Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

Abstract

In this paper, we focus on the multi-view subspace clustering problem under the framework of third order tensor. Recently, tensor nuclear norm (TNN) has been widely used in the multi-view subspace clustering problem. It is known that TNN is a convex surrogate of the tensor rank. However, TNN is linearly proportional to the sum of the singular values. Thus solving the TNN minimization problem will overpenalize the large singular values and lead to a sub-optimal solution. To address this issue, in this paper, a novel tighter tensor log-determinant (TLD) regularizer is proposed to better approximate the tensor rank. Although the proposed method is non-convex, a closed-form solution has been deduced via solving the Euler-Lagrange equation. A corresponding algorithm associated with augmented Lagrangian multipliers is established and the constructed convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments indicate that the proposed model achieves significant improvements compared to the state-of-the-art convex subspace clustering models.