Multi-View Clustering With Cauchy-Schwarz Mutual Information Maximin

Information bottleneck (IB) leverages information theory to guide the learning process of deep multi-view clustering (MVC). It optimizes the trade-off between multi-view compression and preservation by minimizing and maximizing mutual information (MI). Although existing deep MVC based on IB has witnessed great achievements, they usually resort to variational inference to estimate the MI lower bound, which typically introduces estimation errors and results in an unstable lower bound of MI. In this study, we propose a novel Cauchy-Schwarz Mutual Information Maximin (CS-MIM) method, which directly estimates MI with closed-form expressions without requiring variational inference, possessing explicit multi-view information modeling capabilities. Specifically, we first present a non-parametric MI estimation method with Cauchy-Schwarz (CS) divergence, which leverages multi-kernel Gram matrices to capture distributional similarities and avoids the approximation errors introduced by the neural estimators of variational inference. Then, based on the new estimation method, a MI maximin mechanism is devised to parameterize the IB principle with analytical gradients, which facilitates effective compression of multi-view data while preserving the relevant features. Finally, we design a cross-view adaptive attention (CAA) mechanism constrained by the MI based on CS divergence, which further captures the complementarity across views under the guidance of the fused multi-view representation. Extensive evaluation results on 12 public available datasets demonstrate that the CS-MIM remarkably outperforms existing SOTA approaches.