Multi-View Clustering via Bilaterally Constrained Anchor Graph

The anchor similarity matrix, widely used for efficient clustering, exhibits an imbalance between its rows and columns - only the rows are typically constrained by probabilistic properties, unlike the regular similarity matrix where both dimensions are regulated. This paper addresses the critical question of how to impose meaningful constraints on the columns to better capture the data structure. We propose a novel method, termed Multi-view Clustering via Bilaterally constrained anchor Graph (MCBG), which learns a fused anchor similarity matrix with bilateral constraints. To ensure consistency across views, we quantitatively assess their contributions and integrate them into a unified model. By applying distinct constraints to rows and columns, MCBG promotes a balanced and expressive anchor similarity distribution, avoiding degenerate cases. Furthermore, a rank constraint on the Laplacian matrix of an anchor-pairwise graph is incorporated, ensuring a one-step post-processing-free multi-view clustering framework. An efficient alternating iterative optimization algorithm is developed, adapted to the natural properties of the target problem. Extensive experiments validate the superiority of the proposed method.