Information Theoretic Subspace Clustering

Ran He

doi:10.1109/TNNLS.2015.2500600

Information Theoretic Subspace Clustering

2016-12-01

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DOI：10.1109/TNNLS.2015.2500600

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This paper addresses the problem of grouping the data points sampled from a union of multiple subspaces in the presence of outliers. Information theoretic objective functions are proposed to combine structured low-rank representations (LRRs) to capture the global structure of data and information theoretic measures to handle outliers. In theoretical part, we point out that group sparsity-induced measures (l(2,1)-norm, l(alpha)-norm, and correntropy) can be justified from the viewpoint of half-quadratic (HQ) optimization, which facilitates both convergence study and algorithmic development. In particular, a general formulation is accordingly proposed to unify HQ-based group sparsity methods into a common framework. In algorithmic part, we develop information theoretic subspace clustering methods via correntropy. With the help of Parzen window estimation, correntropy is used to handle either outliers under any distributions or sample-specific errors in data. Pairwise link constraints are further treated as a prior structure of LRRs. Based on the HQ framework, iterative algorithms are developed to solve the nonconvex information theoretic loss functions. Experimental results on three benchmark databases show that our methods can further improve the robustness of LRR subspace clustering and outperform other state-of-the-art subspace clustering methods.

Keywords:

Correntropy

group sparsity

low-rank representation (LRR)

subspace clustering

Information Theoretic Subspace Clustering

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