Multi-View Subspace Clustering via Non-Convex Tensor Rank Minimization

Abstract

In this paper, we explore the multi-view subspace clustering problem. Recently, tensor low-rank minimization algorithm has been widely used in the multi-view subspace clustering problem. Since finding the low-rank solution of a tensor is NP-hard, tensor nuclear norm (TNN) is usually used as a convex surrogate of the tensor rank. However, solving the TNN minimization problem often leads to a suboptimal solution due to the over-penalization of large singular values. To address this issue, in this paper, a novel tensor log-regularizer (TLR) is proposed to better approximate the tensor rank. Although the TLR is non-convex, a closed-form solution has been deduced via solving the Euler-Lagrange equation. The alternating direction method of multipliers (ADMM) is used to solve the TLR based multi-view subspace clustering model. Extensive experiments indicate that the proposed model achieves significant improvement compared to the state-of-the-art convex clustering models.