Multiple graphs learning with a new weighted tensor nuclear norm

Abstract

As an effective convex relaxation of the rank minimization model, the tensor nuclear norm minimization based multi-view clustering methods have been attracting more and more interest in recent years. However, most existing clustering methods regularize each singular value equally, restricting their capability and flexibility in tackling many practical problems, where the singular values should be treated differently. To address this problem, we propose a novel weighted tensor nuclear norm minimization (WTNNM) based method for multi-view spectral clustering. Specifically, we firstly calculate a set of transition probability matrices from different views, and construct a 3-order tensor whose lateral slices are composed of probability matrices. Secondly, we learn a latent high-order transition probability matrix by using our proposed weighted tensor nuclear norm, which directly considers the prior knowledge of singular values. Finally, clustering is performed on the learned transition probability matrix, which well characterizes both the complementary information and high-order information embedded in multi-view data. An efficient optimization algorithm is designed to solve the optimal solution. Extensive experiments on five benchmarks demonstrate that our method outperforms the state-of-the-art methods.