Hyper-graph robust non-negative matrix factorization method for cancer sample clustering and feature selection

Non-negative Matrix Factorization (NMF) algorithm is a useful method for data dimensionality reduction, which is performed with the Euclidean distance. However, the basic NMF only assumes that data will be destroyed by Gaussian noise. It ignores both the intrinsic geometrical structure and the influence of sparse noises existing in the gene expression data. To enhance the robustness of the NMF, a novel method called Hyper-graph Robust Non-negative Matrix Factorization (HRNMF) is proposed for cancer sample clustering and feature selection. The merits of the HRNMF mainly consist of two aspects. Firstly, the L_{2, 1}-norm is combined with the objective function, which can effectively handle noise and outliers. Secondly, the manifold information and sparsity are also considered so we add the hyper-graph regularization term and sparse constraints to the error function. It can effectively preserve the geometric structure and enhance matrix sparsity. Experiments on Cancer Genome Atlas (TCGA) gene expression data have demonstrated that HRNMF performs better than other advanced methods in cancer sample clustering and feature selection.