LogDet Rank Minimization with Application to Subspace Clustering. (2nd July 2015)

• Record Type: Journal Article
• Authors: Kang, Zhao; Peng, Chong; Cheng, Jie; Cheng, Qiang
• Other Names: Hernandez José Alfredo Academic Editor.
• Is Part Of: Computational intelligence and neuroscience. Volume 2015(2015)
• Publication Date: 2015-07-02
• Subjects: Neurosciences -- Data processing -- Periodicals; Computational intelligence -- Periodicals; Computational neuroscience -- Periodicals; 612.80285
• DOI: 10.1155/2015/824289
• Languages: English
• ISSNs: 1687-5265

Abstract

Abstract : Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet) function as a smooth and closer, though nonconvex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based nonconvex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.