Multi-view Regression Clustering via Low-Rank Manifold Decomposition

Abstract

Similarity-graph-based multi-view clustering is effective in capturing non-Gaussian cluster structures, yet it suffers from an inherent conflict between scalability and geometry-consistent cluster assignment. In particular, cluster labels are typically inferred via secondary clustering rather than being learned directly from the underlying data geometry. Although anchor-based extensions alleviate the computational burden, they introduce the challenge of anchor-number selection.

To address these limitations, we propose Multi-view Clustering via Manifold Decomposition (MvMD), which directly infers cluster labels from multi-view data without explicit similarity graph construction or anchor selection. MvMD reformulates multi-view clustering as a unified multi-view regression problem, where cluster labels are optimized as model variables. To improve robustness against missing small clusters, a global balance regularization is incorporated. Meanwhile, local geometric consistency and the low-rank structure of cluster assignments are jointly enforced through a symmetric matrix factorization scheme, which is efficiently realized via a truncated SVD-based low-rank approximation.

Extensive experiments on benchmark datasets validate the effectiveness and efficiency of the proposed MvMD. The code is available at https://github.com/Vince-Doit/MvMD.