Tensorial Multi-View Clustering via Low-Rank Constrained High-Order Graph Learning

Multi-view clustering aims to partition multi-view data into different categories by optimally exploring the consistency and complementary information from multiple sources. However, most existing multi-view clustering algorithms heavily rely on the similarity graphs from respective views and fail to comprehend multiple views holistically. Moreover, due to the noise and redundancy maintained in the original data, the original errors of multiple similarity graphs will continue to accumulate in the process of constructing consistent graphs. These situations always lead to the limitation to effective fuse the essential information from multiple views, which always influences the clustering performance and cries out for reliable solutions. Based on the above considerations, we propose a novel method termed Tensorial Multi-view Clustering (TMvC), which learns high-order graph by low-rank tensor constraint to uncover the essential information stored in multiple views. TMvC first learns the Laplacian graphs of all views and stacks them into a tensor which can be viewed as a high-order graph. With the high-order graph, consistency and complementary information from different views can be propagated smoothly across all views. Then, based on low-rank constraint, high-order graph is constrained in the horizontal and vertical directions to better uncover the inter-view and inter-class correlations between multi-view data, which is of vital importance for multi-view clustering. Extensive experiments on document and image datasets demonstrate that TMvC can achieve the state-of-the-art performance for multi-view clustering.