2015 SubspaceClusteringUsingLogDeter

• (Peng et al., 2015) ⇒ Chong Peng, Zhao Kang, Huiqing Li, and Qiang Cheng. (2015). “Subspace Clustering Using Log-determinant Rank Approximation.” In: Proceedings of the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2015). ISBN:978-1-4503-3664-2 doi:10.1145/2783258.2783303

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• http://scholar.google.com/scholar?q=%222015%22+Subspace+Clustering+Using+Log-determinant+Rank+Approximation
• http://dl.acm.org/citation.cfm?id=2783258.2783303&preflayout=flat#citedby

Quotes

Author Keywords

• Clustering; data mining; low-rank representation; nuclear norm; rank approximation; subspace clustering

Abstract

A number of machine learning and computer vision problems, such as matrix completion and subspace clustering, require a matrix to be of low-rank. To meet this requirement, most existing methods use the nuclear norm as a convex proxy of the rank function and minimize it. However, the nuclear norm simply adds all nonzero singular values together instead of treating them equally as the rank function does, which may not be a good rank approximation when some singular values are very large. To reduce this undesirable weighting effect, we use a log-determinant function as a non-convex rank approximation which reduces the contributions of large singular values while keeping those of small singular values close to zero. We apply the method of augmented Lagrangian multipliers to optimize this non-convex rank approximation-based objective function and obtain closed-form solutions for all subproblems of minimizing different variables alternatively. The log-determinant low-rank optimization method is used to solve subspace clustering problem, for which we construct an affinity matrix based on the angular information of the low-rank representation to enhance its separability property. Extensive experimental results on face clustering and motion segmentation data demonstrate the effectiveness of the proposed method.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2015 SubspaceClusteringUsingLogDeter	Chong Peng Zhao Kang Huiqing Li Qiang Cheng			Subspace Clustering Using Log-determinant Rank Approximation				10.1145/2783258.2783303		2015