Find True Collaborators: Banzhaf Index-based Cross View Alignment for Partially View-aligned Clustering

Partially view-aligned clustering (PVC) has emerged as a critical area in multi-view clustering, addressing the inherent instance misalignment across views during data collection. The primary challenge of PVC is accurately establishing correspondences between cross-view samples. The Banzhaf index in cooperative game theory serves as an effective tool for modeling complex relationships between multi-view samples by quantifying the marginal contributions of coalition members to collaborative benefits. To this end, we propose a Banzhaf Index-driven cross-view aligNment method, dubbed BIN, which systematically evaluates each view sample's contribution to joint decision-making within a game-theoretic framework. This approach overcomes the limitations of existing PVC methods reliant on prior alignment information and enhances the robustness of multi-view matching. Specifically, we model multi-view samples as players in a cooperative game and quantify their interactions using a payoff model. Simultaneously, we propose a dual-loss constraint: (1) Banzhaf gain loss, which dynamically captures the marginal contribution of key cross-view sample pairs to reinforce associations; (2) contrast loss, which applies exclusion constraints in the feature space to suppress interference from weakly correlated samples. Together, these losses form an effective optimization mechanism. This game-theoretic approach adaptively learns sample correspondences without pre-alignment and ensures robust matching in complex misalignment scenarios. Extensive experiments demonstrate that our method achieves competitive performance against eight state-of-the-art PVC algorithms.