Robust Structured Convex Nonnegative Matrix Factorization for Data Representation

Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix. However, the nonnegative constraint of the data matrix limits its applicati...

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Autores principales:	Qing Yang, Xuesong Yin, Simin Kou, Yigang Wang
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Convex nonnegative matrix factorization global structure L₂,₁ norm clustering Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/db0a143a19724eb7bfdd940008da7445
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spelling	oai:doaj.org-article:db0a143a19724eb7bfdd940008da74452021-11-26T00:01:55ZRobust Structured Convex Nonnegative Matrix Factorization for Data Representation2169-353610.1109/ACCESS.2021.3128975https://doaj.org/article/db0a143a19724eb7bfdd940008da74452021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9618909/https://doaj.org/toc/2169-3536Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix. However, the nonnegative constraint of the data matrix limits its application. Additionally, the representations learned by NMF fail to respect the intrinsic geometric structure of the data. In this paper, we propose a novel unsupervised matrix factorization method, called Robust Structured Convex Nonnegative Matrix Factorization (RSCNMF). RSCNMF not only achieves meaningful factorizations of the mixed-sign data, but also learns a discriminative representation by leveraging local and global structures of the data. Moreover, it introduces the L<sub>2,1</sub>-norm loss function to deal with noise and outliers, and exploits the L<sub>2,1</sub>-norm feature regularizer to select discriminative features across all the samples. We develop an alternate iterative scheme to solve such a new model. The convergence of RSCNMF is proven theoretically and verified empirically. The experimental results on eight real-world data sets show that our RSCNMF algorithm matches or outperforms the state-of-the-art methods.Qing YangXuesong YinSimin KouYigang WangIEEEarticleConvex nonnegative matrix factorizationglobal structureL₂,₁ normclusteringElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 155087-155102 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Convex nonnegative matrix factorization global structure L₂,₁ norm clustering Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Convex nonnegative matrix factorization global structure L₂,₁ norm clustering Electrical engineering. Electronics. Nuclear engineering TK1-9971 Qing Yang Xuesong Yin Simin Kou Yigang Wang Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
description	Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix. However, the nonnegative constraint of the data matrix limits its application. Additionally, the representations learned by NMF fail to respect the intrinsic geometric structure of the data. In this paper, we propose a novel unsupervised matrix factorization method, called Robust Structured Convex Nonnegative Matrix Factorization (RSCNMF). RSCNMF not only achieves meaningful factorizations of the mixed-sign data, but also learns a discriminative representation by leveraging local and global structures of the data. Moreover, it introduces the L<sub>2,1</sub>-norm loss function to deal with noise and outliers, and exploits the L<sub>2,1</sub>-norm feature regularizer to select discriminative features across all the samples. We develop an alternate iterative scheme to solve such a new model. The convergence of RSCNMF is proven theoretically and verified empirically. The experimental results on eight real-world data sets show that our RSCNMF algorithm matches or outperforms the state-of-the-art methods.
format	article
author	Qing Yang Xuesong Yin Simin Kou Yigang Wang
author_facet	Qing Yang Xuesong Yin Simin Kou Yigang Wang
author_sort	Qing Yang
title	Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
title_short	Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
title_full	Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
title_fullStr	Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
title_full_unstemmed	Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
title_sort	robust structured convex nonnegative matrix factorization for data representation
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/db0a143a19724eb7bfdd940008da7445
work_keys_str_mv	AT qingyang robuststructuredconvexnonnegativematrixfactorizationfordatarepresentation AT xuesongyin robuststructuredconvexnonnegativematrixfactorizationfordatarepresentation AT siminkou robuststructuredconvexnonnegativematrixfactorizationfordatarepresentation AT yigangwang robuststructuredconvexnonnegativematrixfactorizationfordatarepresentation
_version_	1718409998167441408

Robust Structured Convex Nonnegative Matrix Factorization for Data Representation

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