Feature Selection for Consistent Biclustering via Fractional 0–1 Programming
- 254 Downloads
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.
Keywordsfeature selection biclustering classification supervised learning microarrays
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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
- S. Hashizume, M. Fukushima, N. Katoh, and T. Ibaraki, “Approximation algortihms for combinatorial fractional programming problems,” Mathematical Programming, vol. 37, pp. 255–267.Google Scholar
- 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.PubMedGoogle Scholar
- 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.CrossRefPubMedGoogle Scholar
- 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
- 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.Google Scholar
- S. Saipe, “Solving a (0,1) hyperbolic program by branch and bound,” Naval Res. Logist. Quarterly, vol. 22, pp. 497–515, 1975.Google Scholar
- J. Weston, S. Mukherjee, O. Chapelle, M. Pontil, T. Poggio, and V. Vapnik, Feature selection for SVMs. NIPS, 2001.Google Scholar
- 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
- CAMDA 2001 Conference. http://bioinformatics.duke.edu/camda/camda01/.
- HuGE Index.org Website. http://www.hugeindex.org.
- ILOG Inc. CPLEX 9.0 User’s Manual, 2004.Google Scholar