Recovering all generalized order-preserving submatrices: new exact formulations and algorithms

Recovering all generalized order-preserving submatrices: new exact formulations and algorithms Cluster analysis of gene expression data is a popular and successful way of elucidating underlying biological processes. Typically, cluster analysis methods seek to group genes that are differentially expressed across experimental conditions. However, real biological processes often involve only a subset of genes and are activated in only a subset of environmental or temporal conditions. To address this limitation, Ben-Dor et al. (J Comput Biol 10(3–4):373–384, 2003) developed an approach to identify order-preserving submatrices (OPSMs) in which the expression levels of included genes induce the sample linear ordering of experiments. In addition to gene expression analysis, OPSMs have application to recommender systems and target marketing. While the problem of finding the largest OPSM is $${{\mathscr {N}}}{{\mathscr {P}}}$$ N P -hard, there have been significant advances in both exact and approximate algorithms in recent years. Building upon these developments, we provide two exact mathematical programming formulations that generalize the OPSM formulation by allowing for the reverse linear ordering, known as the generalized OPSM pattern, or GOPSM. Our formulations incorporate a constraint that provides a margin of safety against detecting spurious GOPSMs. Finally, we provide two novel algorithms to recover, for any given level of significance, all GOPSMs from a given data matrix, by iteratively solving mathematical programming formulations to global optimality. We demonstrate the computational performance and accuracy of our algorithms on real gene expression data sets showing the capability of our developments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

Recovering all generalized order-preserving submatrices: new exact formulations and algorithms

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-016-2173-9
Publisher site
See Article on Publisher Site

Abstract

Cluster analysis of gene expression data is a popular and successful way of elucidating underlying biological processes. Typically, cluster analysis methods seek to group genes that are differentially expressed across experimental conditions. However, real biological processes often involve only a subset of genes and are activated in only a subset of environmental or temporal conditions. To address this limitation, Ben-Dor et al. (J Comput Biol 10(3–4):373–384, 2003) developed an approach to identify order-preserving submatrices (OPSMs) in which the expression levels of included genes induce the sample linear ordering of experiments. In addition to gene expression analysis, OPSMs have application to recommender systems and target marketing. While the problem of finding the largest OPSM is $${{\mathscr {N}}}{{\mathscr {P}}}$$ N P -hard, there have been significant advances in both exact and approximate algorithms in recent years. Building upon these developments, we provide two exact mathematical programming formulations that generalize the OPSM formulation by allowing for the reverse linear ordering, known as the generalized OPSM pattern, or GOPSM. Our formulations incorporate a constraint that provides a margin of safety against detecting spurious GOPSMs. Finally, we provide two novel algorithms to recover, for any given level of significance, all GOPSMs from a given data matrix, by iteratively solving mathematical programming formulations to global optimality. We demonstrate the computational performance and accuracy of our algorithms on real gene expression data sets showing the capability of our developments.

Journal

Annals of Operations ResearchSpringer Journals

Published: Mar 25, 2016

References

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