Subspace Clustering via Adaptive Low-Rank Model

Abstract

Subspace Clustering has been a major issue in many real-world task and sparse and low-rank representation based methods have received considerable attention during the past decades. However, both above methods need huge computation in order to solve sparse or trace-norm minimization problem, which may not be scalable to large-scale data. In this paper, we develop an efficient and effective sparse and low-rank model for subspace clustering. Starting from the basic idea of Robust Principal Component Analysis (RPCA), we observe that the optimal solution of RPCA can be equivalently solved by an iterative procedure, where the low-rank matrix is reformulated by two factorizations. We thereby further impose the group sparse constraint on such factorizations and additionally non-negative constraint on all variable matrix. As a result, the coefficient matrix S can both achieve sparcity and capture the global structure of whole data, which can be utilized to construct the graph for subspace clustering. Extensive simulations have verified the effectiveness of the proposed methods.