A new nonconvex multi-view subspace clustering via learning a clean low-rank representation tensor

Abstract Recently, low-rank tensor representation has achieved impressive results for multi-view subspace clustering (MSC). The typical MSC methods utilize the tensor nuclear norm as a convex surrogate of the tensor multi-rank to obtain a low-rank representation, which exhibits limited robustness when dealing with noisy and complex data scenarios. In this paper, we introduce an innovative clean low-rank tensor representation approach that combines the idea of tensor robust principal component analysis with a new nonconvex tensor multi-rank approximation regularization. This integration enhances the robustness of the low-rank representation, resulting in improved performance. Furthermore, to better capture the local geometric features, we employ a high-order manifold regularization term. To effectively address our new model, we develop an iterative algorithm that can be proved to converge to the desired Karush-Kuhn-Tucker critical point. The numerical experiments on widely used datasets serve to demonstrate the efficacy and effectiveness of our new method.