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.

The rapid advancement of single-cell sequencing technology has generated vast amounts of multi-omics data, presenting unprecedented opportunities for single-cell multi-omics clustering analysis. However, existing single-cell clustering algorithms focus on extracting shared representations, overlooking the interactions and correlations among cells. This oversight inevitably leads to biased or confounded cell clustering results. In this paper, we propose a cell similarity purified adaptive fusion network for single-cell multi-omics clustering, named scSPAF, which adopts a multi-level fusion approach to thoroughly explore the consistency and complementarity of omics data. Specifically, we design a cell similarity purification module to accurately incorporate neighborhood information among cells into cell features, thereby purifying the latent representation that reflects cell correlations. In addition, we align attribute features from different omics to extract the consistent representation across omics. Simultaneously, by employing an adaptive fusion mechanism, we integrate representations of omics-specific and the consistent representation across omics to generate more discriminative representations of omics, further enhancing the clustering performance. Experimental results obtained from six real-world datasets demonstrate the superiority of the scSPAF algorithm when compared with other state-of-the-art methods.