Multi-view subspace clustering based on multi-order neighbor diffusion

Abstract

Multi-view subspace clustering (MVC) intends to separate out samples via integrating the complementary information from diverse views. In MVC, since the structural information in the graph is crucial to the graph learning, most of the existing algorithms construct the superficial graph from the original data by directly measuring the similarity between the first-order complementary nearest neighbors. However, the information provided by the superficial graph structure would be influenced by contaminated or absent samples. To address this problem, in the proposed method, the higher-order complementary neighbor graphs are exploited to discover the latent structural information between the samples, and fusing the latent structural information across different orders to achieve the MVC. Specifically, the higher-order neighbor graphs under different views are leveraged to estimate the missing samples. Then, to integrate the neighbor graphs of different orders, the multi-order neighbor diffusion fusion is proposed. Nevertheless, the above problem of diffusion fusion is an intractable non-convex issue. Thus, to address it, the multi-order neighbor diffusion fusion is considered as a combination problem of the solution under different order, and the heuristic algorithm is leveraged to solve it. In this way, not only the data representation under different view and also the neighbor structure under different order can be diffused under a joint optimization framework, thus the consistency and integral information among various perspectives and orders can be utilized effectively and simultaneously. Experiments on both incomplete and complete multi-view dataset demonstrate the convincingness of the high-order neighborhood structure based subspace clustering scheme by comparing with the existing approaches.