Scalable incomplete multi-view clustering via tensor Schatten p-norm and tensorized bipartite graph

Abstract

Graph-based incomplete multi-view clustering (IMVC) methods have drawn considerable attention due to their good performance in exploring the nonlinear structure of data. However, they still have the following shortcomings. First, graph construction and eigen decomposition of the Laplacian matrix included in the IMVC methods generally have high computational complexity. Second, most methods do not consider the impact of missing views and neglect the potential relationships between different views. Third, few algorithms consider both intra-view and inter-view information for clustering. Therefore, we innovatively propose a scalable incomplete multi-view clustering via the tensor Schatten p-norm and tensorized bipartite graph (SIMVC/TSTBG) method, which combines tensorized bipartite graph, graph completion, and tensor low-rank constraint into a joint framework. Concretely, we first construct bipartite graphs based on the selected m anchor points and the n data points, reducing the size of the graph from n×n to n×m(m<<n), which considerably reduces the computational complexity. Second, we adaptively complete the missing bipartite graph, which reduces the effect of missing view information on the clustering results. Third, to explore connections between missing views and mine high-order information between views, we splice the bipartite graphs into a tensor and impose a tensor low-rank constraint, i.e., the tensor Schatten p-norm, on it. At the same time, we also design an efficient algorithm to solve SIMVC/TSTBG. To our knowledge, we are the first successful practice to integrate the tensor technique with the scalable IMVC method. Compared with other IMVC methods, the results on seven datasets fully show the high efficiency and effectiveness of SIMVC/TSTBG.