Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
Review
. 2008 Jul 25;4(7):e1000029.
doi: 10.1371/journal.pcbi.1000029.

Nonnegative matrix factorization: an analytical and interpretive tool in computational biology

Karthik Devarajan  1
Affiliations
Review

Nonnegative matrix factorization: an analytical and interpretive tool in computational biology

Karthik Devarajan. PLoS Comput Biol. .

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 pxn 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.

PubMed Disclaimer

Conflict of interest statement

The author has declared that no competing interests exist.

Figures

Figure 1
Figure 1. Gene coefficients.
(A) Histogram of gene coefficients, metagene 1. (B) Histogram of gene coefficients, metagene 2. (C) Density of gene coefficients, metagene 1. (D) Density of gene coefficients, metagene 2.
Figure 2
Figure 2. Expression profile.
(A) Density of expression profile, metagene 1. (B) Density of expression profile, metagene 2. (C) Expression profile across samples, metagene 1. (D) Expression profile across samples, metagene 2.
Figure 3
Figure 3. Cophenetic correlation coefficient.
Figure 4
Figure 4. Heat map of re-ordered consensus matrix, k = 2.
Figure 5
Figure 5. Heat map of re-ordered consensus matrix, k = 3.
See this image and copyright information in PMC

References

    1. Lee DD, Seung SH. Learning the parts of objects by nonnegative matrix factorization. Nature. 1999;401:788–791. - PubMed
    1. Lee DD, Seung SH. Algorithms for nonnegative matrix factorization. Adv Neural Inform Process Syst. 2001;13:556–562.
    1. Paatero P, Tapper U. Positive matrix factorization: A nonnegative factor model with optimal utilization of error estimates of data values. Environmetrics. 1994;5:111–126.
    1. Paatero P. Least-squares formulation of robust non-negative factor analysis. Chemometrics Intelligent Laboratory Sys. 1997;37:23–35.
    1. Paatero P. The Multilinear Engine—A table-driven least squares program for solving multilinear problems, including the n-way parallel factor analysis model. J Computational Graphical Stat. 1999;8:854–888.

Publication types

MeSH terms