Robust Hypergraph Regularized Deep Non-Negative Matrix Factorization for Multi-View Clustering

As the increasing heterogeneous data, mining valuable information from various views is in demand. Currently, deep matrix factorization (DMF) receives extensive attention because of its ability to discover latent hierarchical semantics of the data. However, the existing multi-view DMF methods have the following shortcomings: (1). Most of multi-view DMF methods exploit Frobenius norm as the reconstruction error measure, which is easily affected by noises and outliers. (2). A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>NN-based graph keeps the geometric structure of the representation similar to the raw data, which fails to consider the higher-order relationships between instances. To solve these issues, in this research, a novel robust multi-view hypergraph regularized deep non-negative matrix factorization is proposed. Concretely, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2, 1}$</tex-math></inline-formula>-norm is adopted to measure the factorization error for enhancing the robustness. A hypergraph regularization is designed to discover the higher-order relationships between the instances. Additionally, a pair-wise consistency learning term is utilized to mine consistency information in multi-view data. An optimization algorithm based on iterative updating rules is developed for solving the proposed model, which makes the objective function value monotonically non-increase until convergence. Moreover, the convergence of the proposed optimization algorithm is validated theoretically and experimentally. Finally, abundant experiments are performed on six real world and two synthetic multi-view datasets to evaluate the performance of the proposed method and the comparison methods.