Feature Selection for Consistent Biclustering via Fractional 0–1 Programming


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.

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  1. A. Ben-Dor, L. Bruhn, I. Nachman, M. Schummer, and Z. Yakhini, “Tissue classification with gene expression profiles,” Journal of Computational Biology, vol. 7, pp. 559–584, 2000.

    Article  PubMed  Google Scholar 

  2. A. Ben-Dor, N. Friedman, and Z. Yakhini, “Class discovery in gene expression data,” in Proc. Fifth Annual Inter. Conf. on Computational Molecular Biology (RECOMB), 2001.

  3. S. Busygin, G. Jacobsen, and E. Krámer, “Double Conjugated Clustering Applied to Leukemia Microarray Data,” SDM 2002 Workshop on Clustering High Dimensional Data and its Applications, 2002.

  4. Y. Cheng and G.M. Church, “Biclustering of Expression Data,” in: Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology, 2000, pp. 93–103.

  5. I.S. Dhillon, “Co-Clustering Documents and Words Using Bipartite Spectral Graph Partitioning,” in: Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining(KDD), August 26–29, 2001, San Francisco, CA.

  6. P. Hansen, M. Poggi de Aragão, and C.C. Ribeiro, “Hyperbolic 0–1 programming and query optimization in information retrieval,” Math. Program., vol. 52, pp. 256–263, 1991.

    Google Scholar 

  7. S. Hashizume, M. Fukushima, N. Katoh, and T. Ibaraki, “Approximation algortihms for combinatorial fractional programming problems,” Mathematical Programming, vol. 37, pp. 255–267.

  8. L.-L. Hsiao, F. Dangond, T. Yoshida, R. Hong, R.V. Jensen, J. Misra, W. Dillon, K.F. Lee, KE. Clark, P. Haverty, Z. Weng, G. Mutter, M.P. Frosch, M.E. MacDonald, E.L. Milford, C.P. Crum, R. Bueno, R.E. Pratt, M. Mahadevappa, J.A. Warrington, G. Stephanopoulos, G. Stephanopoulos, and S.R. Gullans, “A Compendium of Gene Expression in Normal Human Tissues,” Physiol. Genomics, vol. 7, pp. 97–104, 2001.

    PubMed  Google Scholar 

  9. T.R. Golub, D.K. Slonim, P. Tamayo, C. Huard, M. Gaasenbeek, J.P. Mesirov, H. Coller, M.L. Loh, J.R. Downing, M.A. Caligiuri, C.D. Bloomfield, and E.S. Lander, “Molecular classification of cancer: Class discovery and class prediction by gene expression monitoring,” Science, vol. 286, pp. 531–537, 1999.

    Article  PubMed  Google Scholar 

  10. Y. Kluger, R. Basri, J.T. Chang, and M. Gerstein, “Spectral biclustering of microarray data: Coclustering genes and conditions,” Genome Res, vol. 13, pp. 703–716, 2003.

    Article  PubMed  Google Scholar 

  11. J.-C. Picard and M. Queyranne, “A network flow solution to some nonlinear 0–1 programming problems, with applications to graph theory,” Networks, vol. 12, pp. 141–159, 1982.

    Google Scholar 

  12. O.A. Prokopyev, H.-X. Huang, and P.M. Pardalos, “On complexity of unconstrained hyperbolic 0–1 programming problems,” Oper. Res. Lett., vol. 33, pp. 312–318, 2005a.

    Article  Google Scholar 

  13. O.A. Prokopyev, C. Meneses, C.A.S. Oliveira, and P.M. Pardalos, “On Multiple-Ratio Hyperbolic 0–1 Programming Problems,” to appear in Pacific Journal of Optimization, 2005b.

  14. S. Saipe, “Solving a (0,1) hyperbolic program by branch and bound,” Naval Res. Logist. Quarterly, vol. 22, pp. 497–515, 1975.

    Google Scholar 

  15. M. Tawarmalani, S. Ahmed, and N. Sahinidis, “Global optimization of 0–1 Hyperbolic Programs,” J. Global Optim., vol. 24, pp. 385–416, 2002.

    Article  Google Scholar 

  16. J. Weston, S. Mukherjee, O. Chapelle, M. Pontil, T. Poggio, and V. Vapnik, Feature selection for SVMs. NIPS, 2001.

  17. T.-H. Wu, “A note on a global approach for general 0–1 fractional programming,” European J. Oper. Res., vol. 101, pp. 220–223, 1997.

    Article  Google Scholar 

  18. E.P. Xing and R.M. Karp “CLIFF: Clustering of high-dimensional microarray data via iterative feature filtering using normalized cuts,” Bioinformatics Discovery Note, vol. 1, pp. 1–9, 2001.

    Google Scholar 

  19. CAMDA 2001 Conference. http://bioinformatics.duke.edu/camda/camda01/.

  20. HuGE Index.org Website. http://www.hugeindex.org.

  21. ILOG Inc. CPLEX 9.0 User’s Manual, 2004.

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Correspondence to Stanislav Busygin.

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This research work was partially supported by NSF, NIH and AirForce grants.

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Busygin, S., Prokopyev, O.A. & Pardalos, P.M. Feature Selection for Consistent Biclustering via Fractional 0–1 Programming. J Comb Optim 10, 7–21 (2005). https://doi.org/10.1007/s10878-005-1856-y

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  • feature selection
  • biclustering
  • classification
  • supervised learning
  • microarrays