Hypergraph regularized NMF by L_2,1-norm for Clustering and Com-abnormal Expression Genes Selection

Non-negative matrix decomposition (NMF) has been widely used for sample clustering and feature selection in the field of bioinformatics. However, the existing methods based on NMF cannot effectively deal with the problem of intrinsic geometrical structure, noise, and outliers in gene expression data. In this paper, a novel method called Robust Hypergraph regularized Non-negative Matrix Factorization (RHNMF) is proposed to solve the above problem. Firstly, the hypergraph Laplacian regularization is introduced to consider the intrinsic geometrical structure of the high dimension data. Secondly, the L_2,1-norm is applied in the error function to reduce effects of the noise and outliers, which may improve the robustness of the algorithm. Finally, we perform clustering and common abnormal expression genes (com-abnormal expression genes) selection on multi-view gene expression data to verify the rationality and validity of the RHNMF method. Extensive experimental results demonstrate that our proposed RHNMF method has better performance than other state-of-the-art methods.