Low-Rank Tensor Learning for Incomplete Multiview Clustering

Incomplete multiview clustering (IMVC) is an effective way to identify the underlying structure of incomplete multiview data. Most existing algorithms based on matrix factorization, graph learning or subspace learning have at least one of the following limitations: (1) the global and local structures of high-dimensional data are not effectively explored simultaneously; (2) the high-order correlations among multiple views are ignored. In this paper, we propose a low-rank tensor learning (LRTL) method that learns a consensus low-dimensional embedding matrix for IMVC. We first take advantage of the self-expressiveness property of high-dimensional data to construct sparse similarity matrices for individual views under low-rank and sparsity constraints. Individual low-dimensional embedding matrices can be obtained from the sparse similarity matrices using spectral embedding techniques. This approach simultaneously explores the global and local structures of incomplete multiview data. Then, we present a multiview embedding matrix fusion model that incorporates individual low-dimensional embedding matrices into a third-norm tensor to achieve a consensus low-dimensional embedding matrix. The fusion model exploits complementary information by finding the high-order correlations among multiple views. In addition, the computational cost of an improved fusion strategy is dramatically reduced. Extensive experimental results demonstrate that the proposed LRTL method outperforms several state-of-the-art approaches.