Multi-View Spectral Clustering with Optimal Neighborhood Laplacian Matrix

Abstract Multi-view spectral clustering aims to group data into different categories by optimally exploring complementary information from multiple Laplacian matrices. However, existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct an optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. In this paper, we propose a novel optimal neighborhood multi-view spectral clustering (ONMSC) algorithm to address these issues. Specifically, the proposed algorithm generates an optimal Laplacian matrix by searching the neighborhood of both the linear combination of the first-order and high-order base Laplacian matrices simultaneously. This design enhances the representative capacity of the optimal Laplacian and better utilizes the hidden high-order connection information, leading to improved clustering performance. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experimental results on 9 datasets demonstrate the superiority of our algorithm against state-of-the-art methods, which verifies the effectiveness and advantages of the proposed ONMSC.