Learning Discriminative Stein Kernel for SPD Matrices and Its Applications.

Zhang, J; Wang, L; Zhou, L; Li, W

Learning Discriminative Stein Kernel for SPD Matrices and Its Applications.

Zhang, J

Wang, L Zhou, L Li, W

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Publisher:: Institute of Electrical and Electronics Engineers (IEEE)
Publication Type:: Journal Article
Citation:: IEEE Trans Neural Netw Learn Syst, 2016, 27, (5), pp. 1020-1033
Issue Date:: 2016-05

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Field	Value	Language
dc.contributor.author	Zhang, J https://orcid.org/0000-0001-5048-5606
dc.contributor.author	Wang, L
dc.contributor.author	Zhou, L
dc.contributor.author	Li, W
dc.date.accessioned	2022-08-21T21:17:38Z
dc.date.available	2022-08-21T21:17:38Z
dc.date.issued	2016-05
dc.identifier.citation	IEEE Trans Neural Netw Learn Syst, 2016, 27, (5), pp. 1020-1033
dc.identifier.issn	2162-237X
dc.identifier.issn	2162-2388
dc.identifier.uri	http://hdl.handle.net/10453/160611
dc.description.abstract	Stein kernel (SK) has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: 1) eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation, and 2) more importantly, eigenvalues reflect only the property of an individual SPD matrix. They are not necessarily optimal for computing SK when the goal is to discriminate different classes of SPD matrices. To address the two issues, we propose a discriminative SK (DSK), in which an extra parameter vector is defined to adjust the eigenvalues of input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three kernel learning criteria that are commonly used in the literature are employed as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare the proposed DSK with the original SK and other methods for evaluating the similarity between SPD matrices. The results demonstrate that the DSK can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original SK and other commonly used methods.
dc.format	Print-Electronic
dc.language	eng
dc.publisher	Institute of Electrical and Electronics Engineers (IEEE)
dc.relation.ispartof	IEEE Trans Neural Netw Learn Syst
dc.relation.isbasedon	10.1109/TNNLS.2015.2435154
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Artificial Intelligence & Image Processing
dc.title	Learning Discriminative Stein Kernel for SPD Matrices and Its Applications.
dc.type	Journal Article
utslib.citation.volume	27
utslib.location.activity	United States
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/A/DRsch The Data Science Institute
utslib.copyright.status	closed_access	*
dc.date.updated	2022-08-21T21:17:36Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	27
utslib.citation.issue	5

Abstract:

Stein kernel (SK) has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: 1) eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation, and 2) more importantly, eigenvalues reflect only the property of an individual SPD matrix. They are not necessarily optimal for computing SK when the goal is to discriminate different classes of SPD matrices. To address the two issues, we propose a discriminative SK (DSK), in which an extra parameter vector is defined to adjust the eigenvalues of input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three kernel learning criteria that are commonly used in the literature are employed as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare the proposed DSK with the original SK and other methods for evaluating the similarity between SPD matrices. The results demonstrate that the DSK can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original SK and other commonly used methods.

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http://hdl.handle.net/10453/160611