Sign consistency for the linear programming discriminant rule

Zhang, Z; Wang, S; Bian, W

Sign consistency for the linear programming discriminant rule

Zhang, Z Wang, S Bian, W

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: Pattern Recognition, 2020, 100, pp. 107083-107083
Issue Date:: 2020-04-01

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Field	Value	Language
dc.contributor.author	Zhang, Z
dc.contributor.author	Wang, S
dc.contributor.author	Bian, W
dc.date.accessioned	2021-06-17T03:44:57Z
dc.date.available	2021-06-17T03:44:57Z
dc.date.issued	2020-04-01
dc.identifier.citation	Pattern Recognition, 2020, 100, pp. 107083-107083
dc.identifier.issn	0031-3203
dc.identifier.uri	http://hdl.handle.net/10453/149586
dc.description.abstract	Linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionality p and a large training sample size n. However, in high-dimensional settings when p ≫ n, LDA is difficult due to the inconsistent estimation of the covariance matrix and the mean vectors of populations. Recently, a linear programming discriminant (LPD) rule was proposed for high-dimensional linear discriminant analysis, based on the sparsity assumption over the discriminant function. It is shown that the LPD rule is Bayes consistent in high-dimensional settings. In this paper, we further show that the LPD rule is sign consistent under the sparsity assumption. Such sign consistency ensures the LPD rule to select the optimal discriminative features for high-dimensional data classification problems. Evaluations on both synthetic and real data validate our result on the sign consistency of the LPD rule.
dc.language	en
dc.publisher	Elsevier BV
dc.relation.ispartof	Pattern Recognition
dc.relation.isbasedon	10.1016/j.patcog.2019.107083
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0806 Information Systems, 0906 Electrical and Electronic Engineering
dc.subject.classification	Artificial Intelligence & Image Processing
dc.title	Sign consistency for the linear programming discriminant rule
dc.type	Journal Article
utslib.citation.volume	100
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0806 Information Systems
utslib.for	0906 Electrical and Electronic Engineering
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/Strength - AAII - Australian Artificial Intelligence Institute
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	closed_access	*
dc.date.updated	2021-06-17T03:44:56Z
pubs.publication-status	Published
pubs.volume	100

Abstract:

Linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionality p and a large training sample size n. However, in high-dimensional settings when p ≫ n, LDA is difficult due to the inconsistent estimation of the covariance matrix and the mean vectors of populations. Recently, a linear programming discriminant (LPD) rule was proposed for high-dimensional linear discriminant analysis, based on the sparsity assumption over the discriminant function. It is shown that the LPD rule is Bayes consistent in high-dimensional settings. In this paper, we further show that the LPD rule is sign consistent under the sparsity assumption. Such sign consistency ensures the LPD rule to select the optimal discriminative features for high-dimensional data classification problems. Evaluations on both synthetic and real data validate our result on the sign consistency of the LPD rule.

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http://hdl.handle.net/10453/149586