Robust Multi-View Spectral Clustering via Low-Rank and Sparse Decomposition

Multi-view clustering, which seeks a partition of the data in multiple views that often provide complementary information to each other, has received considerable attention in recent years. In real life clustering problems, the data in each view may have considerable noise. However, existing clustering methods blindly combine the information from multi-view data with possibly considerable noise, which often degrades their performance. In this paper, we propose a novel Markov chain method for Robust Multi-view Spectral Clustering (RMSC). Our method has a flavor of lowrank and sparse decomposition, where we firstly construct a transition probability matrix from each single view, and then use these matrices to recover a shared low-rank transition probability matrix as a crucial input to the standard Markov chain method for clustering. The optimization problem of RMSC has a low-rank constraint on the transition probability matrix, and simultaneously a probabilistic simplex constraint on each of its rows. To solve this challenging optimization problem, we propose an optimization procedure based on the Augmented Lagrangian Multiplier scheme. Experimental results on various real world datasets show that the proposed method has superior performance over several state-of-the-art methods for multi-view clustering.