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

20 pages
Read Article

Loading next page...
 
/lp/springer_journal/recovering-all-generalized-order-preserving-submatrices-new-exact-D2ceR0j52X
Publisher
Springer Journals
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 Research – Springer Journals

Published: Mar 25, 2016

References

  • Discovering local structure in gene expression data: The order-preserving submatrix problem
    Ben-Dor, A; Chor, B; Karp, R; Yakhini, Z
  • Biclustering in data mining
    Busygin, S; Prokopyev, O; Pardalos, PM
  • Remodeling of yeast genome expression in response to environmental changes
    Causton, HC; Ren, B; Koh, SS; Harbison, CT; Kanin, E; Jennings, EG; Lee, TI; True, HL; Lander, ES; Young, RA
  • Comprehensive analysis of transcriptional promoter structure and function in 1% of the human genome
    Cooper, SJ; Trinklein, ND; Anton, ED; Nguyen, L; Myers, RM
  • Mining bucket order-preserving submatrices in gene expression data
    Fang, Q; Ng, W; Feng, J; Li, Y
  • Mining order-preserving submatrices from probabilistic matrices
    Fang, Q; Ng, W; Feng, J; Li, Y
  • On the deep order-preserving submatrix problem: A best effort approach
    Gao, BJ; Griffith, OL; Ester, M; Xiong, H; Zhao, Q; Jones, SJ
  • Approximation algorithms for a minimization variant of the order-preserving submatrices and for biclustering problems
    Hochbaum, DS; Levin, A
  • Pathway analysis of coronary atherosclerosis
    King, JY; Ferrara, R; Tabibiazar, R; Spin, JM; Chen, MM; Kuchinsky, A; Vailaya, A; Kincaid, R; Tsalenko, A; Deng, DXF
  • Biclustering algorithms for biological data analysis: A survey
    Madeira, SC; Oliveira, AL
  • Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization
    Spellman, PT; Sherlock, G; Zhang, MQ; Iyer, VR; Anders, K; Eisen, MB; Brown, PO; Botstein, D; Futcher, B
  • Solving the order-preserving submatrix problem via integer programming
    Trapp, AC; Prokopyev, OA
  • Mining order-preserving submatrices from data with repeated measurements
    Yip, KY; Kao, B; Zhu, X; Chui, CK; Lee, SD; Cheung, DW

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial