(<reflink idref="bib5" id="ref11">5</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mrow><mi>w</mi><mo>⁢</mo><mi>p</mi></mrow></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mtext>shortest</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mrow></math> </ephtml></p> <p>Graph: Figure 2.Illustrative example of factors.</p> <p>In Blázquez del Toro et al. (2008), semantic similarity between two concepts is obtained considering the local density of the nodes in the shortest path that links those concepts, considering that the greater the density of the nodes in the path, the higher the similarity between the concepts. Initially, their measure was intended to be applied when ontologies are the knowledge source involved. However, they only use the hypernym-hyponym relations and, therefore, their measure can be applied to hierarchical structures in general. In fact, their experiments are finally made with a simplified version of WordNet, which had to be transformed into an ontology, eliminating associations that were not is-a relations. Their measure can be reduced to the following form:</p> <p>(<reflink idref="bib6" id="ref12">6</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>blazquez</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><munder><mo movablelimits="false">max</mo><mrow><mtext>������</mtext><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo lspace="17.5pt">{</mo><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle><mo>}</mo></mrow></math> </ephtml></p> <p>Multiple inheritance can appear in the taxonomy, so they choose the <emph>lcs</emph> of all the possible <emph>lcs's</emph> of the two concepts (LCSs(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mo mathvariant="normal">,</mo><mprescripts /><mn mathvariant="normal">1</mn><none /></mmultiscripts><msub><mi>c</mi><mn mathvariant="normal">2</mn></msub></mrow></math> </ephtml> )) that yields the best value (<emph>max</emph>). To measure the similarity between a concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> and an <emph>lcs</emph>, they apply the following formula:</p> <p>(<reflink idref="bib7" id="ref13">7</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext mathvariant="italic">c,lcs</mtext><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mrow><mrow><mi>k</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mrow><mi>k</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo stretchy="false">(</mo><mrow><msub><mi>E</mi><mtext>������</mtext></msub><mo>/</mo><msub><mi>E</mi><mi>c</mi></msub></mrow><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mrow></math> </ephtml></p> <p>The main assumption here is that, the more specific a concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> is, the less is the difference between it and its parent in the hierarchy. This feature is the information ratio between <emph>lcs</emph> and c, <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mtext>lcs</mtext></msub></math> </ephtml> / <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>c</mi></msub></math> </ephtml> . To calculate this ratio, consider that a node has the 100% of the information of the subhierarchy of which is root of, (in Fig. 3, <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mtext>lcs</mtext></msub></math> </ephtml> is 100), whereas each of its children will have an equitative fraction of that mass of information, E/number of children (as density of <emph>lcs</emph> is 4 in Fig. 3, each of its children has a mass of information of 25%).</p> <p>Graph: Figure 3.Illustrative example of information ratio.</p> <p>Then, considering parents ( <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>c</mi><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></mrow></math> </ephtml> as the set of hypernyms of <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> in the path to that <emph>lcs</emph>, including the <emph>lcs</emph>:</p> <p>(<reflink idref="bib8" id="ref14">8</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>E</mi><mtext>lcs</mtext></msub><mo>/</mo><msub><mi>E</mi><mi>c</mi></msub></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" movablelimits="false" symmetric="true">∏</mo><mrow><mi>p</mi><mo>∈</mo><mrow><mtext>parents</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mtext>lcs</mtext></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>density(p)</mtext></mrow></mrow></math> </ephtml></p> <p>Therefore, going back to the example in Fig. 3:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mi>E</mi><mtext>lcs</mtext></msub><mo>/</mo><msub><mi>E</mi><mi>c</mi></msub></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mn>100</mn><mn>1.25</mn></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true"><mfrac><mn>100</mn><mrow><mrow><mn>100</mn><mo>/</mo><mn>4</mn></mrow><mo>⋅</mo><mn>5</mn><mo>⋅</mo><mn>4</mn></mrow></mfrac></mstyle><mo>=</mo><mrow><mn>4</mn><mo>⋅</mo><mn>5</mn><mo>⋅</mo><mn>4</mn></mrow><mo>=</mo><mn>80</mn></mrow></math> </ephtml> </p> <p>The taxonomy selected to compute these metrics has an important impact on the results. If these path-based measures are used in the hierarchy of verbs in WordNet, instead of the hierarchy of nouns, the results obtained are worse because the verb hierarchy is shallower and not so well formed (Pedersen et al., 2005). Besides, an implicit problem of the structure of taxonomies such as WordNet is that a comparison can only be made between concepts representing the same part of speech (nouns with nouns, verbs with verbs, etc.).</p> <hd id="AN0138480701-7">3.3 Multi-source measures</hd> <p>These methods use different path-based techniques from taxonomies and combine them with statistical information obtained from corpora.</p> <p>The <bold>information-content</bold> approach is the most used in this group; it is based in Information Theory and was proposed by Resnik (1995). Resnik defined the semantic similarity of two concepts as the maximum of the information content of their <emph>lcs</emph>:</p> <p>(<reflink idref="bib9" id="ref15">9</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>resnik</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><munder><mo movablelimits="false">max</mo><mrow><mtext>������</mtext><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder><mrow><mo stretchy="false">{</mo><mtext mathvariant="italic">ic(lcs)</mtext><mo stretchy="false">}</mo></mrow></mrow></mrow></math> </ephtml></p> <p>Where the information content (<emph>ic</emph>) of a concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> refers to the probability of occurrence of the concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> in a large text corpus:</p> <p>(<reflink idref="bib10" id="ref16">10</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>i</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mo>-</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mi>p</mi><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></math> </ephtml></p> <p>If the probability of finding a word in a set of documents is 100% (that is, the word is on every document), it has no information content; a concept with high information content is more specific. To set an example, <emph>fork</emph> has more information content than <emph>thing</emph>. Some implementations use the function <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mn>1</mn><mo>/</mo><mi>p</mi></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml> instead of <emph>-log (p(c))</emph>. The frequencies of concepts in the taxonomy are estimated using a large collection of text (Resnik's and similar works used the Brown Corpus of American English). Each noun that occurred in the corpus was accounted as an occurrence of the concept (taxonomic class) containing it; that is, the frequency of a concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> is calculated counting each time a word <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math> </ephtml> appears in the corpus (<emph>count(w)</emph>), where <emph>words(c)</emph> is the set of words subsumed by concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> :</p> <p>(<reflink idref="bib11" id="ref17">11</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>freq(c)</mtext><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" movablelimits="false" symmetric="true">∑</mo><mrow><mi>w</mi><mo>∈</mo><mtext mathvariant="italic">words(c)</mtext></mrow></munder></mstyle><mtext>count(w)</mtext></mrow></mrow></math> </ephtml></p> <p>The probability is computed simply as relative frequency where <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> </ephtml> is the total number of words observed, excluding those not included in any WordNet synset:</p> <p>(<reflink idref="bib12" id="ref18">12</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>p</mi><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mi>c</mi><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mtext>freq(c)</mtext><mi>W</mi></mfrac></mstyle></mrow></math> </ephtml></p> <p>Graph: Figure 4.Illustrative example of information content.</p> <p>An illustrative example can be found in Fig. 4, from Jiang and Conrath (1997). It depicts a fragment of the WordNet noun hierarchy, and numbers in parentheses are the corresponding information content values of a node. The similarity between <emph>car</emph> and <emph>bicycle</emph> is the information content value of the concept <emph>vehicle</emph>, 8.30, which has the maximum value among all the concepts that subsume both <emph>car</emph> and <emph>bicycle</emph>. In contrast, the similarity between <emph>car</emph> and <emph>fork</emph> is 3.53. These results conform to human perception that cars and forks are less similar than cars and bicycles.</p> <p>The information content feature is considered coarse-grained because it does not differentiate the similarity between any pair of concepts in a taxonomy if their <emph>lcs</emph> are the same. Given the extract on Fig. 1, semantic similarity between <emph>boy</emph> and <emph>instructor</emph> would be the same as <emph>boy</emph> and <emph>girl</emph>, as both pairs share the same <emph>lcs</emph>.</p> <p>Jiang and Conrath (1997) propose a modification where the similarity between two concepts is twice the shared information content subtracted from the sum of the individual information contents of each concept:</p> <p>(<reflink idref="bib13" id="ref19">13</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>jc</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mtext>ic</mtext><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow><mo>+</mo><mtext>ic</mtext><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>-</mo><mn>2</mn><mo>⋅</mo><mrow><mtext>ic</mtext><mtext>������</mtext></mrow><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo stretchy="false">)</mo></mrow></math> </ephtml></p> <p>Lin (1998) also proposes a normalization, but via ratio:</p> <p>(<reflink idref="bib14" id="ref20">14</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>lin</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mstyle displaystyle="true"><mfrac><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>ic</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mtext>ic</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><mtext>ic</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mrow></math> </ephtml></p> <p>If multiple inheritance is considered, the selected <emph>lcs</emph> is the one that maximizes the value.</p> <p>These measures take into consideration simple terms, not word senses; therefore, strange results can arise. For example, <emph>tobacco</emph> and <emph>horse</emph> are not similar at all, but if we take the noun <emph>horse</emph> as the colloquial term to refer to <emph>heroin</emph>, they are quite similar; as the maximum value is selected, the information content measure will yield this best value. To partially avoid this problem, the frequency of a concept in Richardson and Smeaton (1995) is divided by the number of possible senses that the word <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math> </ephtml> may have, <emph>senses(w)</emph>:</p> <p>(<reflink idref="bib15" id="ref21">15</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>freq(c)</mtext><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" movablelimits="false" symmetric="true">∑</mo><mrow><mi>w</mi><mo>∈</mo><mtext mathvariant="italic">words(c)</mtext></mrow></munder></mstyle><mstyle displaystyle="true"><mfrac><mtext>count(w)</mtext><mrow><mo>|</mo><mtext>senses(w)</mtext><mo>|</mo></mrow></mfrac></mstyle></mrow></mrow></math> </ephtml></p> <p>An information content-based measure still uses a hierarchical structure, but is less sensitive to it; however, results with this approach, as with general corpora-based measures, also depend on the corpus used.</p> <p>Li et al. (2003) tried different strategies, using the length of the shortest path between two words, the information content and the depth of their <emph>lcs</emph>. They assumed that semantic similarity does not only depend on different factors, but the correct combination of them. For that, they tried different linear and non-linear measures. At the end, the formula that yielded best results was the following:</p> <p>(<reflink idref="bib16" id="ref22">16</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>li</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><msup><mi>e</mi><mrow><mo>-</mo><mrow><mrow><mi>α</mi><mo>⋅</mo><mtext>shortest</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></msup><mo>⋅</mo><mstyle displaystyle="true"><mfrac><mrow><msup><mi>e</mi><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow></msup><mo>-</mo><msup><mi>e</mi><mrow><mo>-</mo><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow></mrow></msup></mrow><mrow><msup><mi>e</mi><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow><mo>-</mo><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>depth</mtext></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mrow><mtext>������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">)</mo></mrow></mrow></mrow></msup></mrow></mfrac></mstyle></mrow></mrow></math> </ephtml></p> <p>Every factor is transformed into non-linear functions. In the case of the shortest path function, shortest(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mo mathvariant="normal">,</mo><mprescripts /><mn mathvariant="normal">1</mn><none /></mmultiscripts><msub><mi>c</mi><mn mathvariant="normal">2</mn></msub><mo mathvariant="normal" stretchy="false">)</mo></mrow></math> </ephtml> , they use an exponential (non-linear) and monotonically decreasing function. In the case of <emph>depth</emph> factor, they use a monotonically increasing function. They also played with the information content feature; however, outcomes showed that it did not influence the results.</p> <hd id="AN0138480701-8">4. Reported results of previous works</hd> <p>In the study by Rubenstein and Goodenough (1965), human subjects gave a similarity score to 65 pair of terms. Miller and Charles (1991) replicated the experiment, providing human evaluation for 30 of those initial 65 pairs. These datasets are considered as the ground truth, and similarity measures must verify how well its ratings correlate with those human ratings.</p> <p>Table 1 shows the Pearson correlation coefficients reported by the most relevant measures explained. In order to evaluate and compare results, the reported works took into account a subset of 28 pairs (henceforth, <bold>test set</bold>) from the 30 pairs of Miller and Charles (1991), except Jiang and Conrath's, who took the 30 pairs as their test set-, and they correlated their results with the human ratings obtained with either Miller and Charles (1991) or Rubenstein and Goodenough's experiments (1965).</p> <p>Table 1 Correlation coefficients for the test set by the most relevant measures of each group</p> <p> <ephtml> <table><thead><tr><th valign="top" align="left">Semantic similarity measure</th><th valign="top" align="left">Reported correlation</th></tr></thead><tbody><tr><td valign="top" align="left">Co-occurrence based</td><td /></tr><tr><td valign="top" align="left"> Cilibrasi and Vitanyi (2007)</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left"> Bollegalla (2007)</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left">Path based</td><td /></tr><tr><td valign="top" align="left"> Shortest path (1989)</td><td valign="top" align="left">0.66</td></tr><tr><td valign="top" align="left"> Wu and Palmer (1994)</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left"> Leacock and Chodorow (1994)</td><td valign="top" align="left">0.83</td></tr><tr><td valign="top" align="left"> Blázquez-del-Toro et al. (2008)</td><td valign="top" align="left">0.81</td></tr><tr><td valign="top" align="left">Multi-sources based</td><td /></tr><tr><td valign="top" align="left"> Resnik (1995)</td><td valign="top" align="left">0.74</td></tr><tr><td valign="top" align="left"> Jiang and Conrath (1997)</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left"> Lin (1998)</td><td valign="top" align="left">0.75</td></tr><tr><td valign="top" align="left"> Li et al. (2003)</td><td valign="top" align="left">0.89</td></tr></tbody></table> </ephtml> </p> <p>The three measures with higher coefficients (higher than 0.80) are multi-source methods and path-based approaches. Just one of those (Jiang & Conrath's model (1997)) uses the information content as a key feature. These results show that using a lexical structure with paths yields better coefficients. Cilibrasi et al.'s methods (2007) have a broader coverage than the rest of measures, because they have the World Wide Web as source, but their results are not better than simple path-based models such as the Wu and Palmer's metric (Wu & Palmer, 1994).</p> <p>In general, all these approaches address some problems, most of them related to the source they are applied to. Part of the measures use taxonomies or dictionaries, despite their clear disadvantages: (<reflink idref="bib1" id="ref23">1</reflink>) they cannot be used for general applications or scenarios that require a great coverage of the real world; words such as some proper nouns (e.g. <emph>Angela Merkel</emph>) or specific terminology (e.g. <emph>hyperpolarization</emph>) are not usually defined; (<reflink idref="bib2" id="ref24">2</reflink>) new words or modifications in the structure are managed slowly in time; (<reflink idref="bib3" id="ref25">3</reflink>) most of those sources are only developed in English; and (<reflink idref="bib4" id="ref26">4</reflink>) sometimes the source must be transformed previously, such as in Blázquez-del-Toro et al.'s measure (2008). On the other hand, web-based measures take advantage of the huge amount of information stored over the World Wide Web, using web search engines to compute similarity, but these measures cannot benefit from path-based features, so results obtained are worse.</p> <p>Wikipedia, though, provides a vast knowledge for computing semantic similarity between word senses. It was created in 2001 and has 5,7 million articles in English (October 2018). The articles are pages representing <bold>concepts</bold> of the real world that express well-defined word senses. Concepts can be assigned to one or more <bold>categories</bold>. Articles have versions in different languages and are updated constantly by a large community. It is built upon a more defined structure than that from results obtained through web search engines and has more coverage than WordNet or specific taxonomies, offering objects in a great variety of domains, such as science, geography, history, etc. Furthermore, concepts belonging to different parts of speech are located under the same structure, whereas in many vocabularies they are separated (nouns with nouns, verbs with verbs), which makes it difficult to analyse their similarity.</p> <p>Taking this into account, in this article we propose a set of techniques that can be used to adapt semantic similarity metrics to use Wikipedia information. We propose the usage of the Wikipedia categorization structure as an alternative to traditional lexical structures such as WordNet. Henceforth, our analysis focuses on path-based and multi-source metrics, as these perform better than corpus-based metrics.</p> <hd id="AN0138480701-9">5. Characteristics of Wikipedia: Categorization structure</hd> <p>The categorization schema in Wikipedia has the form of a directed cyclic graph; it is not a hierarchical acyclic structure as WordNet. Due to this aspect, potential problems can arise, mainly: selection of a root node, cycles, and multiple inheritance.</p> <p>Graph: Figure 5.Top levels in the structure of Wikipedia categories.</p> <p>Graph: Figure 6.Extract of a cyclic subgraph in Wikipedia.</p> <p>Figure 5 shows an extract of the top level of the structure of categories in Wikipedia (henceforth, categories are identified with the prefix <emph>Cat:</emph>). The <bold>root node</bold> is <emph>Cat:Contents</emph>. This category groups every page type existing in Wikipedia in a variety of forms. Among its direct children, <emph>Cat:Articles</emph> divides Wikipedia pages by content. Other subcategories under <emph>Cat:Contents</emph> distribute articles by administrative characteristics, such as their state. In order to facilitate further processing, a single root node must be considered. Below <emph>Cat: Articles</emph>, <emph>Cat: Fundamental categories</emph> distributes the articles in a more logic and progressive way than the rest of subcategories, which make merely a division by main broad topics. Therefore, we consider <emph>Cat: Fundamental categories</emph> as the actual root node for the categorization scheme in this work.</p> <p>Figure 6 shows an example of existing <bold>cycles</bold>, where categories <emph>Cat: Coastal geography</emph>, <emph>Cat: Coasts</emph> and <emph>Cat: Coastal and oceanic landforms</emph> form a cycle. These cycles must be considered when processing the structure, in order to avoid infinite loops.</p> <p> <bold>Multiple inheritance</bold> among categories and concepts coexists in Wikipedia. The first form of multiple inheritance involves categories. Figure 7 shows an extract where <emph>Cat: Fruit</emph> has 3 different parents.</p> <p>Graph: Figure 7.Wikipedia extract with multiple inheritance.</p> <p>The second form of multiple inheritance involves both categories and concepts, and refers to the categories a concept may belong to, making the scheme of categorization of concepts resemble a tagging system more than a taxonomy. The example of Fig. 8, which shows the categories for the concept <emph>Barack Obama,</emph> illustrates this form of multiple inheritance. Besides, there are categories which do not represent hyponymy relations, such as <emph>Cat: Living people</emph>, but they indicate characteristics of the concept. Due to this multiple inheritance, factors applied in well-formed taxonomies, such as a unique <emph>lcs</emph> between nodes, cannot be directly obtained in the structure of Wikipedia.</p> <p>Graph: Figure 8.Screenshot of the categories established for Barack Obama.</p> <p>Because Wikipedia is crowd-sourced self-organized human knowledge, it undergoes constant change and development. Its branching factor and depth steadily increase over time and does not follow the strict rules of well-formed taxonomies, making more difficult to find efficient mining methods. In this article, we create techniques that, being applied on the features in the Wikipedia categorization structure, can be integrated in existing metrics, as it is explored in the next sections.</p> <hd id="AN0138480701-10">6. Adapting similarity metrics to Wikipedia</hd> <p>In this section we describe the elements used to address the difficulties in adapting path-based and multi-source metrics to Wikipedia. In Section 6.1, we briefly describe the main components involved in our proposal and introduce some nomenclature. In Section 6.2 we show how the different features from path-based and multi-source similarities are shaped to use Wikipedia categorization information.</p> <hd id="AN0138480701-11">6.1 Information elements and nomenclature</hd> <p>The information considered is the following.</p> <p> <emph>Articles related to specific concepts</emph>: Disambiguation pages, redirection pages or lists pages are not considered for the conceptual model.</p> <p></p> <ulist> <item> • <emph>Articles related to categories</emph>: The URLs of these articles start with the prefix <emph>Category</emph>.</item> <p></p> <item> • <emph>Relations between pairs of concepts and categories</emph>: A concept can belong to one or more categories. <emph>cats(c)</emph> is the set of parent categories a concept <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> </ephtml> belongs to.</item> <p></p> <item> • <emph>Relations between categories</emph>: A category can belong to one or more categories. <emph>cats(cat)</emph> is the set of parent categories a category <emph>cat</emph> belongs to, forming a hierarchy.</item> </ulist> <p>Parent categories are the immediately above categories in the graph structure of Wikipedia. Taking as an example the structure fragment of Fig. 7, then:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext class="ltx_markedasmath" mathvariant="italic">cats(Cat:Fruit)</mtext><mo>=</mo><mi mathvariant="normal">{</mi><mtext mathvariant="italic">Cat:Edible plants, Cat:Plant morphology,</mtext><mtext mathvariant="italic">Cat:Plant reproduction</mtext><mo stretchy="false">}</mo></mrow></math> </ephtml> </p> <p>Figure 9 illustrates the page of a category (top) and the items implied in the information model (bottom). In the example, there are 2 subcategories and 4 concepts (section <emph>Pages</emph>). For each category, the elements to store are:</p> <p></p> <ulist> <item> • The category itself (cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">3</mn></msub></math> </ephtml> in the example of Fig. 9)</item> <p></p> <item> • Concepts belonging to the category ( <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>3</mn></msub></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>4</mn></msub></math> </ephtml> )</item> <p></p> <item> • The relation of the concepts and the category they belong to (<emph>belongs_to</emph> arrows)</item> <p></p> <item> • The relation between the category and their parent categories (<emph>is_parent_of</emph> arrows)</item> </ulist> <p>Graph: Figure 9.Example of a Wikipedia category page (top) and its information model (bottom).</p> <p>After this, the pages of the two subcategories are processed and their information stored, and so on with their children, until the categorization structure is completely crawled. If this crawling algorithm goes through an element (a category, concept, or a relation among them) which has been already visited, this element is ignored. Currently, English Wikipedia has 5,734,479 articles. According to Bairi et al. (2015), there are 942,045 categories. For our approach, just the titles and URLs of concepts, categories and their relations are stored; articles texts are obviated.</p> <hd id="AN0138480701-12">6.2 Features adaptation</hd> <p>Features used on path-based and multi-source approaches must be redefined to be aligned with the Wikipedia characteristics seen in Section 5, because Wikipedia categorization scheme is not a well-formed taxonomy. Even though semantic similarity is measured for concepts, any model applied to Wikipedia will work with the structure of categories those concepts belong to. Next, we will explain the different features involved in our proposal; for that, we make use of Fig. 10 as an example to illustrate how the features are computed.</p> <p>Graph: Figure 10.Illustrative example to explain features in Wikipedia</p> <p>The first feature to consider is the <bold>maximum depth</bold>, D, associated to a hierarchical tree, used in some of the traditional measures. It refers to the longest path from the root to the deepest node (a <emph>leaf</emph>) in the tree – loops are eliminated in this computing process. In the case of Wikipedia, maximum depth is 20 edges.</p> <p>The second feature to consider is the <bold>lcs</bold> between two concepts. First, the categories lists from <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> and <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> , cats(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mo mathvariant="normal" stretchy="false">)</mo><mprescripts /><mn mathvariant="normal">1</mn><none /></mmultiscripts></math> </ephtml> and cats(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mo mathvariant="normal" stretchy="false">)</mo><mprescripts /><mn mathvariant="normal">2</mn><none /></mmultiscripts></math> </ephtml> respectively, are extracted. Given these lists, for each category pair {cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mi>x</mi></msub></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="normal">∈</mo></math> </ephtml> cats(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> ), cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mi>y</mi></msub></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="normal">∈</mo></math> </ephtml> cats(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">2</mn></msub></math> </ephtml> )}, all their <emph>lcs's</emph> are extracted in subsets, LCSs(cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mi>x</mi></msub></math> </ephtml> ,cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mo mathvariant="normal" stretchy="false">)</mo><mprescripts /><mi>y</mi><none /></mmultiscripts></math> </ephtml> . The final set of <emph>lcs's</emph> between <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> and <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> , LCSs(c <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mo mathvariant="normal">,</mo><mprescripts /><mn mathvariant="normal">1</mn><none /></mmultiscripts><msub><mi>c</mi><mn mathvariant="normal">2</mn></msub><mo mathvariant="normal" stretchy="false">)</mo></mrow></math> </ephtml> , is calculated as the union of the previous subsets:</p> <p>(<reflink idref="bib17" id="ref27">17</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>������</mtext><mi>s</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mrow><mrow><mo rspace="7.5pt">∀</mo><msub><mtext>������</mtext><mi>x</mi></msub></mrow><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow><mo>,</mo><mrow><msub><mtext>������</mtext><mi>y</mi></msub><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mrow></munder></mstyle><mrow><msub><mtext>������</mtext><mi>s</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mtext>������</mtext><mi>x</mi></msub><mo>,</mo><msub><mtext>������</mtext><mi>y</mi></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mrow></math> </ephtml></p> <p>The third feature is the <bold>shortest path</bold> between two concepts, through their <emph>lcs</emph> that subsumes them. Given the multiple inheritance existing in Wikipedia categories, there may be multiple shortest paths - with a different <emph>lcs</emph> – between concepts. In Fig. 10 there is a shortest path between <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> and <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> associated to lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> , another shortest path associated to lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">2</mn></msub></math> </ephtml> , and so on.</p> <p>To compute this feature, a second vector is introduced, <emph>shortest</emph>, with the same number of elements than <emph>LCSs</emph>. Each dimension in <emph>shortest</emph> vector corresponds to an <emph>lcs</emph> from <emph>LCSs</emph> and is calculated as follows:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>��ℎ������������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mrow><munder><mo movablelimits="false">min</mo><mrow><mrow><mo>∀</mo><msub><mtext>������</mtext><mi>x</mi></msub></mrow><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder><mrow><mo stretchy="false">{</mo><mrow><mtext>��ℎ������������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mtext>������</mtext><mi>x</mi></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow><mo>+</mo></mrow></mrow></mrow></math> </ephtml> (<reflink idref="bib18" id="ref28">18</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><munder><mo lspace="12.5pt" movablelimits="false">min</mo><mrow><mrow><mo>∀</mo><msub><mtext>������</mtext><mi>y</mi></msub></mrow><mo>∈</mo><mrow><mtext>��������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder><mrow><mo stretchy="false">{</mo><mrow><mtext>��ℎ������������</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mtext>������</mtext><mi>y</mi></msub><mo>,</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></math> </ephtml></p> <p>In Eq. (6.2), do not confuse <emph>shortest</emph><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi /><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mi /></mrow></math> </ephtml> with <emph>shortest</emph> ( <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> , <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> ). The former refers to the vector; the latter refers to the minimal shortest path function. Considering Fig. 10, lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> is the unique <emph>lcs</emph> between categories cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">11</mn></msub></math> </ephtml> and cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">21</mn></msub></math> </ephtml> . There are several paths joining these categories through lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> , but the shortest is selected; that is, the path between cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">11</mn></msub></math> </ephtml> and lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> with one edge, and the path between lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> and cat <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">21</mn></msub></math> </ephtml> with 2 edges (Fig. 11).</p> <p>Graph: Figure 11.Illustrative example of shortest vector.</p> <p>The fourth feature to be considered is the <bold>depth of a node</bold>. It is commonly used in traditional measures to compute the length between the <emph>lcs</emph> of two concepts and the root of the hierarchy. Again, given the multiple inheritance existing in Wikipedia classification of categories, there may be multiple <emph>lcs's</emph> between concepts and, given one of these <emph>lcs's</emph>, there may be multiple paths between that <emph>lcs</emph> and the root. In Fig. 10 , lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> has several paths leading to the root, with 2, 1 and 3 edges respectively. To deal with this case, in this work we consider every single path to the root and apply three functions (minimum, average and maximum) to them. A new vector is introduced, <emph>depth</emph>, with the same number of elements as <emph>LCSs</emph>. Each dimension in <emph>depth</emph> vector corresponds to an <emph>lcs</emph> from <emph>LCSs</emph>. Being <emph>distances (x, y)</emph> the set of lengths of the different paths from node <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> </ephtml> to <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> </ephtml> , the value of each dimension is composed of three new values and are calculated as follows:</p> <p>(<reflink idref="bib19" id="ref29">19</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mo stretchy="false">(</mo><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo stretchy="false">)</mo></mrow><mo>,</mo></mrow></math> </ephtml></p> <p>where:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mtext>disstances</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext mathvariant="italic">lcs,root</mtext><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></mrow><mo>,</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mtext mathvariant="italic">depth </mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mtext>disstances</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext mathvariant="italic">lcs,root</mtext><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></mrow><mo>,</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>��������ℎ</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mtext>disstances</mtext><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext mathvariant="italic">lcs,root</mtext><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></mrow></math> </ephtml> </p> <p>The first dimension (related to lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mo mathvariant="normal" stretchy="false">)</mo><mprescripts /><mn mathvariant="normal">1</mn><none /></mmultiscripts></math> </ephtml> of depth vector on the subgraph in Fig. 10 will have the following set of values (Fig. 12).</p> <p>Graph: Figure 12.Illustrative example of depth vector.</p> <hd id="AN0138480701-13">7. Similarity metrics adaptation</hd> <p>Here we apply the features described in the previous section to adapt the most important similarity measures in the state of the art. There are two basic steps in the general procedure of adaptation: (<reflink idref="bib1" id="ref30">1</reflink>) Obtaining an intermediate vector with the measure's values for every <emph>lcs</emph> in <emph>LCSs</emph> vector, using <emph>shortest</emph> and/or <emph>depth</emph> vector; and (<reflink idref="bib2" id="ref31">2</reflink>) applying basic functions (minimum, average, maximum) to that vector.</p> <hd id="AN0138480701-14">7.1 Rada et al. (1989) adaptation</hd> <p>Rada et al. (1989) use the shortest path between two concepts to calculate their semantic similarity (see Eq. (<reflink idref="bib3" id="ref32">3</reflink>)). Its adaptation is made by means of the <emph>shortest</emph> vector. First, a new vector is obtained, <emph>rada</emph><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo></mrow></math> </ephtml> , with the result of the measure for every <emph>lcs</emph>, ranging from 0 to 2 <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi /><mo>⋅</mo><mi>D</mi></mrow></math> </ephtml> :</p> <p>(<reflink idref="bib20" id="ref33">20</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mtext>��������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mrow><mn>2</mn><mo>⋅</mo><mi>D</mi></mrow><mo>-</mo><mtext>��ℎ������������</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow></mrow></mrow></math> </ephtml></p> <p>Graph: Figure 13.Illustrative example of rada vector.</p> <p>The first dimension (related to lcs <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mn mathvariant="normal">1</mn></msub></math> </ephtml> ) of this vector on the subgraph in Fig. 10 will have the following values (Fig. 13).</p> <p>Second, 3 different adapted measures are obtained by selecting the minimum, average and maximum values of <emph>rada</emph> vector.</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>rada%5fmin</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mtext>��������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> (<reflink idref="bib21" id="ref34">21</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>rada%5favg</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mtext>avg</mtext><mrow><mo stretchy="false">{</mo><mtext>��������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mo stretchy="false">}</mo></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>rada%5fmax </mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mi>max</mi><mrow><mo stretchy="false">{</mo><mtext>��������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mo stretchy="false">}</mo></mrow></mrow></math> </ephtml></p> <hd id="AN0138480701-15">7.2 Wu and Palmer (1994) adaptation</hd> <p>Wu and Palmer (1994) use the shortest path between two concepts and the depth of their <emph>lcs</emph> (see Equation 5). Then, its adaptation is made by means of <emph>shortest</emph> and <emph>depth</emph> vector. In this case, every dimension in <emph>depth</emph> vector has 3 different values (the shortest path to the root (minimum), the longest path (maximum), and an average of lengths all paths). So first, a new vector is obtained, <emph>wp</emph>, with the measure calculated for every <emph>lcs</emph> and every depth value, ranging from 0 to 1:</p> <p>(<reflink idref="bib22" id="ref35">22</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mo stretchy="false">(</mo><mtext mathvariant="italic">wp </mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml></p> <p>where:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow><mrow><mrow><mrow><mtext>��ℎ������������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>+</mo><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></mfrac></mstyle></mpadded><mo>,</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow><mrow><mrow><mrow><mtext>��ℎ������������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>+</mo><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></mfrac></mstyle></mpadded><mo>,</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow><mrow><mrow><mrow><mtext>��ℎ������������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>+</mo><mrow><mn>2</mn><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></mfrac></mstyle></mpadded></math> </ephtml> </p> <p>Graph: Figure 14.Illustrative example of wp subsets.</p> <p>Then, 3 subsets are obtained by grouping the results generated in the previous step depending on the depth used (see example in Fig. 14):</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> (<reflink idref="bib23" id="ref36">23</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml></p> <p>Finally, with the help of these 3 subsets, 9 adapted measures are obtained:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>wp%5fmin _min</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mi>min</mi><msub><mtext>����</mtext><mtext>������</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo stretchy="false">}</mo><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5fmin%5favg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5fmin _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5favg%5fmin</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5favg%5favg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> (<reflink idref="bib24" id="ref37">24</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5favg%5fmax</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5fmax _min</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5fmax _avg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>wp%5fmax _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></math> </ephtml></p> <hd id="AN0138480701-16">7.3 Leacock and Chodorow (1994) adaptation</hd> <p>Leacock and Chodorow (1994) use the shortest path between two concepts to calculate their semantic similarity, as Rada et al. (1989); therefore, its adaptation is also made by means of <emph>shortest</emph> vector, used to compute the <emph>lc</emph> vector Eq. (<reflink idref="bib25" id="ref38">25</reflink>), obtaining 3 different adapted measures Eq. (7.3):</p> <p>(<reflink idref="bib25" id="ref39">25</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mo>-</mo><mrow><mi>log</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><mtext>��ℎ������������</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>+</mo><mrow><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mrow><mn>2</mn><mo>⋅</mo><mi>D</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></math> </ephtml></p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>lc%5fmin</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mi>min</mi><mrow><mo stretchy="false">{</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mo stretchy="false">}</mo></mrow><mo>;</mo></mrow></math> </ephtml> (<reflink idref="bib26" id="ref40">26</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>lc%5favg</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mtext>avg</mtext><mrow><mo stretchy="false">{</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mo stretchy="false">}</mo></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mtext>sim</mtext><mtext>lc%5fmax</mtext></msub><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><mo>=</mo><mi>max</mi><mrow><mo stretchy="false">{</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mo stretchy="false">}</mo></mrow></mrow></math> </ephtml></p> <hd id="AN0138480701-17">7.4 Blázquez-del-Toro et al. (2008) adaptation</hd> <p>The adaptation of this measure uses <emph>depth</emph> vector and a constant <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> </ephtml> . Besides, the shortest path is needed to obtain the information ratio, <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mtext>������</mtext></msub><mo>/</mo><msub><mi>E</mi><mi>c</mi></msub></mrow></math> </ephtml> , and the value of sim <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi /><mtext mathvariant="italic">to_lcs</mtext></msub></math> </ephtml> (see Fig. 4, Eqs (<reflink idref="bib6" id="ref41">6</reflink>) and (<reflink idref="bib7" id="ref42">7</reflink>). Again, an intermediate vector is obtained, <emph>bl</emph>, with the measure for every <emph>lcs</emph> and the corresponding depth value, ranging from 0 to 1:</p> <p>(<reflink idref="bib27" id="ref43">27</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>b</mi><mi>l</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mo stretchy="false">(</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mi>b</mi><mi>l</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mtext>����</mtext><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml></p> <p>Where:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>b</mi><mo>⁢</mo><mi>l</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mpadded><mo>,</mo></mrow></math> </ephtml> </p> <p>using depth <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi /><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> ;</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>b</mi><mo>⁢</mo><mi>l</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mpadded><mo>,</mo></mrow></math> </ephtml> </p> <p>using depth <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi /><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> ;</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>b</mi><mo>⁢</mo><mi>l</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mpadded lspace="20pt" width="+20pt"><mstyle displaystyle="true"><mfrac><mrow><mrow><mrow><msub><mtext>������</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>+</mo><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>⋅</mo><msub><mtext>sim</mtext><mtext mathvariant="italic">to_lcs</mtext></msub></mrow><mo>⁢</mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></mfrac></mstyle></mpadded><mo>,</mo></mrow></math> </ephtml> </p> <p>using depth <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi /><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> .</p> <p>Then, 3 subsets are obtained by grouping the results generated in the previous step depending on the depth value used, as done in Wu and Palmer's adaptation (Wu & Palmer, 1994):</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> (<reflink idref="bib28" id="ref44">28</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml></p> <p>With the help of these 3 subsets, 9 adapted measures are obtained:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmin _min</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmin _avg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmin _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5favg%5fmin</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5favg%5favg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> (<reflink idref="bib29" id="ref45">29</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5favg%5fmax </mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmax _min</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmax _avg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>bl%5fmax _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>b</mi><mo>⁢</mo><msub><mi>l</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></math> </ephtml></p> <hd id="AN0138480701-18">7.5 Li et al. (2003) adaptation</hd> <p>Li, Bandar, and McLean's measure (2003) is based on the non-linear combination of the shortest path between <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>1</mn></msub></math> </ephtml> and <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>c</mi><mn>2</mn></msub></math> </ephtml> and the depth of their <emph>lcs</emph>. A new vector is obtained, <emph>li</emph>, with the measure for every <emph>lcs</emph> and every depth value, ranging from 0 to 1:</p> <p>(<reflink idref="bib30" id="ref46">30</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>l</mi><mi>i</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mi>l</mi><mi>i</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>,</mo><mi>l</mi><mi>i</mi><mo><</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml></p> <p>Where:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>l</mi><mo>⁢</mo><mi>i</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msup><mpadded lspace="20pt" width="+20pt"><mi>e</mi></mpadded><mrow><mrow><mrow><mo>-</mo><mrow><mi>α</mi><mo>⋅</mo><mtext>��ℎ������������</mtext></mrow></mrow><mo><</mo><mrow><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub></mrow></mrow><mo>⁣</mo><mo>></mo></mrow></msup><mo>⋅</mo><mstyle displaystyle="true"><mfrac><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>-</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow></mfrac></mstyle></mrow><mo>,</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>l</mi><mo>⁢</mo><mi>i</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msup><mpadded lspace="20pt" width="+20pt"><mi>e</mi></mpadded><mrow><mrow><mrow><mo>-</mo><mrow><mi>α</mi><mo>⋅</mo><mtext>��ℎ������������</mtext></mrow></mrow><mo><</mo><mrow><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub></mrow></mrow><mo>⁣</mo><mo>></mo></mrow></msup><mo>⋅</mo><mstyle displaystyle="true"><mfrac><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>-</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mrow><mi>l</mi><mo>⁢</mo><mi>c</mi><mo>⁢</mo><mi>s</mi></mrow><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow></mfrac></mstyle></mrow><mo>⁢</mo><mtext> ,</mtext></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>l</mi><mo>⁢</mo><mi>i</mi></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub><mo>=</mo><mi /></mrow></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mpadded lspace="20pt" width="+20pt"><mi>e</mi></mpadded><mrow><mrow><mrow><mo>-</mo><mrow><mi>α</mi><mo>⋅</mo><mtext>��ℎ������������</mtext></mrow></mrow><mo><</mo><mrow><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub></mrow></mrow><mo>⁣</mo><mo>></mo></mrow></msup><mo>⋅</mo><mstyle displaystyle="true"><mfrac><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>-</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow><mrow><msup><mi>e</mi><mrow><mrow><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup><mo>+</mo><msup><mi>e</mi><mrow><mrow><mrow><mo>-</mo><mrow><mi>β</mi><mo>⋅</mo><mtext>��������ℎ</mtext></mrow></mrow><mo><</mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></msup></mrow></mfrac></mstyle></mrow></math> </ephtml> </p> <p>Three subsets are obtained by grouping the results generated in the previous step depending on the depth value used:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml> (<reflink idref="bib31" id="ref47">31</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>����</mtext><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mstyle displaystyle="true"><munder><mo largeop="true" mathsize="160%" movablelimits="false" stretchy="false" symmetric="true">⋃</mo><mrow><mpadded width="+5pt"><mtext>������</mtext></mpadded><mo rspace="7.5pt">∈</mo><mrow><msub><mtext>������</mtext><mi>S</mi></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow></mrow></munder></mstyle><mtext>����</mtext></mrow><mo>></mo><msub><mi>c</mi><mn>1</mn></msub></mrow><mo>,</mo><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>></mo><msub><mrow><mo stretchy="false">(</mo><mtext>������</mtext><mo stretchy="false">)</mo></mrow><mtext>������</mtext></msub></mrow></mrow></math> </ephtml></p> <p>Finally, with the help of these 3 subsets, 9 adapted measures are obtained:</p> <p> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmin _min</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmin _avg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmin _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5favg%5fmin</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml> (<reflink idref="bib32" id="ref48">32</reflink>) <ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5favg%5favg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5favg%5fmax</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mtext>avg</mtext><mo>⁢</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmax _min</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmax _avg</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow><mo>;</mo></mrow></math> </ephtml><ephtml> <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mtext>sim</mtext><mtext>li%5fmax _max</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo>=</mo><mrow><mi>max</mi><mo>⁡</mo><mrow><mo stretchy="false">{</mo><mrow><mi>l</mi><mo>⁢</mo><msub><mi>i</mi><mtext>������</mtext></msub><mo>⁢</mo><mrow><mo stretchy="false">(</mo><msub><mi>c</mi><mn>1</mn></msub><mo>,</mo><msub><mi>c</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mrow><mo stretchy="false">}</mo></mrow></mrow></mrow></math> </ephtml></p> <hd id="AN0138480701-19">8. Evaluation</hd> <p>Our hypothesis is that Wikipedia is a valid source to calculate semantic similarity. Its application in existing path-based or multi-source semantic similarity methods can yield as good results as those obtained with other well-formed knowledge sources. To support this hypothesis, the evaluation compares the correlation coefficient obtained by the adapted semantic similarity metrics described in the previous section with the correlation coefficient obtained by the original techniques.</p> <hd id="AN0138480701-20">8.1 Implementation and results</hd> <p>We have taken the same data set used in the evaluations of previous works, that of Rubenstein and Goodenough's (1965). More specifically, our test set is composed by the 28 pairs traditionally used for evaluation, and the training set to tune the adapted measures is composed of the remaining 37 pairs out the 65.</p> <p>With these sets, we have recalculated the correlation coefficients of the traditional measures explained in section 3 to homogenise the results. The reason for doing this task is twofold. First, metrics results were compared with distinct human judgements for the dataset – some reported correlations were obtained after comparing the results of the metrics to the human values of Rubenstein and Goodenough's experiments (1965) and some other were obtained after the comparison with those of Miller and Charles's (1991). Second, the metrics which used the WordNet taxonomy as their knowledge source did not use the same version – versions used goes from WordNet 1.5 to WordNet 1.7.</p> <p>To solve the first issue, results obtained after the replication have been compared with a single set of human judgements - the ones of Rubenstein and Goodenough's work (1965), avoiding the problem of correlating with different set values. For the second issue, we have used 1) Semantic Similarity System (SSST) to replicate path-based and multi-source methods; and 2) the Google web searcher to replicate the co-occurrence metrics. The replication has been made for both the test and training sets. The usage of SSST allows working with the same WordNet version for every measure – the tool uses WordNet 2.0, and the replication of co-occurrence metrics through Google allows working with the same Web status.</p> <p>Table 2 Replicated correlation coefficients for existing measures</p> <p> <ephtml> <table><thead><tr><th valign="top" align="left">Measure</th><th valign="top" align="left">Training set</th><th valign="top" align="left">Test set</th><th valign="top" align="left">Whole set</th></tr></thead><tbody><tr><td valign="top" align="left">Co-occurrence based</td><td /><td /><td /></tr><tr><td valign="top" align="left"> Cilibrasi and Vetanyi (2007)</td><td valign="top" align="left">0.54</td><td valign="top" align="left">0.51</td><td valign="top" align="left">0.52</td></tr><tr><td valign="top" align="left"> Bollegalla (2007)</td><td valign="top" align="left">0.67</td><td valign="top" align="left">0.76</td><td valign="top" align="left">0.70</td></tr><tr><td valign="top" align="left">Path-based</td><td /><td /><td /></tr><tr><td valign="top" align="left"> Shortest path (1989)</td><td valign="top" align="left">0.55</td><td valign="top" align="left">0.62</td><td valign="top" align="left">0.58</td></tr><tr><td valign="top" align="left"> Wu and Palmer (1994)</td><td valign="top" align="left">0.81</td><td valign="top" align="left">0.75</td><td valign="top" align="left">0.78</td></tr><tr><td valign="top" align="left"> Leacock and Chodorow (1994)</td><td valign="top" align="left">0.86</td><td valign="top" align="left">0.83</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left">Multi-source based</td><td /><td /><td /></tr><tr><td valign="top" align="left"> Resnik (1995)</td><td valign="top" align="left">0.88</td><td valign="top" align="left">0.77</td><td valign="top" align="left">0.83</td></tr><tr><td valign="top" align="left"> Jiang and Conrath (1997)</td><td valign="top" align="left">0.85</td><td valign="top" align="left">0.83</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left"> Lin (1998)</td><td valign="top" align="left">0.89</td><td valign="top" align="left">0.82</td><td valign="top" align="left">0.85</td></tr><tr><td valign="top" align="left"> Li et al. (2003)</td><td valign="top" align="left">0.87</td><td valign="top" align="left">0.82</td><td valign="top" align="left">0.84</td></tr></tbody></table> </ephtml> </p> <p>Table 2 shows the replicated correlation coefficient values for test and training sets. As far as the test set is concerned, notice that some methods yield lower values than the reported ones (see Table 1). This can be due to an increment in the number of concepts in the taxonomy for new versions of WordNet, and the increment of indexed documents for the co-occurrence web-based methods, but this issue is out of the scope of this article. Besides, a weighted average coefficient has been also calculated for the whole collection (65 pairs), to obtain an approximation without overfitting to a subset.</p> <p>Table 3 Correlation coefficients for adapted measures</p> <p> <ephtml> <table><thead><tr><th valign="top" align="left">Measure</th><th valign="top" align="left">Training set</th><th valign="top" align="left">Test set</th><th valign="top" align="left">Whole set</th></tr></thead><tbody><tr><td valign="top" align="left">Shortest path (1989)</td><td /><td /><td /></tr><tr><td valign="top" align="left"> rada_min</td><td valign="top" align="left">0.72</td><td valign="top" align="left">0.78</td><td valign="top" align="left">0.74</td></tr><tr><td valign="top" align="left"> rada_avg</td><td valign="top" align="left">0.57</td><td valign="top" align="left">0.54</td><td valign="top" align="left">0.55</td></tr><tr><td valign="top" align="left"> rada_max</td><td valign="top" align="left">0.09</td><td valign="top" align="left">0.24</td><td valign="top" align="left">0.15</td></tr><tr><td valign="top" align="left">Wu and Palmer (1994)</td><td /><td /><td /></tr><tr><td valign="top" align="left"> wp_min_ (using wp<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>max</mtext></msub></math></p> set)</td><td valign="top" align="left">0.19</td><td valign="top" align="left">0.18</td><td valign="top" align="left">0.18</td></tr><tr><td valign="top" align="left"> wp_avg_ (using wp<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>min</mtext></msub></math></p> set)</td><td valign="top" align="left">0.75</td><td valign="top" align="left">0.77</td><td valign="top" align="left">0.75</td></tr><tr><td valign="top" align="left"> wp_max_ (using wp<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>avg</mtext></msub></math></p> set)</td><td valign="top" align="left">0.78</td><td valign="top" align="left">0.81</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left">Leacock and Chodorow (1994)</td><td /><td /><td /></tr><tr><td valign="top" align="left"> lc_min</td><td valign="top" align="left">0.74</td><td valign="top" align="left">0.63</td><td valign="top" align="left">0.69</td></tr><tr><td valign="top" align="left"> lc_avg</td><td valign="top" align="left">0.62</td><td valign="top" align="left">0.49</td><td valign="top" align="left">0.56</td></tr><tr><td valign="top" align="left"> lc_max</td><td valign="top" align="left">0.41</td><td valign="top" align="left">0.32</td><td valign="top" align="left">0.37</td></tr><tr><td valign="top" align="left">Blázquez-del-Toro et al. (2008)</td><td /><td /><td /></tr><tr><td valign="top" align="left"> bl_min_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>k</mi><mo>=</mo><mi /></mrow></math></p> 2.5, using bl<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>max</mtext></msub></math></p> set)</td><td valign="top" align="left">0.30</td><td valign="top" align="left">0.21</td><td valign="top" align="left">0.26</td></tr><tr><td valign="top" align="left"> bl_avg_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>k</mi><mo>=</mo><mi /></mrow></math></p> 2.0, using bl<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>������</mtext></msub></math></p> or bl<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>������</mtext></msub></math></p> set)</td><td valign="top" align="left">0.78</td><td valign="top" align="left">0.82</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left"> bl_max_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>k</mi><mo>=</mo><mi /></mrow></math></p> 0.25, using bl<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>������</mtext></msub></math></p> set)</td><td valign="top" align="left">0.80</td><td valign="top" align="left">0.84</td><td valign="top" align="left">0.81</td></tr><tr><td valign="top" align="left">Li et al. (2003)</td><td /><td /><td /></tr><tr><td valign="top" align="left"> li_min_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>α</mi><mo>=</mo><mi /></mrow></math></p> 0.4; <p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>β</mi><mo>=</mo><mi /></mrow></math></p> 1, using li<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>max</mtext></msub></math></p> set)</td><td valign="top" align="left">0.77</td><td valign="top" align="left">0.84</td><td valign="top" align="left">0.80</td></tr><tr><td valign="top" align="left"> li_avg_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>α</mi><mo>=</mo><mi /></mrow></math></p> 0.35; <p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>β</mi><mo>=</mo><mi /></mrow></math></p> 1, using li<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>max</mtext></msub></math></p> set)</td><td valign="top" align="left">0.77</td><td valign="top" align="left">0.82</td><td valign="top" align="left">0.79</td></tr><tr><td valign="top" align="left"> li_max_ (<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>α</mi><mo>=</mo><mi /></mrow></math></p> 0.35; <p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow xmlns=""><mi>β</mi><mo>=</mo><mi /></mrow></math></p> 0.2, using li<p><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub xmlns=""><mi /><mtext>avg</mtext></msub></math></p> set)</td><td valign="top" align="left">0.77</td><td valign="top" align="left">0.85</td><td valign="top" align="left">0.80</td></tr></tbody></table> </ephtml> </p> <p>The adapted measures were trained with the training set and then executed with the test set. Table 3 shows the results of these adapted measures for Wikipedia. When parameters are needed, the table displays the value which maximises the results. In the same way, when adapted approach is composed of 9 different measures, they are grouped in 3 main subsets (the set which applies the minimum, average and maximum functions respectively), and only the best value is selected.</p> <hd id="AN0138480701-21">8.2 Discussion and related work</hd> <p>After the experiments, best results for training and test datasets are achieved with the adapted measure of Blázquez-del-Toro et al.'s (2008) and Li et al.'s (2003) respectively, where Blázquez-del-Toro et al's measure maximizes the whole data collection. From the results reported in Table 3, some conclusions can be drawn. First, when the category distance is the only feature of the measure to adapt, the minimum value among all the LCSs is that with best results (see <emph>rada_min</emph> and <emph>lc_min</emph> values). Second, when taking depth feature as one of the factors, the set of values obtained with the average of depths of the set of the LCSs between two concepts yields better correlation values. Therefore, it gives better correlation to consider the average height of every <emph>lcs</emph> between the categories of concepts, instead of selecting a minimum or maximum value.</p> <p>Table 4 Correlation coefficients for test and whole set</p> <p> <ephtml> <table><thead><tr><th valign="top" align="left">Measure</th><th valign="top" align="left">Test set</th><th valign="top" align="left">Measure</th><th valign="top" align="left">Whole set</th></tr></thead><tbody><tr><td valign="top" align="left">Shortest path</td><td valign="top" align="left">0.62</td><td valign="top" align="left">Cilibrasi and Vetanyi</td><td valign="top" align="left">0.52</td></tr><tr><td valign="top" align="left">Wu and Palmer</td><td valign="top" align="left">0.75</td><td valign="top" align="left">Shortest path</td><td valign="top" align="left">0.58</td></tr><tr><td valign="top" align="left">Bollegalla</td><td valign="top" align="left">0.76</td><td valign="top" align="left">Bollegalla</td><td valign="top" align="left">0.70</td></tr><tr><td valign="top" align="left">Resnik</td><td valign="top" align="left">0.77</td><td valign="top" align="left">Wu and Palmer</td><td valign="top" align="left">0.78</td></tr><tr><td valign="top" align="left">Blázquez-del-Toro et al.</td><td valign="top" align="left">0.81</td><td valign="top" align="left">Adapted (bl_max_avg)</td><td valign="top" align="left">0.81</td></tr><tr><td valign="top" align="left">Lin</td><td valign="top" align="left">0.82</td><td valign="top" align="left">Resnik</td><td valign="top" align="left">0.83</td></tr><tr><td valign="top" align="left">Li et al.</td><td valign="top" align="left">0.82</td><td valign="top" align="left">Leacock and Chodorow</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left">Leacock and Chodorow</td><td valign="top" align="left">0.83</td><td valign="top" align="left">Jiang and Conrath</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left">Jiang and Conrath</td><td valign="top" align="left">0.83</td><td valign="top" align="left">Li et al.</td><td valign="top" align="left">0.84</td></tr><tr><td valign="top" align="left">Adapted (li_max_avg)</td><td valign="top" align="left">0.85</td><td valign="top" align="left">Lin</td><td valign="top" align="left">0.85</td></tr></tbody></table> </ephtml> </p> <p>Results show that Wikipedia is a source of knowledge as reliable as other well-formed taxonomies such as WordNet or other dictionaries and corpora for calculating semantic similarity. For comparative purposes, Table 4 shows, in ascending order, the correlation coefficients for both the test set (28 pairs) and the whole set (65 pairs).</p> <p>Best adapted results approximate and even improve traditional approaches with WordNet, as in the case of the test set. Even though the best correlation obtained for the whole set is slightly smaller than those obtained with other traditional sources, it is still over a correlation of 0.80. Besides, adapted measures take the inherent advantages of using Wikipedia, such as greater coverage, multiple domains, or the possibility of comparing concepts from different parts of speech.</p> <p>The general process to compute the semantic similarity of two concepts with our adapted measures is simple and cost-effective, because there is no need to process big amounts of text corpora such as in Resnik (1995). The structure - the Wikipedia categories - is used as it is; there is no need to modify the underlying taxonomy as in the original measure from Blazquez del Toro et al. (2008) or generate a new taxonomy from the category structure such as in Natase and Strube (2013).</p> <p>There are works which use traditional semantic measures adapted to Wikipedia, such as <emph>WikiRelate!</emph> (Strube & Ponzetto, 2006), where authors apply a combination of several existing techniques adapted to the structure of categories of Wikipedia, obtaining a correlation of 0.56. However, most of these existing works focus on measuring semantic relatedness. In Gabrilovich and Markovitch (2007) or Wee and Hassan (2008), authors calculate the semantic relatedness using the text of Wikipedia articles and applying traditional vector measures. In other works (Milne & Witten, 2008; Yeh et al., 2009; Zhang et al., 2011), authors calculate relationships based on the hyperlinks within articles. More recent is the work of Nastase & Strube (2013), which also uses Wikipedia structure, but they must previously transform it into a large-scale network. These works cannot be compared to our approach as their goal is computing relatedness in general. In fact, these works made their experiments with specific datasets for evaluating relatedness instead of similarity, such as the WordSim353 collection (Finkelstein et al. 2002), obtaining correlations from 0.60 to 0.75.</p> <hd id="AN0138480701-22">9. Conclusions</hd> <p>There is a broad consensus about the good results obtained using visual learning objects in the classroom. Concept maps help to understand complex relationships, to infer implications and consolidate learning. In this article, we have proposed a method to adapt semantic distance metrics to concept map construction. The method aims to adapt path-based and multi-source similarity metrics in order to work with the Wikipedia categorization structure as their knowledge source, instead of traditional lexical structures such as WordNet. To achieve this goal, we have analysed the features that are commonly used within these existing approaches and have adapted these features to use Wikipedia structure.</p> <p>The extraction of these features is not as straightforward as in well-structured taxonomies like WordNet, due to the inherent structure of Wikipedia categories. The most remarkable fact in this structure is the existence of multiple inheritances both between categories and between categories and concepts, which makes the structure of this categorization scheme like that of tagging systems.</p> <p>Our approach takes advantage of existing path-based and multi-source measures, avoiding the development of new measures from scratch, and it does not require natural language processing techniques to achieve good results, which makes our approach quite effective.</p> <p>Results obtained show that Wikipedia is an appropriate source to calculate the semantic similarity between well-defined concepts. Among its advantages with respect to other sources, we can find the following:</p> <p></p> <ulist> <item> • More coverage over a great variety of domains</item> <p></p> <item> • Inclusion of specific concepts such as named entities</item> <p></p> <item> • Flexible and rapid updates</item> <p></p> <item> • Elaborated by consensus of a community</item> <p></p> <item> • Different parts of speech (nouns, verbs, adjectives) coexisting in the same structure</item> <p></p> <item> • Translated to different languages</item> </ulist> <p>In the past semantic distances have been employed to adapt learning objects to different learning profiles (Aeiad, 2017), thanks to our approach this adaptation could be done in a more robust way and with guarantees to get best results.</p> <p>These results are promising; Wikipedia can be used for applications where a broad-coverage of the real world is needed, improving the correlation coefficients obtained with approaches using World Wide Web documents, or existing Wikipedia-based techniques.</p> <p>One of the main difficulties in evaluating a semantic similarity technique is the lack of gold standards with a huge number of pair concepts. Our work has used the Rubenstein and Goodenough's collection of 65 pairs, which has been thoroughly used in recent decades, but we plan to evaluate our approach also with other collections, applying cross-validation to avoid possible overfitting, such as the WorldSimilarity-353 Test Collection, even though it is not appropriate to measure semantic similarity (Jarmasz & Szpakowicz, 2003). Besides, our adapted measures will be tested in other Wikipedia dumps and versions apart from English, to see their effectiveness in different times and in different languages.</p> <hd id="AN0138480701-23">Acknowledgments</hd> <p>We would like to acknowledge Danushka Bollegala, who facilitated his software to replicate his measure for our experiments. This work has been partially funded by the Spanish Ministerio de Economía y Competitividad through the project CSO2017-86747-R, developed between Carlos III and Complutense Universities.</p> <ref id="AN0138480701-24"> <title> References </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> Aeiad, E. (2017). A framework for an adaptable and personalised e-learning system based on free web resources (PhD thesis). University of Salford. Retrieved from <ulink href="http://usir.salford.ac.uk/42531/">http://usir.salford.ac.uk/42531/</ulink>.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref2" type="bt">2</bibl> <bibtext> Blázquez del Toro, J. M., Fisteus, J. A., Centeno, V. L., & Fernandez, L. S. (2008). A semantic similarity measure in the context of semantic queries. International Journal of Computer Applications in Technology. 33 (4), 285. Retrieved from https://doi.org/10.1504/IJCAT.2008.022424.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref3" type="bt">3</bibl> <bibtext> Bollegala, D., Matsuo, Y., & Ishizuka, M. (2007). Measuring Semantic Similarity between Words using Web Search Engines. In Proceedings of the 16th International Conference on World Wide Web (WWW '07) (pp. 757-766). Banff, Alberta, Canada.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref10" type="bt">4</bibl> <bibtext> Church, K. W., & Hanks, P. (1990). Word Association Norms, Mutual Information, and Lexicography. Computational Linguistic, 16 (1), 22-29.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref11" type="bt">5</bibl> <bibtext> Cilibrasi, R. L., & Vitanyi, P. M. B. (2007). The Google Similarity Distance. IEEE Transactions on Knowledge and Data Engineering, 19 (3), 370-383. Retrieved from https://doi.org/10.1109/TKDE.2007.48.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref12" type="bt">6</bibl> <bibtext> Davies, M. (2011). Concept mapping, mind mapping and argument mapping. what are the differences and do they matter. Higher Education, 62 (3), 279-301. Retrieved from https://doi.org/10.1007/s10734-010-9387-6.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref13" type="bt">7</bibl> <bibtext> Dewan, P. (2015). Words Versus Pictures. Leveraging the Research on Visual Communication. Partnership. The Canadian Journal of Library and Information Practice and Research, 10 (1). Retrieved from https://doi.org/10.21083/partnership.v10i1.3137</bibtext> </blist> <blist> <bibl id="bib8" idref="ref14" type="bt">8</bibl> <bibtext> Fernández, N., Fisteus, J. A., Fuentes, D., Sánchez, L., & Luque, V. (2011). A Wikipedia-based framework for collaborative semantic annotation. International Journal on Artificial Intelligence Tools, 20 (5), 847-886. Retrieved from https://doi.org/10.1142/S0218213011000413.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref15" type="bt">9</bibl> <bibtext> Finkelstein, L., Gabrilovich, E., Matias, Y., Rivlin, E., Solan, Z., Wolfman, G., & Ruppin, E. (2002). Placing search in context. the concept revisited. ACM Transactions on Information Systems, 20 (1), 116-131. Retrieved from https://doi.org/10.1145/503104.503110.</bibtext> </blist> <blist> <bibtext> Fuentes-Lorenzo, D., Fernández, N., Fisteus, J. A., & Sánchez, L. (2013). Improving large-scale search engines with semantic annotations. Expert Systems with Applications, 40 (6), 2287-2296. Retrieved from https://doi.org/10.1016/j.eswa.2012.10.042.</bibtext> </blist> <blist> <bibtext> Gabrilovich, E., & Markovitch, S. (2007). Computing Semantic Relatedness Using Wikipedia-based Explicit Semantic Analysis. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (pp. 1606-1611). San Francisco, CA, USA. Morgan Kaufmann Publishers Inc. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=1625275.1625535">http://dl.acm.org/citation.cfm?id=1625275.1625535</ulink>.</bibtext> </blist> <blist> <bibtext> Imran, A. S., Mansoor, A., & Islam, A. T. (2014). An Automatic and Innovative Approach for Converting Pedagogical Text Documents to Visual Learning Object. In C. Stephanidis (Ed.), HCI International 2014-Posters' Extended Abstracts (Vol. 435, pp. 84-88). Cham. Springer International Publishing. Retrieved from https://doi.org/10.1007/978-3-319-07854-0_15.</bibtext> </blist> <blist> <bibtext> Imran, A. S., Rahadianti, L., Cheikh, F. A., & Yayilgan, S. Y. (2012). Semantic Tags for Lecture Videos. In 2012 IEEE Sixth International Conference on Semantic Computing (pp. 117-120). Palermo, Italy. IEEE. Retrieved from https://doi.org/10.1109/ICSC.2012.36.</bibtext> </blist> <blist> <bibtext> Jarmasz, M., & Szpakowicz, S. (2003). Roget's Thesaurus and Semantic Similarity. Proceedings of the International Conference on Recent Advances in Natural Language Processing, pp. 212-9, Borovets, Bulgaria. Retrieved from <ulink href="http://arxiv.org/abs/1204.0245">http://arxiv.org/abs/1204.0245</ulink>.</bibtext> </blist> <blist> <bibtext> Jiang, J. J., & Conrath, D. W. (1997). Semantic similarity based on corpus statistics and lexical taxonomy. In Proc of 10th International Conference on Research in Computational Linguistics, 19-33. ROCLING'97 Taiwan.</bibtext> </blist> <blist> <bibtext> Jiang, P., Hou, H., Chen, L., Chen, S., Yao, C., Li, C., & Wang, M. (2013). Wiki3C. exploiting wikipedia for context-aware concept categorization. In Proceedings of the sixth ACM international conference on Web search and data mining – WSDM '13 (p. 345). Rome, Italy. ACM Press. Retrieved from https://doi.org/10.1145/2433396.2433441.</bibtext> </blist> <blist> <bibtext> Kardan, A. A., Sani, F. M., & Modaberi, S. (2016). Implicit learner assessment based on semantic relevance of tags. Computers in Human Behavior, 55, 743-749. Retrieved from https://doi.org/10.1016/j.chb.2015.10.027.</bibtext> </blist> <blist> <bibtext> Kumar, R, Sarukesi, K., & Uma, G.V. (2012). Assessment of Understanding using Concept Map. A Novel Approach. International Journal of Computer Applications, 54 (4), 42-46. Retrieved from https://doi.org/10.5120/8557-2124.</bibtext> </blist> <blist> <bibtext> Kumaran, V. S., & Sankar, A. (2013). An Automated Assessment of Students' Learning in e-Learning Using Concept Map and Ontology Mapping. In J.-F. Wang & R. Lau (Eds.), Advances in Web-Based Learning – ICWL 2013 (pp. 274-283). Berlin, Heidelberg. Springer Berlin Heidelberg.</bibtext> </blist> <blist> <bibtext> Leacock, C., & Chodorow, M. (1994). Filling in a sparse training space for word sense identification. PhD thesis, Sidney. Macquarie University.</bibtext> </blist> <blist> <bibtext> Lee, J. H., Kim, M. H., & Lee, Y. J. (1993). Information Retrieval Based on Conceptual Distance in is-a Hierarchies. Journal of Documentation, 49 (2), 188-207. Retrieved from https://doi.org/10.1108/eb026913.</bibtext> </blist> <blist> <bibtext> Lesk, M. (1986). Automatic sense disambiguation using machine readable dictionaries. how to tell a pine code from an ice cream cone. In Proceedings of the 5th annual international conference on Systems documentation – SIGDOC '86 (pp. 24-26). Toronto, Ontario, Canada. ACM Press. Retrieved from https://doi.org/10.1145/318723.318728.</bibtext> </blist> <blist> <bibtext> Li, C., Sun, A., & Datta, A. (2011). A Generalized Method for Word Sense Disambiguation Based on Wikipedia. In Proceedings of the 33rd European Conference on Advances in Information Retrieval (pp. 653-664). Berlin, Heidelberg. Springer-Verlag. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=1996889.1996972">http://dl.acm.org/citation.cfm?id=1996889.1996972</ulink>.</bibtext> </blist> <blist> <bibtext> Li, Y., Bandar, Z. A., & McLean, D. (2003). An approach for measuring semantic similarity between words using multiple information sources. IEEE Transactions on Knowledge and Data Engineering, 15 (4), 871-882. Retrieved from https://doi.org/10.1109/TKDE.2003.1209005.</bibtext> </blist> <blist> <bibtext> Lin, D. (1998). An Information-Theoretic Definition of Similarity. In Proceedings of the Fifteenth International Conference on Machine Learning (pp. 296-304). San Francisco, CA, USA. Morgan Kaufmann Publishers Inc. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=645527.657297">http://dl.acm.org/citation.cfm?id=645527.657297</ulink>.</bibtext> </blist> <blist> <bibtext> Makris, C., Plegas, Y., & Theodoridis, E. (2013). Improved text annotation with Wikipedia entities. In Proceedings of the 28th Annual ACM Symposium on Applied Computing – SAC '13 (p. 288). Coimbra, Portugal. ACM Press. Retrieved from https://doi.org/10.1145/2480362.2480425.</bibtext> </blist> <blist> <bibtext> Miller, G. A. (1995). WordNet. a lexical database for English. Communications of the ACM, 38 (11), 39-41. Retrieved from https://doi.org/10.1145/219717.219748.</bibtext> </blist> <blist> <bibtext> Miller, G. A., & Charles, W. G. (1991). Contextual correlates of semantic similarity. Language and Cognitive Processes, 6 (1), 1-28. Retrieved from https://doi.org/10.1080/01690969108406936.</bibtext> </blist> <blist> <bibtext> Milne, D., & Witten, I. H. (2008). An Effective, Low-Cost Measure of Semantic Relatedness Obtained from Wikipedia Links. In Proceedings of the First AAAI Workshop on Wikipedia and Artificial Intelligence (WIKIAI'08) (pp. 25-30). Chicago.</bibtext> </blist> <blist> <bibtext> Morato, J., Sanchez-Cuadrado, S., Ruiz-Robles, A., & Moreiro, J.A. (2014). Visualization and Information Retrival on the Semantic Web. 23 (3), 319-329. Retrieved from <ulink href="http://dx.doi.org/10.3145/epi.2014.may.12">http://dx.doi.org/10.3145/epi.2014.may.12</ulink>.</bibtext> </blist> <blist> <bibtext> Nastase, V., & Strube, M. (2013). Transforming Wikipedia into a large scale multilingual concept network. Artificial Intelligence, 194, 62-85. Retrieved from https://doi.org/10.1016/j.artint.2012.06.008.</bibtext> </blist> <blist> <bibtext> Pedersen, T., Banerjee, S., & Patwardhan, S. (2005). Maximizing Semantic Relatedness to Perform Word Sense Disambiguation (Research Report No. 2005/25) (p. 34), University of Minnesota, Supercomputing Institute. Retrieved from <ulink href="http://www.patwardhans.net/papers/PedersenBP05.pdf">http://www.patwardhans.net/papers/PedersenBP05.pdf</ulink>.</bibtext> </blist> <blist> <bibtext> Quillian, M. R. (1967). Word concepts. A theory and simulation of some basic semantic capabilities. Behavioral Science, 12 (5), 410-430. Retrieved from https://doi.org/10.1002/bs.3830120511.</bibtext> </blist> <blist> <bibtext> Rada, R., Mili, H., Bicknell, E., & Blettner, M. (1989). Development and application of a metric on semantic nets. IEEE Transactions on Systems, Man, and Cybernetics, 19 (1), 17-30. Retrieved from https://doi.org/10.1109/21.24528.</bibtext> </blist> <blist> <bibtext> Resnik, P. (1995). Using Information Content to Evaluate Semantic Similarity in a Taxonomy. In Proceedings of the 14th International Joint Conference on Artificial Intelligence – Volume 1 (pp. 448-453). San Francisco, CA, USA. Morgan Kaufmann Publishers Inc. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=1625855.1625914">http://dl.acm.org/citation.cfm?id=1625855.1625914</ulink>.</bibtext> </blist> <blist> <bibtext> Richardson, R., & Smeaton, A. F. (1995). Using WordNet in a Knowledge-Based Approach to Information Retrieval (Technical Report No. CA-0395). Dublin. Dublin City University. Retrieved from <ulink href="http://www.computing.dcu.ie/wpapers/1995/0395.ps">http://www.computing.dcu.ie/wpapers/1995/0395.ps</ulink>.</bibtext> </blist> <blist> <bibtext> Rubenstein, H., & Goodenough, J. B. (1965). Contextual correlates of synonymy. Communications of the ACM, 8 (10), 627-633. Retrieved from https://doi.org/10.1145/365628.365657.</bibtext> </blist> <blist> <bibtext> Strube, M., & Ponzetto, S. P. (2006). WikiRelate! Computing Semantic Relatedness Using Wikipedia. In Proceedings of the 21st National Conference on Artificial Intelligence – Volume 2 (pp. 1419-1424). Boston, Massachusetts. AAAI Press. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=1597348.1597414">http://dl.acm.org/citation.cfm?id=1597348.1597414</ulink>.</bibtext> </blist> <blist> <bibtext> Sussna, M. (1993). Word sense disambiguation for free-text indexing using a massive semantic network. In Proceedings of the second international conference on Information and knowledge management – CIKM '93 (pp. 67-74). Washington, D.C., United States. ACM Press. Retrieved from https://doi.org/10.1145/170088.170106.</bibtext> </blist> <blist> <bibtext> Trillo, R., Gracia, J., Espinoza, M., & Mena, E. (2007). Discovering the Semantics of User Keywords. Journal of Universal Computer Science, 13 (12), 1908-35.</bibtext> </blist> <blist> <bibtext> Wee, L. C., & Hassan, S. (2008). Exploiting Wikipedia for Directional Inferential Text Similarity. Proceedings of the Fifth International Conference on Information Technology. New Generations (ITNG '08), pp. 686-91, Las Vegas, Nevada, USA.</bibtext> </blist> <blist> <bibtext> Wilks, Y., Fass, D., Guo, C., McDonald, J. E., Plate, T., & Slator, B. M. (1990). Providing machine tractable dictionary tools. Machine Translation, 5 (2), 99-154. Retrieved from https://doi.org/10.1007/BF00393758.</bibtext> </blist> <blist> <bibtext> Wu, Z., & Palmer, M. (1994). Verbs semantics and lexical selection. In Proceedings of the 32nd annual meeting on Association for Computational Linguistics (pp. 133-138). Las Cruces, New Mexico. Association for Computational Linguistics. Retrieved from https://doi.org/10.3115/981732.981751.</bibtext> </blist> <blist> <bibtext> Yeh, E., Ramage, D., Manning, C. D., Agirre, E., & Soroa, A. (2009). WikiWalk. Random Walks on Wikipedia for Semantic Relatedness. In Proceedings of the 2009 Workshop on Graph-based Methods for Natural Language Processing (pp. 41-49). Stroudsburg, PA, USA. Association for Computational Linguistics. Retrieved from <ulink href="http://dl.acm.org/citation.cfm?id=1708124.1708133">http://dl.acm.org/citation.cfm?id=1708124.1708133</ulink>.</bibtext> </blist> <blist> <bibtext> Zhang, X., Asano, Y., & Yoshikawa, M. (2011). A Generalized Flow Based Method for Analysis of Implicit Relationships on Wikipedia. Knowledge and Data Engineering, IEEE Transactions On, 6 (1), 14.</bibtext> </blist> </ref> <aug> <p>By Damaris Fuentes-Lorenzo; Jorge Morato; Sonia Sanchez-Cuadrado; Luis Sanchez; Audilio Gonzalez Aguilar, Guest-editor and Francisco Carlos Paletta Arezes, Guest-editor</p> <p>Reported by Author; Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib10" firstref="ref16"></nolink> <nolink nlid="nl2" bibid="bib11" firstref="ref17"></nolink> <nolink nlid="nl3" bibid="bib12" firstref="ref18"></nolink> <nolink nlid="nl4" bibid="bib13" firstref="ref19"></nolink> <nolink nlid="nl5" bibid="bib14" firstref="ref20"></nolink> <nolink nlid="nl6" bibid="bib15" firstref="ref21"></nolink> <nolink nlid="nl7" bibid="bib16" firstref="ref22"></nolink> <nolink nlid="nl8" bibid="bib17" firstref="ref27"></nolink> <nolink nlid="nl9" bibid="bib18" firstref="ref28"></nolink> <nolink nlid="nl10" bibid="bib19" firstref="ref29"></nolink> <nolink nlid="nl11" bibid="bib20" firstref="ref33"></nolink> <nolink nlid="nl12" bibid="bib21" firstref="ref34"></nolink> <nolink nlid="nl13" bibid="bib22" firstref="ref35"></nolink> <nolink nlid="nl14" bibid="bib23" firstref="ref36"></nolink> <nolink nlid="nl15" bibid="bib24" firstref="ref37"></nolink> <nolink nlid="nl16" bibid="bib25" firstref="ref38"></nolink> <nolink nlid="nl17" bibid="bib26" firstref="ref40"></nolink> <nolink nlid="nl18" bibid="bib27" firstref="ref43"></nolink> <nolink nlid="nl19" bibid="bib28" firstref="ref44"></nolink> <nolink nlid="nl20" bibid="bib29" firstref="ref45"></nolink> <nolink nlid="nl21" bibid="bib30" firstref="ref46"></nolink> <nolink nlid="nl22" bibid="bib31" firstref="ref47"></nolink> <nolink nlid="nl23" bibid="bib32" firstref="ref48"></nolink>
Header DbId: eric
DbLabel: ERIC
An: EJ1228204
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Building Concept Maps by Adapting Semantic Distance Metrics to Wikipedia
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Fuentes-Lorenzo%2C+Damaris%22">Fuentes-Lorenzo, Damaris</searchLink><br /><searchLink fieldCode="AR" term="%22Morato%2C+Jorge%22">Morato, Jorge</searchLink><br /><searchLink fieldCode="AR" term="%22Sanchez-Cuadrado%2C+Sonia%22">Sanchez-Cuadrado, Sonia</searchLink><br /><searchLink fieldCode="AR" term="%22Sanchez%2C+Luis%22">Sanchez, Luis</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Education+for+Information%22"><i>Education for Information</i></searchLink>. 2019 35(3):209-240.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: IOS Press. Nieuwe Hemweg 6B, Amsterdam, 1013 BG, The Netherlands. Tel: +31-20-688-3355; Fax: +31-20-687-0039; e-mail: info@iospress.nl; Web site: http://www.iospress.nl
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 32
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2019
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Evaluative
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Concept+Mapping%22">Concept Mapping</searchLink><br /><searchLink fieldCode="DE" term="%22Web+Sites%22">Web Sites</searchLink><br /><searchLink fieldCode="DE" term="%22Collaborative+Writing%22">Collaborative Writing</searchLink><br /><searchLink fieldCode="DE" term="%22Information+Sources%22">Information Sources</searchLink><br /><searchLink fieldCode="DE" term="%22Taxonomy%22">Taxonomy</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+Linguistics%22">Computational Linguistics</searchLink><br /><searchLink fieldCode="DE" term="%22Nouns%22">Nouns</searchLink><br /><searchLink fieldCode="DE" term="%22Vocabulary%22">Vocabulary</searchLink><br /><searchLink fieldCode="DE" term="%22Natural+Language+Processing%22">Natural Language Processing</searchLink><br /><searchLink fieldCode="DE" term="%22Comparative+Analysis%22">Comparative Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Measurement%22">Measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Semantics%22">Semantics</searchLink><br /><searchLink fieldCode="DE" term="%22Visual+Learning%22">Visual Learning</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.3233/EFI-190279
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0167-8329
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Building and checking concept maps is an active research topic in visual learning. Concept maps are intended to show visual representations of interrelated concepts in educational and professional settings. For the last decades, numerous formulas have been proposed to compute the semantic proximity between any pair of concepts in the map. A review of the employment of semantic distances in concept map construction shows the lack of a clear criterion to select a suitable formula. Traditional metrics can be basically grouped depending on the representation of their knowledge source: statistic approaches based on co-occurrence of words in big corpora; path-based methods using lexical structures, like taxonomies; and multi-source methods which combine statistic approaches and path-based methods. On the one hand, path-based measures give better results than corpora-based metrics, but they cannot be used to process specific concepts or proper nouns due to the limited vocabulary of the taxonomies used. On the other side, information obtained from big corpora -- including the World Wide Web -- is not organized in a specific way and natural language processing techniques are usually needed in order to obtain acceptable results. In this research Wikipedia is proposed since it does not have such limitations. This article defines an approach to adapt path-based semantic similarity measures to Wikipedia for building concept maps. Experimental evaluation with a well-known set of human similarity judgments shows that the Wikipedia adapted metrics obtains equal or even better results when compared with the non-adapted approaches.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2019
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1228204
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1228204
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.3233/EFI-190279
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 32
        StartPage: 209
    Subjects:
      – SubjectFull: Concept Mapping
        Type: general
      – SubjectFull: Web Sites
        Type: general
      – SubjectFull: Collaborative Writing
        Type: general
      – SubjectFull: Information Sources
        Type: general
      – SubjectFull: Taxonomy
        Type: general
      – SubjectFull: Computational Linguistics
        Type: general
      – SubjectFull: Nouns
        Type: general
      – SubjectFull: Vocabulary
        Type: general
      – SubjectFull: Natural Language Processing
        Type: general
      – SubjectFull: Comparative Analysis
        Type: general
      – SubjectFull: Measurement
        Type: general
      – SubjectFull: Semantics
        Type: general
      – SubjectFull: Visual Learning
        Type: general
    Titles:
      – TitleFull: Building Concept Maps by Adapting Semantic Distance Metrics to Wikipedia
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Fuentes-Lorenzo, Damaris
      – PersonEntity:
          Name:
            NameFull: Morato, Jorge
      – PersonEntity:
          Name:
            NameFull: Sanchez-Cuadrado, Sonia
      – PersonEntity:
          Name:
            NameFull: Sanchez, Luis
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2019
          Identifiers:
            – Type: issn-print
              Value: 0167-8329
          Numbering:
            – Type: volume
              Value: 35
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Education for Information
              Type: main
ResultId 1