A Robust Manifold Graph Regularized Nonnegative Matrix Factorization Algorithm for Cancer Gene Clustering

Abstract

Detecting genomes with similar expression patterns using clustering techniques plays an important role in gene expression data analysis. Non-negative matrix factorization (NMF) is an effective method for clustering the analysis of gene expression data. However, the NMF-based method is performed within the Euclidean space, and it is usually inappropriate for revealing the intrinsic geometric structure of data space. In order to overcome this shortcoming, Cai et al. proposed a novel algorithm, called graph regularized non-negative matrices factorization (GNMF). Motivated by the topological structure of the GNMF-based method, we propose improved graph regularized non-negative matrix factorization (GNMF) to facilitate the display of geometric structure of data space. Robust manifold non-negative matrix factorization (RM-GNMF) is designed for cancer gene clustering, leading to an enhancement of the GNMF-based algorithm in terms of robustness. We combine the $l_{2,1}$-norm NMF with spectral clustering to conduct the wide-ranging experiments on the three known datasets. Clustering results indicate that the proposed method outperforms the previous methods, which displays the latest application of the RM-GNMF-based method in cancer gene clustering.