Nonconvex Low-Rank Tensor Representation With Self-Enhanced Structure Penalty for Multi-View Subspace Clustering

Abstract

In addition to the high dimensionality and heterogeneity of multi-view data, its underlying subspaces contain a wealth of intrinsic correlation information. However, existing MvSC models still remain struggling in effectively exploiting the high-order complementary information and handling the confusing points in disjoint subspaces. To this end, we propose a novel tensorized MvSC model by integrating the nonconvex tensor Schatten- $2/3$ quasi-norm with a self-enhanced structure penalty constraint. The proposed model can not only characterize high-order correlation through adaptive subspace components encoding, but also manipulate the confusing points meticulously by capturing the refined geometric structure of multiple disjoint subspaces. As a result, a promising representation can be learned for the authentic subspaces revealment. More importantly, an effective algorithm has been proposed to solve the challenging nonconvex optimization problem of the proposed model, and the resulting solution sequence is theoretically guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. Furthermore, it can be proven that several key variable sequences are Cauchy ones. Extensive experiments conducted on various datasets demonstrate the superiority of our proposed model in comparison with many state-of-the-art models. MATLAB code is available at https://github.com/wangzhi-swu/SeT-MvSC