Robust Sparse Low-rank Hypergraph Learning under Complex Noise

Tianhao Cui, Lei Chen, Jie Xu, Lei Xu

Abstract: As a natural extension of the traditional graph model, hypergraph has been extensively exploited and applied in many tasks such as image clustering, classification, etc. The performance of these tasks highly depends on building an informative hypergraph to accurately and robustly formulate the underlying data correlation. Existing hypergraph construction methods can only be suitable for simple Gaussian or outlier noise assumptions, which cannot be applied to more complex noise scenario in practical applications. To address this challenge, we propose a robust hypergraph learning model by adopting the Mixture of Gaussians (MoG) noise modeling strategy. In particular, our model adopts low-rank representation and sparse representation simultaneously to construct an informative hypergraph. The Correlation among nodes and the weights of edges can be obtained by seeking a low-rank and sparse representation matrix. The so-obtained hypergraph can capture both the global mixture of subspaces structure (by low-rank) and the locally linear structure (by sparse) of the data. Furthermore, an efficient Expectation-Maximization-like optimization algorithm is designed to solve the proposed model. Finally, the superiority of our model is demonstrated by extensive experiments on image clustering.