Block spectral clustering for multiple graphs with inter-relation

Clustering methods for multiple graphs explore and exploit multiple graphs simultaneously to obtain a more accurate and robust partition of the data than that using single graph clustering methods. In this paper, we study the clustering of multiple graphs with inter-relation among vertices in different graphs. The main contribution is to propose and develop a block spectral clustering method for multiple graphs with inter-relation. Our idea is to construct a block Laplacian matrix for multiple graphs and make use of its eigenvectors to perform clustering very efficiently. Global optimal solutions are obtained in the proposed method and they are solutions of relaxation of multiple graphs ratio cut and normalized cut problems. In contrast, existing clustering methods cannot guarantee optimal solutions and their solutions are dependent on initial guesses. Experimental results on both synthetic and real-world data sets are given to demonstrate that the clustering accuracy achieved and computational time required by the proposed block clustering method are better than those by the testing clustering methods in the literature.