Rank-Constrained Block Diagonal Representation for Subspace Clustering

Abstract

The affinity matrix is a key in designing different subspace clustering methods. Many existing methods obtain correct clustering by indirectly pursuing block-diagonal affinity matrix. In this paper, we propose a novel subspace clustering method, called rank-constrained block diagonal representation (RCBDR), for subspace clustering. RCBDR method benefits mostly from three aspects: (1) the block diagonal affinity matrix is directly pursued by inducing rank constraint to Laplacian regularizer; (2) RCBDR guarantees not only between-cluster sparsity because of its block diagonal property, but also preserves the within-cluster correlation by considering the Frobenius norm of coefficient matrix; (3) a simple and efficient solver for RCBDR is proposed. Experimental results on both synthetic and real-world data sets demonstrate the effectiveness of the proposed algorithm.