A subspace clustering algorithm based on simultaneously sparse and low-rank representation

Abstract

Sparse subspace clustering (SSC) and low-rank representation (LRR) are the state-of-the-art methods for subspace clustering, which force the representation matrix to be sparse and low-rank, respectively. Considering that sparsity and low rankness are of complementarity and the clean data matrix can be expressed as the combination of itself, in this paper, a new algorithm, named sparse and low-rank subspace clustering (SSC_LRR for short), was proposed. SSC_LRR decomposes the data matrix as the sum of a self-express clean dictionary and an error matrix, and forces the linear representation coefficient matrix to be simultaneously sparse and low-rank. An alternating direction method of multipliers (ADMM) based algorithm was developed to solve the SSC_LRR problem. Experimental results on synthetic data, motion segmentation and face clustering tasks demonstrate the effectiveness of our approach.