IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v20y2010i1d10.1007_s10878-008-9186-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-008-9186-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10878-008-9186-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Tien Mai & Arunesh Sinha, 2022. "Safe Delivery of Critical Services in Areas with Volatile Security Situation via a Stackelberg Game Approach," Papers 2204.11451, arXiv.org.
    4. Georg Bechler & Claudius Steinhardt & Jochen Mackert, 2021. "On the Linear Integration of Attraction Choice Models in Business Optimization Problems," SN Operations Research Forum, Springer, vol. 2(1), pages 1-13, March.
    5. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    6. 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.
    7. König, Eva & Schön, Cornelia, 2021. "Railway delay management with passenger rerouting considering train capacity constraints," European Journal of Operational Research, Elsevier, vol. 288(2), pages 450-465.
    8. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    9. Chang, Ching-Ter, 2001. "On the polynomial mixed 0-1 fractional programming problems," European Journal of Operational Research, Elsevier, vol. 131(1), pages 224-227, May.
    10. Mavrotas, G. & Diakoulaki, D. & Caloghirou, Y., 2006. "Project prioritization under policy restrictions. A combination of MCDA with 0-1 programming," European Journal of Operational Research, Elsevier, vol. 171(1), pages 296-308, May.
    11. Bechler, Georg & Steinhardt, Claudius & Mackert, Jochen & Klein, Robert, 2021. "Product line optimization in the presence of preferences for compromise alternatives," European Journal of Operational Research, Elsevier, vol. 288(3), pages 902-917.
    12. 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.
    13. Juan José Miranda Bront & Isabel Méndez-Díaz & Gustavo Vulcano, 2009. "A Column Generation Algorithm for Choice-Based Network Revenue Management," Operations Research, INFORMS, vol. 57(3), pages 769-784, June.
    14. Cornelia Schön & Pratibha Saini, 2018. "Market-Oriented Service Network Design When Demand is Sensitive to Congestion," Transportation Science, INFORMS, vol. 52(5), pages 1253-1275, October.
    15. Billionnet, Alain, 2004. "Mixed integer programming for the 0-1 maximum probability model," European Journal of Operational Research, Elsevier, vol. 156(1), pages 83-91, July.
    16. Shuyu Zhou & Yeming (Yale) Gong & René de Koster, 2016. "Designing self-storage warehouses with customer choice," International Journal of Production Research, Taylor & Francis Journals, vol. 54(10), pages 3080-3104, May.
    17. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    18. 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.
    19. Samyukta Sethuraman & Sergiy Butenko, 2015. "The maximum ratio clique problem," Computational Management Science, Springer, vol. 12(1), pages 197-218, January.
    20. Jose Joaquin del Pozo-Antúnez & Francisco Fernández-Navarro & Horacio Molina-Sánchez & Antonio Ariza-Montes & Mariano Carbonero-Ruz, 2021. "The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession," Mathematics, MDPI, vol. 9(15), pages 1-16, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:20:y:2010:i:1:d:10.1007_s10878-008-9186-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.