Rigidly Self-Expressive Sparse Subspace Clustering

摘要

Sparse subspace clustering is a well-known algorithm, and it is widely used in many research field nowadays, and a lot effort has been contributed to improve it. In this paper, we propose a novel approach to obtain the coefficient matrix. Compared with traditional sparse subspace clustering (SSC) approaches, the key advantage of our approach is that it provides a new perspective of the self-expressive property. We call it rigidly self-expressive (RSE) property. This new formulation captures the rigidly self-expressive property of the data points in the same subspace, and provides a new formulation for sparse subspace clustering. Extensions to traditional SSC could also be cooperating with this new formulation. We present a first-order algorithm to solve the nonconvex optimization, and further prove that it converges to a KKT point of the nonconvex problem under certain standard assumptions. Extensive experiments on the Extended Yale B dataset, the USPS digital images dataset, and the Columbia Object Image Library shows that for images with up to 30% missing pixels the clustering quality achieved by our approach outperforms the original SSC.