A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification

This paper proposes a new group-sparsity-inducing regularizer to approximate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo>&l...

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Autores principales:	Yang Chen, Masao Yamagishi, Isao Yamada
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	convex optimization proximal splitting algorithm generalized Moreau enhancement group sparsity weighted <i>ℓ</i><sub>2,1</sub>-norm sparse representation-based classification Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/64f9e46ca8f4408a91b5946d0094eaf3
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spelling	oai:doaj.org-article:64f9e46ca8f4408a91b5946d0094eaf32021-11-25T16:13:03ZA Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification10.3390/a141103121999-4893https://doaj.org/article/64f9e46ca8f4408a91b5946d0094eaf32021-10-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/312https://doaj.org/toc/1999-4893This paper proposes a new group-sparsity-inducing regularizer to approximate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> pseudo-norm. The regularizer is nonconvex, which can be seen as a linearly involved generalized Moreau enhancement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula>-norm. Moreover, the overall convexity of the corresponding group-sparsity-regularized least squares problem can be achieved. The model can handle general group configurations such as weighted group sparse problems, and can be solved through a proximal splitting algorithm. Among the applications, considering that the bias of convex regularizer may lead to incorrect classification results especially for unbalanced training sets, we apply the proposed model to the (weighted) group sparse classification problem. The proposed classifier can use the label, similarity and locality information of samples. It also suppresses the bias of convex regularizer-based classifiers. Experimental results demonstrate that the proposed classifier improves the performance of convex <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula> regularizer-based methods, especially when the training data set is unbalanced. This paper enhances the potential applicability and effectiveness of using nonconvex regularizers in the frame of convex optimization.Yang ChenMasao YamagishiIsao YamadaMDPI AGarticleconvex optimizationproximal splitting algorithmgeneralized Moreau enhancementgroup sparsityweighted <i>ℓ</i><sub>2,1</sub>-normsparse representation-based classificationIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 312, p 312 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	convex optimization proximal splitting algorithm generalized Moreau enhancement group sparsity weighted <i>ℓ</i><sub>2,1</sub>-norm sparse representation-based classification Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
spellingShingle	convex optimization proximal splitting algorithm generalized Moreau enhancement group sparsity weighted <i>ℓ</i><sub>2,1</sub>-norm sparse representation-based classification Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Yang Chen Masao Yamagishi Isao Yamada A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
description	This paper proposes a new group-sparsity-inducing regularizer to approximate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> pseudo-norm. The regularizer is nonconvex, which can be seen as a linearly involved generalized Moreau enhancement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula>-norm. Moreover, the overall convexity of the corresponding group-sparsity-regularized least squares problem can be achieved. The model can handle general group configurations such as weighted group sparse problems, and can be solved through a proximal splitting algorithm. Among the applications, considering that the bias of convex regularizer may lead to incorrect classification results especially for unbalanced training sets, we apply the proposed model to the (weighted) group sparse classification problem. The proposed classifier can use the label, similarity and locality information of samples. It also suppresses the bias of convex regularizer-based classifiers. Experimental results demonstrate that the proposed classifier improves the performance of convex <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>ℓ</mo><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula> regularizer-based methods, especially when the training data set is unbalanced. This paper enhances the potential applicability and effectiveness of using nonconvex regularizers in the frame of convex optimization.
format	article
author	Yang Chen Masao Yamagishi Isao Yamada
author_facet	Yang Chen Masao Yamagishi Isao Yamada
author_sort	Yang Chen
title	A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
title_short	A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
title_full	A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
title_fullStr	A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
title_full_unstemmed	A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification
title_sort	linearly involved generalized moreau enhancement of <i>ℓ</i><sub>2,1</sub>-norm with application to weighted group sparse classification
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/64f9e46ca8f4408a91b5946d0094eaf3
work_keys_str_mv	AT yangchen alinearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification AT masaoyamagishi alinearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification AT isaoyamada alinearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification AT yangchen linearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification AT masaoyamagishi linearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification AT isaoyamada linearlyinvolvedgeneralizedmoreauenhancementofilisub21subnormwithapplicationtoweightedgroupsparseclassification
_version_	1718413260003213312

A Linearly Involved Generalized Moreau Enhancement of <i>ℓ</i><sub>2,1</sub>-Norm with Application to Weighted Group Sparse Classification

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