Consensus latent incomplete multi-view clustering with low-rank tensor constraint

Traditional multi-view clustering (MVC) assumes that all views are complete and it cannot address a lack of views. In real life, a lack of views often occurs, thus leading to the problem of incomplete MVC (IMVC). Although the existing IMVC methods have achieved good performance, they have the following weaknesses. (1) The completion method is not flexible enough for the case where view information is arbitrarily missing. (2) They fail to adequately explore the higher-order correlations among views. (3) The cluster structure of the input data is not considered. Thus, to solve these problems, in this paper, we propose a novel method, i.e., consensus latent incomplete multi-view clustering with low-rank tensor constraint (CLIMVC/LTC). Specifically, we first use a latent model to generate the missing views to make the completion process more flexible. Then, we utilize the low-rank tensor constraint and consensus representation term to jointly explore the higher-order correlations, the cluster structure of the data and the consistency between different views. That is, CLIMVC/LTC combines missing view completion, which is implemented by a latent model, low-rank tensor constraint and consensus representation learning into a unified framework, and their interaction yields improved clustering performance. An optimization procedure based on the augmented Lagrange multiplier (ALM) method is also designed to solve CLIMVC/LTC. The effectiveness of CLIMVC/LTC is verified on several well-known datasets, and it has good clustering performance.