NDLI: Robust Subspace Clustering via Smoothed Rank Approximation

Content Provider	IEEE Xplore Digital Library
Author	Zhao Kang Chong Peng Qiang Cheng
Copyright Year	1994
Abstract	Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world applications, nuclear norm approximation to the rank function can only produce a result far from the optimum. To seek a solution of higher accuracy than the nuclear norm, in this letter, we propose a rank approximation based on Logarithm-Determinant. We consider using this rank approximation for subspace clustering application. Our framework can model different kinds of errors and noise. Effective optimization strategy is developed with theoretical guarantee to converge to a stationary point. The proposed method gives promising results on face clustering and motion segmentation tasks compared to the state-of-the-art subspace clustering algorithms.
Sponsorship	IEEE Signal Processing Society
Starting Page	2088
Ending Page	2092
Page Count	5
File Size	992324
File Format	PDF
ISSN	10709908
Volume Number	22
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Approximation methods Approximation algorithms Clustering algorithms Signal processing algorithms Optimization Minimization Linear programming subspace clustering Matrix rank minimization nonconvex optimization nuclear norm
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing Electrical and Electronic Engineering

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