Discrete Co-Evolution of Multi-Resolution Partition Hypergraphs for Multi-View Clustering

Multi-view clustering (MVC) aims to exploit complementary information across different views to uncover a reliable consensus partition. However, existing methods often treat view-specific structures as fixed inputs to consensus learning, resulting in one-way information flow in which local structures guide the consensus but cannot be refined by it. Moreover, intrinsically categorical assignments are frequently optimized through continuous relaxation followed by post-hoc discretization, creating a mismatch between optimization and the final solution. To address these limitations, we propose DCoE, a discrete co-evolution framework for multi-view clustering. DCoE treats resolution-specific partitions as learnable discrete latent structures and jointly refines them with a common discrete consensus. These partitions induce multi-resolution hypergraphs that capture complementary group-wise structures, with adaptive weighting integrating their contributions. All partition variables are optimized directly in the discrete domain through exact reassignment gains, avoiding relaxation and post-hoc discretization while guaranteeing monotonic objective improvement. We further analyze a faithful row-simplex relaxation and show that, under a verifiable structural–spectral condition, every local maximizer is one-hot. A resolution–balance guarantee further connects this categorical geometry to the learned multi-resolution structures. Sparse anchor relations and group-level sufficient statistics enable matrix-free optimization with linear storage in the number of samples. Extensive experiments demonstrate the effectiveness and efficiency of DCoE.