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

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  • Karthik Devarajan

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.

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  • Karthik Devarajan, 2008. "Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology," PLOS Computational Biology, Public Library of Science, vol. 4(7), pages 1-12, July.
    • Handle: RePEc:plo:pcbi00:1000029
    DOI: 10.1371/journal.pcbi.1000029
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    Cited by:

    1. GILLIS, Nicolas & GLINEUR, François, 2008. "Nonnegative factorization and the maximum edge biclique problem," LIDAM Discussion Papers CORE 2008064, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. José M. Maisog & Andrew T. DeMarco & Karthik Devarajan & Stanley Young & Paul Fogel & George Luta, 2021. "Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    3. GILLIS, Nicolas & GLINEUR, François, 2011. "Accelerated multiplicative updates and hierarchical als algorithms for nonnegative matrix factorization," LIDAM Discussion Papers CORE 2011030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Jingu Kim & Yunlong He & Haesun Park, 2014. "Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework," Journal of Global Optimization, Springer, vol. 58(2), pages 285-319, February.
    5. Gregory Lepeu & Ellen Maren & Kristina Slabeva & Cecilia Friedrichs-Maeder & Markus Fuchs & Werner J. Z’Graggen & Claudio Pollo & Kaspar A. Schindler & Antoine Adamantidis & Timothée Proix & Maxime O., 2024. "The critical dynamics of hippocampal seizures," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    6. Minghao Li & Zicheng Zhang & Qianrong Wang & Yan Yi & Baosheng Li, 2022. "Integrated cohort of esophageal squamous cell cancer reveals genomic features underlying clinical characteristics," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    7. Arun Varghese & Michelle Cawley & Tao Hong, 2018. "Supervised clustering for automated document classification and prioritization: a case study using toxicological abstracts," Environment Systems and Decisions, Springer, vol. 38(3), pages 398-414, September.
    8. Paul Fogel & Yann Gaston-Mathé & Douglas Hawkins & Fajwel Fogel & George Luta & S. Stanley Young, 2016. "Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health," IJERPH, MDPI, vol. 13(5), pages 1-14, May.
    9. Hui-Min Wang & Ching-Lin Hsiao & Ai-Ru Hsieh & Ying-Chao Lin & Cathy S J Fann, 2012. "Constructing Endophenotypes of Complex Diseases Using Non-Negative Matrix Factorization and Adjusted Rand Index," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-12, July.
    10. Richard Nock & Natalia Polouliakh & Frank Nielsen & Keigo Oka & Carlin R Connell & Cedric Heimhofer & Kazuhiro Shibanai & Samik Ghosh & Ken-ichi Aisaki & Satoshi Kitajima & Jun Kanno & Taketo Akama & , 2020. "A Geometric Clustering Tool (AGCT) to robustly unravel the inner cluster structures of time-series gene expressions," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-19, July.
    11. Haixuan Yang & Cathal Seoighe, 2016. "Impact of the Choice of Normalization Method on Molecular Cancer Class Discovery Using Nonnegative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-17, October.
    12. Flavia Esposito, 2021. "A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments," Mathematics, MDPI, vol. 9(9), pages 1-17, April.

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