Reliable Correspondence Learning for Incomplete and Unaligned Multi-View Clustering

Incomplete and unaligned multi-view clustering (IUMVC) has emerged as a challenging paradigm for discovering shared cluster structures from multiple views, where observations may be missing and cross-view sample correspondence is unknown. However, the unknown correspondence makes reliable cross-view matching difficult, as missing observations can result in multiple plausible matches, while erroneous correspondences may propagate errors to subsequent representation learning and multi-view consensus. To address these challenges, we propose a reliable correspondence learning framework, termed CAMVC, for robust clustering of unaligned incomplete multi-view data. Specifically, we first establish a canonical coordinate system without using paired samples and develop a cluster-routed local sparse transport mechanism to identify plausible correspondences, avoiding both premature hard matching and exhaustive global matching. Furthermore, we exploit correspondence-induced reconstruction consistency to quantify sample-level reliability and feature-dependent residual variation, allowing unreliable correspondences to exert less influence on subsequent representation learning. Finally, we integrate cross-view geometric consistency with reliability-aware consensus and high-order tensor regularization to capture complementary and higher-order dependencies across views, followed by reliability- and coverage-aware fusion for clustering. Extensive experiments on six benchmarks under varying levels of missingness and misalignment demonstrate that CAMVC improves clustering performance and effectively learns cross-view correspondences, even as the common sample-order assumption is progressively relaxed.