FC$^{2}$2: Fast Co-Clustering With Small-Scale Similarity Graph and Bipartite Graph Learning

Bipartite graph-based co-clustering is efficient in modeling cluster manifold structures. However, existing methods decouple bipartite graph construction from the learning of pseudo-labels for samples and anchors, often leading to suboptimal clustering performance. Moreover, neglecting local manifold relationships among anchors yields inferior anchor pseudo-labels, which further degrades the quality of sample pseudo-labels. To overcome these limitations, we propose a novel model termed Fast Co-Clustering (FC$^{2}$2), which jointly captures both local and global correlations between samples and anchors. Specifically, to model the coupling between the one-hot pseudo-labels of samples and anchors, we construct a bipartite graph with adaptively updated weights during the clustering process. To prevent severely imbalanced cluster assignments, we prove the equivalence between maximizing pseudo-label covariance and balancing cluster proportions, and incorporate a balanced regularization term to enhance the rationality of the resulting clusters. Furthermore, the local smoothness of anchor pseudo-labels is preserved via a low-rank decomposition of a compact anchor similarity graph. These two components jointly ensure that spatially adjacent anchors tend to share similar cluster identities, and that samples and anchors in close proximity are also assigned to similar clusters. We develop an efficient iterative optimization algorithm to update all model variables. Extensive experiments on benchmark and synthetic datasets validate the superior performance and efficiency of the proposed method compared with state-of-the-art approaches.