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

By Karthik Devarajan. 2008

455 citations recorded by the source corpus.

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.

Subfields: Molecular Biology

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Molecular Biology

Citations in the corpus

Learning a hierarchical representation of the yeast transcriptomic machinery using an autoencoder model (2016, methodology): “When we use the low-dimensional NMF metagenes space, it performs slightly better than using original gene expression space.”
A flexible R package for nonnegative matrix factorization (2010, methodology): “Since its formal definition in [1,2], the NMF approach has been applied successfully in several fields including image and pattern recognition, signal processing and text mining [3].”
A Deep Matrix Factorization Method for Learning Attribute Representations (2015, background): “It has been shown that they can be a successful dimensionality reduction technique over a variety of areas including, but not limited to, environ-metrics [1], microarray data analysis [2], [3], document clustering [4], face recognition [5], [6], blind audio source separation [7] and more.”
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “Over the last decade, NMF has received enormous attention and has been successfully applied to a broad range of important problems in areas including text mining [77,85], computer vision [47,69], bioinformatics [10,23,52], spectral data analysis [76], and blind source separation [22] among many othe”
Machine learning in cell biology – teaching computers to recognize phenotypes (2013, background): “To overcome these limitations, some applications of unsupervised learning have incorporated additional knowledge about the data, such as, for example, temporal constraints on morphological transitions (Zhong et al., 2012) or non-negativity constraints on gene expression data (Devarajan, 2008).”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, background): “Due to the nonnegativity, the factors of low rank approximation give a natural interpretation: Each data item can be explained by an additive linear combination of physically-meaningful basis components [22].”
The Why and How of Nonnegative Matrix Factorization (2014, background): “Other applications include air emission control [97], computational biology [34], blind source separation [22], single-channel source separation [82], clustering [35], music analysis [42], collaborative ﬁltering [92], and community detection [106].”