Robust tensor ring-based graph completion for incomplete multi-view clustering

Incomplete multi-view clustering (IMVC) aims to enhance clustering performance by leveraging complementary information from multi-view data, even in the presence of missing instances. This is challenging due to the interference caused by these missing data points. Current IMVC algorithms generally adopt two main strategies: either disregarding the missing instances and focusing on observable data for clustering, or complementing the missing instances within each view to improve the clustering results. However, effectively leveraging the latent information within these missing instances remains a challenge. In response, we propose a novel IMVC framework that complements the tensor consisting of similarity matrices learned from the available instances to enhance the relationships among samples from different views. In addition, we integrate tensor ring completion and M-estimator-based methods into the IMVC approach. This promotes the integration of inter-view information and mitigates errors introduced by missing instances in the model, respectively. Furthermore, we develop two efficient half-quadratic (HQ) based iterative algorithms with soft/hard threshold or multivariate generalization of minimax-concave (GMC) penalty to regularize the low-rank property. Comprehensive evaluations on seven benchmark datasets demonstrate that our method outperforms state-of-the-art IMVC approaches across various metrics.