Prior-Corrected Anchor Learning with Direct Discrete Partitioning for Multi-View Clustering

Anchor-based multi-view clustering improves computational efficiency by representing the relationships among samples using a small number of anchors. However, existing methods typically employ shared semantic priors across different views. Since individual views may contain view-specific noise, feature distortions, and outliers, a shared semantic prior may fail to accurately characterize each view. Moreover, learning representations and performing clustering assignments in separate stages may result in representations that are not directly optimized toward the final clustering objective.To address these issues, we propose a Prior-Corrected Anchor Learning method, termed PCAL, which jointly learns view-specific anchor matrices, a shared anchor representation, and discrete clustering assignments within a unified framework. PCAL reconstructs each view through the shared anchor representation and aligns the anchor matrix of each view with the shared semantic prior via orthogonal projection. Building upon this mechanism, we further introduce regularized view-specific correction matrices, enabling the shared prior to adapt to the feature discrepancies across different views. In addition, a discrete factorization term is incorporated to directly connect anchor representation learning with cluster label assignment, thereby avoiding additional spectral clustering post-processing.For the proposed model, we develop an alternating optimization algorithm, in which each variable subproblem can be efficiently solved either in closed form or through singular value decomposition. Experimental results demonstrate that, compared with other multi-view clustering methods, the proposed PCAL method reduces computational time while achieving competitive clustering performance in terms of metrics such as ACC and NMI.