Kernelized vector quantization in gradient-descent learning.
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| Title: | Kernelized vector quantization in gradient-descent learning. |
|---|---|
| Authors: | Villmann, Thomas1 thomas.villmann@hs-mittweida.de, Haase, Sven1, Kaden, Marika1 |
| Source: | Neurocomputing. Jan2015, Vol. 147, p83-95. 13p. |
| Subjects: | Vector quantization, Prototypes, Support vector machines, Kernel functions, Hilbert space |
| Abstract: | Prototype based vector quantization is usually proceeded in the Euclidean data space. In the last years, also non-standard metrics became popular. For classification by support vector machines, Hilbert space representations, which are based on so-called kernel metrics, seem to be very successful. In this paper we show that gradient based learning in prototype-based vector quantization is possible by means of kernel metrics instead of the standard Euclidean distance. We will show that an appropriate handling requires differentiable universal kernels defining the feature space metric. This allows a prototype adaptation in the original data space but equipped with a metric determined by the kernel and, therefore, it is isomorphic to respective kernel Hilbert space. However, this approach avoids the Hilbert space representation as known for support vector machines. We give the mathematical justification for the isomorphism and demonstrate the abilities and the usefulness of this approach for several examples including both artificial and real world datasets. [ABSTRACT FROM AUTHOR] |
| Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 98357021 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Kernelized vector quantization in gradient-descent learning. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Villmann%2C+Thomas%22">Villmann, Thomas</searchLink><relatesTo>1</relatesTo><i> thomas.villmann@hs-mittweida.de</i><br /><searchLink fieldCode="AR" term="%22Haase%2C+Sven%22">Haase, Sven</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Kaden%2C+Marika%22">Kaden, Marika</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Neurocomputing%22">Neurocomputing</searchLink>. Jan2015, Vol. 147, p83-95. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Vector+quantization%22">Vector quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Prototypes%22">Prototypes</searchLink><br /><searchLink fieldCode="DE" term="%22Support+vector+machines%22">Support vector machines</searchLink><br /><searchLink fieldCode="DE" term="%22Kernel+functions%22">Kernel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Prototype based vector quantization is usually proceeded in the Euclidean data space. In the last years, also non-standard metrics became popular. For classification by support vector machines, Hilbert space representations, which are based on so-called kernel metrics, seem to be very successful. In this paper we show that gradient based learning in prototype-based vector quantization is possible by means of kernel metrics instead of the standard Euclidean distance. We will show that an appropriate handling requires differentiable universal kernels defining the feature space metric. This allows a prototype adaptation in the original data space but equipped with a metric determined by the kernel and, therefore, it is isomorphic to respective kernel Hilbert space. However, this approach avoids the Hilbert space representation as known for support vector machines. We give the mathematical justification for the isomorphism and demonstrate the abilities and the usefulness of this approach for several examples including both artificial and real world datasets. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Neurocomputing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.neucom.2013.11.048 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 83 Subjects: – SubjectFull: Vector quantization Type: general – SubjectFull: Prototypes Type: general – SubjectFull: Support vector machines Type: general – SubjectFull: Kernel functions Type: general – SubjectFull: Hilbert space Type: general Titles: – TitleFull: Kernelized vector quantization in gradient-descent learning. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Villmann, Thomas – PersonEntity: Name: NameFull: Haase, Sven – PersonEntity: Name: NameFull: Kaden, Marika IsPartOfRelationships: – BibEntity: Dates: – D: 05 M: 01 Text: Jan2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 09252312 Numbering: – Type: volume Value: 147 Titles: – TitleFull: Neurocomputing Type: main |
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