Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

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 over-penalize 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.