Risk-Certified Topology Guidance for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) seeks shared clusters despite missing views. Existing methods transfer cross-view relations and graph-propagate them to construct high-confidence pseudo-targets, but transfer errors can produce stable yet inaccurate predictions. Sharp predictions do not certify topology reliability, and auxiliary guidance may conflict with contrastive representation learning.We propose the Risk-certified Topology Guidance framework (RTG-IMVC). For each missing sample, we construct an admissible topology set via donor substitution, degree-preserving edge perturbation, and neighborhood bootstrapping. The certificate combines prediction diameter and topology-cover radius to produce risk-normalized weights for a logarithmic opinion pool and bound each view's log-odds influence on the consensus teacher. We project the joint gradient onto a half-space preserving descent of the instance- and cluster-level contrastive objectives.Under local Lipschitz, smoothness, topology-coverage, and bounded-probability conditions, we prove teacher robustness to admissible perturbations within the certified radius and one-step decrease of the surrogate base objective for a suitable learning rate. RTG-IMVC makes high-confidence guidance testable and risk-controlled.