Scalable Subspace Clustering via Adaptive Low-rank Model

Abstract

Graph based Subspace Clustering (SC) has been a major issue in many real-world task and low-rank representation based methods have widely been used in graph construction. However, both above methods need huge computation in order to solve trace-norm minimization problem, which may not be scalable to large-scale data. In this paper, we develop an scalable and effective low-rank model for subspace clustering. Motivated by the basic idea of Robust Principal Component Analysis (RPCA), we adopt an iterative procedure to calculate the optimal solution of RPCA, where the low-rank matrix is reformulated by two factorizations. By further imposing the group sparse constraint on such factorizations, the coefficient matrix S can both achieve sparcity and capture the global structure of whole data. Benefitting from S, we then develop a new Graph based SC framework, where we have involved the adaptive low-rank model and SC into a single optimization problem. Therefore, the discriminative information learned by SC can be provided to improve the discriminative ability of low-rank graph construction, while the updated graph can further enhance the Clustering results of SC. Extensive simulations have verified the effectiveness of the proposed methods.