Subspace clustering based on latent low rank representation with Frobenius norm minimization

Abstract

Abstract The problem of subspace clustering which refers to segmenting a collection of data samples approximately drawn from a union of linear subspaces is considered in this paper. Among existing subspace clustering algorithms, low rank representation (LRR) based subspace clustering is a very powerful method and has demonstrated that its performance is good. Latent low rank representation (LLRR) subspace clustering algorithm is an improvement of the original LRR algorithm when the observed data samples are insufficient. The clustering accuracy of LLRR is higher than that of LRR. Recently, Frobenius norm minimization based LRR algorithm has been proposed and its clustering accuracy is higher than that of LRR demonstrating the effectiveness of Frobenius norm as another convex surrogate of the rank function. Combining LLRR and Frobenius norm, a new low rank representation subspace clustering algorithm is proposed in this paper. The nuclear norm in the LLRR algorithm is replaced by the Frobenius norm. The resulting optimization problem is solved via alternating direction method of multipliers (ADMM). Experimental results show that compared with LRR, LLRR and several other state-of-the-art subspace clustering algorithms, the proposed algorithm can get higher clustering accuracy. Compared with LLRR, the running time of the proposed algorithm is reduced significantly.