Mixed-noise robust tensor multi-view clustering via adaptive dictionary learning

Multi-view clustering (MVC) has received extensive attention by exploiting the consistent and complementary information among views. To improve the robustness of MVC, most MVC methods assume that the noise implicit in the data follows a predefined distribution. However, due to equipment limitations and transmission environment, the collected multi-view data often contains mixed noise. The predefined distribution assumption may not be able to effectively suppress complex mixed noise, resulting in a decrease in clustering performance. For solving the above problem, we propose a novel mixed-noise robust tensor multi-view clustering method (MRTMC) via adaptive dictionary learning. To accurately characterize the mixed noise, we consider mixed noise as a combination of structural noise and Gaussian noise and characterize both respectively. Specially, we design adaptive dictionary learning to accurately model structural noise containing semantic information and use Frobenius norm to constrain Gaussian noise. To fully mine the consistency among multiple views, we introduce a nonconvex tensor nuclear norm on the self-representation tensor to explore the high-order correlation among multiple views. Moreover, the weight of each view is learned through an adaptive weighting strategy. For solving the model, we develop an effective algorithm based on the alternating direction method of multipliers (ADMM) framework and provide the convergence guarantee of the algorithm under mild conditions. Extensive experimental results on simulated and real-world datasets indicate the clustering performance of the proposed MRTMC method is superior to the compared methods. • We propose a novel mixed-noise robust tensor multi-view clustering method via adaptive dictionary learning. • We introduce a nonconvex tensor nuclear norm and the adaptive weighting strategy to fully explore the high-order correlation among views. • The mixed noise learning based on adaptive dictionary, nonconvex low-rank tensor approximation, and affinity matrix learning are optimized in a unified framework. • An efficient algorithm based on ADMM framework is developed to solve the proposed model and the theoretical convergence is provided. • Extensive simulated and real-world experiments show the superiority of the proposed method.