Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology

Abstract

In the last decade, advances in high-throughput technologies such as DNA microarrays have made it possible to simultaneously measure the expression levels of tens of thousands of genes and proteins. This has resulted in large amounts of biological data requiring analysis and interpretation. Nonnegative matrix factorization (NMF) was introduced as an unsupervised, parts-based learning paradigm involving the decomposition of a nonnegative matrix V into two nonnegative matrices, W and H, via a multiplicative updates algorithm. In the context of a p×n gene expression matrix V consisting of observations on p genes from n samples, each column of W defines a metagene, and each column of H represents the metagene expression pattern of the corresponding sample. NMF has been primarily applied in an unsupervised setting in image and natural language processing. More recently, it has been successfully utilized in a variety of applications in computational biology. Examples include molecular pattern discovery, class comparison and prediction, cross-platform and cross-species analysis, functional characterization of genes and biomedical informatics. In this paper, we review this method as a data analytical and interpretive tool in computational biology with an emphasis on these applications.

A non-negative matrix factorization framework for identifying modular patterns in metagenomic profile data

“…Whereas NMF is widely utilized in other fields (Brunet et al 2004;Devarajan 2008), to our knowledge this is the first application of NMF to metagenomic data. Although we focused on metagenomic data sets in this paper, both the NMF approach in general, and the framework developed here, have potential applications to a variety of different kinds of biological profiles, including transcriptional profiles and protein expression profiles.…”

“…The modern approach to NMF (Lee and Seung 1999) has been used in a wide range of data mining and pattern recognition applications (Lee and Seung 1999; in the last decade, as well as in large-scale biological data analysis (Kim and Tidor 2003;Devarajan 2008;Brunet et al 2004;Kim and Park 2007). Advantages of this method include its ability to simultaneously cluster the columns and rows of a data matrix (bi-clustering) , and unsupervised discovery of hierarchical structures (Brunet et al 2004).…”

Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

“…in ranging from biology (Sotiras et al, 2015, Brunet et al, 2004, nuclear sciences or in to computer sciences (e. g. signal processing and pattern recognition; Smaragdis et al, 2003, Buciu et al, 2004). Devarajan's work focuses on the field of computational biology, however it also gives a remarkable outlook to the capabilities of NMF-analysis (Devarajan, 2008).…”

Unexpected functional similarities between gatekeeper tumour suppressor genes and proto-oncogenes revealed by systems biology

“…The term (NNMF) refers to a method in which algorithms in multivariate analysis are factorized into matrices by incorporating different constraints, for example, using principal component analysis, in which all elements must be X0. [66][67][68] We therefore conducted analysis of the coding sequence pattern with an NNMF method that is ideal for non-zero variables, in addition to a linear normalization and transform demonstrated by principal component analysis. We used NNMF to ask the question: given the dinucleotide composition of the 116 putative cancer genes, how many meta-genes and meta-dinucleotides have an informational content similar to the data matrix therein?…”