Low-Rank Structure Learning via Nonconvex Heuristic Recovery

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity i...

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Vydané v:	IEEE transaction on neural networks and learning systems Ročník 24; číslo 3; s. 383 - 396
Hlavní autori:	Deng, Yue, Dai, Qionghai, Liu, Risheng, Zhang, Zengke, Hu, Sanqing
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.03.2013 Institute of Electrical and Electronics Engineers
Predmet:	Adaptation models Applied sciences Artificial intelligence Clustering algorithms Compressive sensing Computer science; control theory; systems Data processing. List processing. Character string processing Detection, estimation, filtering, equalization, prediction Exact sciences and technology Heuristic algorithms Information, signal and communications theory Learning and adaptive systems log-sum heuristic matrix learning Memory organisation. Data processing Minimization nuclear norm minimization Optimization Signal and communications theory Signal processing algorithms Signal, noise Software Sparse matrices sparse optimization Telecommunications and information theory Structure learning log-sum heuristic Partial ordering Minimization nuclear norm minimization Modeling Optimization Subsampling Stationary condition matrix learning Upper bound Experimental result Compressive sensing sparse optimization Heuristic method Sparse representation Objective function Data structure Principal component analysis Non convex analysis
ISSN:	2162-237X, 2162-2388
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Popis
Shrnutí:	In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓ p norm (0 <; p <; 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 <; p <; 1) for both data with higher rank and with denser corruptions.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	2162-237X 2162-2388
DOI:	10.1109/TNNLS.2012.2235082