Multiview Clustering of Images with Tensor Rank Minimization via Nonconvex Approach
Ming Yang, Qilun Luo, Wen Li, Mingqing Xiao
Abstract
In this paper, we study the image multiview subspace clustering problem via a nonconvex low-rank representation under the framework of tensors. Most of the recent studies of tensor based multiview subspace clustering use the tensor nuclear norm as a convex surrogate of the tensor rank, i.e., the t-SVD based multiview subspace clustering model. However, since the tensor nuclear norm is linearly proportional to the sum of singular values, the tensor rank approximation by using the tensor nuclear norm may become problematic if the ratios of the nonzero singular values are far from 1. In this paper, a nonconvex tensor log-determinant function is proposed as the objective function regularizer, aiming to achieve a better tensor low-rank approximation. Instead of directly solving the minimization problem in its original setting, the corresponding non-convex optimization is conducted in the Fourier domain, which is shown not only to be feasible but also to be quite effective. A corresponding algorithm associated with the augmented Lagrangian multipliers is established and the constructed convergent sequence to the desirable Karush--Kuhn--Tucker critical point solution is mathematically validated in detail. Extensive simulations on eight benchmark image datasets are provided, along with full comparisons with the latest existing approaches. The obtained results demonstrate that our proposed method significantly outperforms those convex approaches currently available in the literature.