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Feature Selection for Consistent Biclustering via Fractional 0–1 Programming

Author

Listed:
  • Stanislav Busygin

    (University of Florida)

  • Oleg A. Prokopyev

    (University of Florida)

  • Panos M. Pardalos

    (McKnight Brain Institute, University of Florida)

Abstract

Biclustering consists in simultaneous partitioning of the set of samples and the set of their attributes (features) into subsets (classes). Samples and features classified together are supposed to have a high relevance to each other which can be observed by intensity of their expressions. We define the notion of consistency for biclustering using interrelation between centroids of sample and feature classes. We prove that consistent biclustering implies separability of the classes by convex cones. While previous works on biclustering concentrated on unsupervised learning and did not consider employing a training set, whose classification is given, we propose a model for supervised biclustering, whose consistency is achieved by feature selection. The developed model involves solution of a fractional 0–1 programming problem. Preliminary computational results on microarray data mining problems are reported.

Suggested Citation

  • Stanislav Busygin & Oleg A. Prokopyev & Panos M. Pardalos, 2005. "Feature Selection for Consistent Biclustering via Fractional 0–1 Programming," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 7-21, August.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:1:d:10.1007_s10878-005-1856-y
    DOI: 10.1007/s10878-005-1856-y
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    References listed on IDEAS

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    1. Wu, Tai-Hsi, 1997. "A note on a global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 220-223, August.
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    Cited by:

    1. Andrew Trapp & Oleg A. Prokopyev & Stanislav Busygin, 2010. "Finding checkerboard patterns via fractional 0–1 programming," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 1-26, July.
    2. Erfan Mehmanchi & Andrés Gómez & Oleg A. Prokopyev, 2019. "Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations," Journal of Global Optimization, Springer, vol. 75(2), pages 273-339, October.
    3. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    4. Panos Pardalos & Vera Tomaino & Petros Xanthopoulos, 2009. "Optimization and data mining in medicine," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 215-236, December.
    5. Erfan Mehmanchi & Andrés Gómez & Oleg A. Prokopyev, 2021. "Solving a class of feature selection problems via fractional 0–1 programming," Annals of Operations Research, Springer, vol. 303(1), pages 265-295, August.
    6. Peter DiMaggio & Scott McAllister & Christodoulos Floudas & Xiao-Jiang Feng & Joshua Rabinowitz & Herschel Rabitz, 2010. "A network flow model for biclustering via optimal re-ordering of data matrices," Journal of Global Optimization, Springer, vol. 47(3), pages 343-354, July.
    7. Andrew C. Trapp & Oleg A. Prokopyev, 2010. "Solving the Order-Preserving Submatrix Problem via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 387-400, August.

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