Flexible Non-Negative Matrix Factorization to Unravel Disease-Related Genes

Recently, non-negative matrix factorization (NMF) has been shown to perform well in the analysis of omics data. NMF assumes that the expression level of one gene is a linear additive composition of metagenes. The elements in metagene matrix represent the regulation effects and are restricted to non-negativity. However, according to the real biological meaning, there are two kinds of regulation effects, i.e., up-regulation and down-regulation. Few methods based on NMF have considered this biological meaning. Therefore, we designed a flexible non-negative matrix factorization (FNMF) algorithm by further considering the biological meaning of gene expression data. It allows negative numbers in the metagene matrix, and negative numbers represent down-regulation effects. We separated gene expression data into disease-driven gene expression and background gene expression. Subsequently, we computed disease-driven gene relative expression, and a ranked list of genes was obtained. The top ranked genes are considered to be involved in some disease-related biological processes. Experimental results on two real-world gene expression data demonstrate the feasibility and effectiveness of FNMF. Compared with conventional disease-related gene identification algorithms, FNMF has superior performance in analyzing gene expression data of diseases with complex pathology.