Enhanced deep non-negative matrix factorization for multi-view clustering

Multi-view clustering(MVC) seeks to group similar samples into the same clusters by exploiting complementary and consistent information between different views. Recently, MVC has been successfully used in various areas, such as social network analysis, bioinformatics, and computer vision. Among the existing multi-view clustering algorithms, deep nonnegative matrix factorization(DNMF) is a promising and widely-used technique. However, the existing DNMF-based methods overlook low-dimensional representation learning and the specificity of each view. To address the aforementioned issues, we propose an enhanced DNMF algorithm(EDNMF) for MVC, which fuses deep encoding and decoding into a unified framework. Specifically, the decoding and encoding stages correspond the reconstruction of the original data and low-dimensional representation learning, respectively. The smoothness strategy is introduced to connect feature matrices of various views with consensus representation matrix by learning a project matrix for each view, which considers the specificity of each view. To preserve the local geometric structure information of multi-view data, a new graph regularization is fused to EDNMF model. Furthermore, if prior information indicating that some samples belong to the same cluster is available, a semi-supervised EDNMF (SEDNMF) for MVC is proposed by integrating this prior information into the graph regularization term of EDNMF. Numerical experiments on nine datasets are carried out to demonstrate that the effectiveness and superiority of the proposed methods.