Multi-view Spectral Clustering via Tensor-SVD Decomposition

Multi-view clustering has attracted considerable attention in recent years, some related approaches always use matrices to represent views, and model by capturing two dimensional structure among views. The critical deficiency of these work is ignoring the space structure information of all views, which results in the mediocre performance of clustering. In this paper, we propose a novel Tensor-SVD decomposition based Multi-view Spectral Clustering algorithm(TMSC) to iron out flaws. Our method firstly puts transition probability matrices of all views into a three-order tensor, which naturally reserves the whole structure information of data. Then it establishes a low multi-rank tensor model based on tensor-SVD decomposition by fully mining the complementary information among multiple views. Another difficulty in this paper is that the optimal objective of TMSC has a low multirank constraint on the transition probability tensor, and a probabilistic simplex constraint on each fiber of the tensor. To tackle this challenging problem, we design an optimization procedure based on the Augmented Lagrangian Multiplier scheme. Experimental results on real word datasets show that TMSC has superior clustering quality over several state-of-theart multi-view clustering approaches.