title: LogDet Rank Minimization with Application to Subspace Clustering.
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.
authors.affiliation: Computer Science Department, Southern Illinois University, Carbondale, IL 62901, USA.
authors.forename: Zhao
authors.initials: Z
authors.lastname: Kang
authors.affiliation: Computer Science Department, Southern Illinois University, Carbondale, IL 62901, USA.
authors.forename: Chong
authors.initials: C
authors.lastname: Peng
authors.affiliation: Department of Computer Science and Engineering, University of Hawaii at Hilo, Hilo, HI 96720, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Cheng
authors.affiliation: Computer Science Department, Southern Illinois University, Carbondale, IL 62901, USA.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Cheng
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D003627:Data Interpretation, Statistical; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D000069550:Machine Learning; D010363:Pattern Recognition, Automated / Q000379:methods