Block-Diagonal Subspace Clustering with Laplacian Rank Constraint

How to construct the block-diagonal affinity matrix is a focus in subspace clustering based on spectral clustering. Most of existing methods pursue the block-diagonal affinity matrix by indirect methods. In this paper, we propose a directly pursuing block-diagonal affinity matrix method, called Block-Diagonal Subspace Clustering with Laplacian Rank Constrain-t(BDLRC), for subspace clustering. Specifically, a block-diagonal structure of an ideal graph is recovered from its affinity matrix by imposing a rank constraint on the Laplacian matrix. Meanwhile, an adaptive affinity matrix learning approach is employed to construct exactly block-diagonal affinity matrix. BDLRC method is superior to previous subspace clustering methods in that: 1) BDLRC is able to generate an exactly block-diagonal affinity matrix by pursuing block diagonal priors; 2) a simple and efficient solver is proposed for solving the problem of complex non-convex rank constraint. Experimental results on both synthetic and real-world data sets demonstrate the effectiveness of the proposed algorithm.