D.C. programming for sparse proximal support vector machines

•New SPSVMs model is proposed by using l0-norm rather than l1-norm.•Introduce a new nonconvex continuous approximation of l0-norm.•An alternating scheme based on DCA is proposed for SPSVMs.•Preliminary experimental results are presented to show the efficiency of the proposed method. Proximal support...

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Vydané v:Information sciences Ročník 547; s. 187 - 201
Hlavní autori: Li, Guoquan, Yang, Linxi, Wu, Zhiyou, Wu, Changzhi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 08.02.2021
Predmet:
DC Algorithm
DC programming
Sparse proximal support vector machine
Support vector machine
DC programming
Support vector machine
Sparse proximal support vector machine
DC Algorithm
ISSN:0020-0255, 1872-6291
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Shrnutí:•New SPSVMs model is proposed by using l0-norm rather than l1-norm.•Introduce a new nonconvex continuous approximation of l0-norm.•An alternating scheme based on DCA is proposed for SPSVMs.•Preliminary experimental results are presented to show the efficiency of the proposed method. Proximal support vector machine (PSVM), as a variant of support vector machine (SVM), is to generate a pair of non-parallel hyperplanes for classification. Although PSVM is one of the powerful classification tools, its ability on feature selection is still weak. To overcome this defect, we introduce ℓ0-norm regularization in PSVM which enables PSVM to select important features and remove redundant features simultaneously for classification. This PSVM is called as a sparse proximal support vector machine (SPSVM). Due to the presence of ℓ0-norm, the resulting optimization problem of SPSVM is neither convex nor smooth and thus, is difficult to solve. In this paper, we introduce a continuous nonconvex function to approximate ℓ0-norm, and propose a novel difference of convex functions algorithms (DCA) to solve SPSVM. The main merit of the proposed method is that all subproblems are smooth and admit closed form solutions. The effectiveness of the proposed method is illustrated by theoretical analysis as well as some numerical experiments on both simulation datasets and real world datasets.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2020.08.038