Relaxed multi-view clustering in latent embedding space

Although many multi-view clustering approaches have been developed recently, one common shortcoming of most of them is that they generally rely on the original feature space or consider the two components of the similarity-based clustering separately (i.e., similarity matrix construction and cluster indicator matrix calculation), which may negatively affect the clustering performance. To tackle this shortcoming, in this paper, we propose a new method termed Multi-view Clustering in Latent Embedding Space (MCLES), which jointly recovers a comprehensive latent embedding space, a robust global similarity matrix and an accurate cluster indicator matrix in a unified optimization framework. In this framework, each variable boosts each other in an interplay manner to achieve the optimal solution. To avoid the optimization problem of quadratic programming, we further propose to relax the constraint of the global similarity matrix, based on which an improved version termed Relaxed Multi-view Clustering in Latent Embedding Space (R-MCLES) is proposed. Compared with MCLES, R-MCLES achieves lower computational complexity with more correlations between pairs of data points. Extensive experiments conducted on both image and document datasets have demonstrated the superiority of the proposed methods when compared with the state-of-the-art.