NDLI: Matrix Factorization with Column L0-Norm Constraint for Robust Multi-subspace Analysis

Content Provider	IEEE Xplore Digital Library
Author	Binghui Wang Risheng Liu Chuang Lin Xin Fan
Copyright Year	2015
Description	Author affiliation: Dept. of Neurorehabilitation Eng., Georg-August Univ., Gottingen, Germany (Chuang Lin) \|\| Sch. of Software, Dalian Univ. of Technol., Dalian, China (Binghui Wang; Risheng Liu; Xin Fan)
Abstract	We aim to study the subspace structure of data approximately generated from multiple categories and remove errors (e.g., noise, corruptions, and outliers) in the data as well. Most previous methods for subspace analysis learn only one subspace, failing to discover the intrinsic complex structure, while state-of-the-art methods use data itself as the basis (self-expressiveness property), showing degraded performance when data contain errors. To tackle the problem, we propose a novel method, called Matrix Factorization with Column $L_{0}-norm$ constraint $(MFC_{0}),$ from the matrix factorization perspective. $MFC_{0}$ simultaneously discovers the multi-subspace structure of either clean or contaminated data, and learns the basis for each subspace. Specifically, the learnt basis with the orthonormal constraint shows high robustness to errors by adding a regularization term. Owing to the column $l_{0}-norm$ constraint, the generated representation matrix can be (approximate) block-diagonal after reordering its columns, with each block characterizing one subspace. We develop an efficient first-order optimization scheme to stably solve the nonconvex and nonsmooth objective function of $MFC_{0}.$ Experimental results on synthetic data and real-world face datasets demonstrate the superiority over traditional and state-of-the-art methods on both representation learning, subspace recovery and clustering.
Starting Page	1189
Ending Page	1195
File Size	380901
Page Count	7
File Format	PDF
ISSN	23759259
e-ISBN	9781467384933
DOI	10.1109/ICDMW.2015.80
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-11-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Conferences Linear programming Robustness Yttrium Matrix decomposition Optimization Principal component analysis
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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