Tensorial Multi-Linear Multi-View Clustering via Schatten-p Norm

Abstract

Despite satisfactory clustering performance, current subspace-based multi-view clustering methods still suffer from the following limitations. 1) They usually concentrate on the data features in linear subspaces and ignore the features in nonlinear subspaces. 2) They treat all singular values equally without considering their different contribution degrees, leading to suboptimal problems. Based on the above considerations, we propose tensorial multi-linear multi-view clustering via the weighted Schatten-p norm, named TM2vC. TM2vC integrates high-order relationships learning and latent structure learning of multi-view data into one framework. We apply third-order tensors stacked by low-dimensional representations to capture high-order relationships among multivariate data and the weighted Schatten-p norm to distinguish different singular values. Additionally, we employ hypergraph constraints to conserve high-order local geometric structures in the high-dimensional subspace. Comprehensive experiments on diverse datasets verify the effectiveness and superiority of the proposed TM2vC on six indicators.