Graph regularized robust non-negative matrix factorization for clustering and selecting differentially expressed genes

Non-negative Matrix Factorization (NMF) is widely used as a data dimensionality reduction tool. However, the assumption of most conventional NMF-based methods is that the gene expression data are only destroyed by Gaussian noise. In practice, the gene expression data are unavoidably destroyed by sparse noise. Although Sparsity-Regularized Robust NMF by using L_1/2 constraint (L_1/2-RNMF) can achieve satisfactory results when the sparse noise exists, it does not consider the intrinsic geometric structure in data. Hence, we introduce graph regularization into L_1/2-RNMF. In this paper, we developed a novel NMF method named Graph regularized Robust Nonnegative Matrix Factorization (GrRNMF), which mainly consists of two aspects: Firstly, the Gaussian noise and sparse noise are modeled, respectively. Secondly, it can reveal the geometric information in data by adding graph regularization term. Extensive experimental results on The Cancer Genome Atlas (TCGA) data indicate that the GrRNMF method has higher accuracy than other state-of-the-art methods in samples clustering and the selection of differentially expressed genes.