Multi-View Spectral Clustering via Integrating Global and Local Graphs

Robust multi-view spectral clustering (RMSC) minimizes the rank of probability matrix to recover a common transition probability matrix from the matrices calculated by each single view and achieves promising performance. However, for the clustering task, the underlying structure of the low-rank probability matrix is readily accessible. Yet, RMSC ignores a priori target rank information, and it does not efficiently depict the complementary information between different views. To address these problems, we propose a novel multi-view Markov chain spectral clustering method with a priori rank information. To be specific, we encourage the target rank constraint by minimizing the partial sum of singular values instead of the nuclear norm and construct a global graph from the concatenated features to exploit the complementary information embedded in different views. The objective function can be optimized efficiently by using the augmented Lagrangian multiplier algorithm. Extensive experimental results on one synthetic and eight benchmark datasets demonstrate that the proposed method outperforms the state-of-the-art approaches.