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Finding checkerboard patterns via fractional 0–1 programming

Author

Listed:
  • Andrew Trapp

    (University of Pittsburgh)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

  • Stanislav Busygin

    (University of Florida)

Abstract

Biclustering is a data mining technique used to simultaneously partition the set of samples and the set of their attributes (features) into subsets (clusters). Samples and features clustered together are supposed to have a high relevance to each other. In this paper we provide a new mathematical programming formulation for unsupervised biclustering. The proposed model involves the solution of a fractional 0–1 programming problem. A linear-mixed 0–1 reformulation as well as two heuristic-based approaches are developed. Encouraging computational results on clustering real DNA microarray data sets are presented. In addition, we also discuss theoretical computational complexity issues related to biclustering.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:1:d:10.1007_s10878-008-9186-5
    DOI: 10.1007/s10878-008-9186-5
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    References listed on IDEAS

    as
    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.
    2. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Andrew C. Trapp & Wen Liu & Soussan Djamasbi, 2019. "Identifying Fixations in Gaze Data via Inner Density and Optimization," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 459-476, July.

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