A network flow model for biclustering via optimal re-ordering of data matrices

Journal of Global Optimization

Volumn 47, Issue 3, 2010, Pages 343-354

  Dimaggio Jr , Peter A ^a   McAllister, Scott R ^a   Floudas, Christodoulos A ^a   Feng, Xiao Jiang ^b   Rabinowitz, Joshua D ^b   Rabitz, Herschel A ^b  

^a Princeton University   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Biclustering; Mixed integer linear optimization (MILP)

Indexed keywords

BICLUSTERING; CLUSTER BOUNDARIES; CLUSTERING METHODS; CLUSTERING TECHNIQUES; DATA MATRICES; DATA SETS; ITERATIVE FRAMEWORK; LINEAR OPTIMIZATION; METABOLITE CONCENTRATIONS; NETWORK FLOW MODEL; OBJECTIVE FUNCTIONS; ONE DIMENSION; SUB-MATRICES; TRADITIONAL CLUSTERING;

CLUSTER ANALYSIS; HEURISTIC METHODS; INTEGER PROGRAMMING; OPTIMIZATION;

MATRIX ALGEBRA;

EID: 77954762860     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-008-9349-z     Document Type: Article

References (52)

1. Anderberg, M. R.: Cluster Analysis for Applications. Academic Press, New York (1973)
2. Jain, A. K., Flynn, P. J.: Image segmentation using clustering. In: Ahuja, N., Bowyer, K. (eds.) Advances in Image Understanding: A Festschrift for Azriel Rosenfeld, pp. 65-83. IEEE Press, Piscataway (1996)
3. Salton, G.: Developments in automatic text retrieval. Science 253, 974-980 (1991)
4. Eisen, M. B., Spellman, P. T., Brown, P. O., Botstein, D.: Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA 95, 14863-14868 (1998)
5. Zhang, Y., Skolnick, J.: SPICKER: a clustering approach to identify near-native protein folds. J. Comput. Chem. 25, 865-871 (2004)
6. Mönnigmann, M., Floudas, C. A.: Protein loop structure prediction with flexible stem geometries. Protein: Struct. Funct. Bioinform. 61, 748-762 (2005)
7. Edwards, A. W. F., Cavalli-Sforza, L. L.: A method for cluster analysis. Biometrics 21, 362-375 (1965)
8. Wolfe, J. H.: Pattern clustering by multivariate mixture analysis. Multivariate Behav. Res. 5, 329-350 (1970)
9. Jain, A. K., Mao, J.: Artificial neural networks: a tutorial. IEEE Comput. 29, 31-44 (1996)
10. Klein, R. W., Dubes, R. C.: Experiments in projection and clustering by simulated annealing. Pattern Recognit. 22, 213-220 (1989)
11. Raghavan, V. V., Birchand, K.: A clustering strategy based on a formalism of the reproductive process in a natural system. In: Proceedings of the Second International Conference on Information Storage and Retrieval, pp. 10-22 (1979)
12. Bhuyan, J. N., Raghavan, V. V., Venkatesh, K. E.: Genetic algorithm for clustering with an ordered representation. In: Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 408-415 (1991)
13. Slonim, N., Atwal, G. S., Tkacik, G., Bialek, W.: Information-based clustering. Proc. Natl. Acad. Sci. USA 102 (51), 18297-18302 (2005)
14. Tan, M. P., Broach, J. R., Floudas, C. A.: A novel clustering approach and prediction of optimal number of clusters: global optimum search with enhanced positioning. J. Glob. Optim. 39 (3), 323-346 (2007)
15. Tan, M. P., Broach, J. R., Floudas, C. A.: Evaluation of normalization and pre-clustering issues in a novel clustering approach: global optimum search with enhanced positioning. J. Bioinform. Comput. Biol. 5 (4), 895-913 (2007)
16. Tan, M. P., Smith, E. R., Broach, J. R., Floudas, C. A.: Microarray data mining: a novel optimization-based approach to uncover biologically coherent structures. BMC Biol. 9, 268-283 (2008)
17. Busygin, S., Prokopyev, O. A., Pardalos, P. M.: An optimization based approach for data classification. Optim. Methods Softw. 22 (1), 3-9 (2007)
18. Lenstra, J. K.: Clustering a data array and the traveling-salesman problem. Oper. Res. 22 (2), 413-414 (1974)
19. Lenstra, J. K., Rinnooy Kan, A. H. G.: Some simple applications of the traveling-salesman problem. Oper. Res. Q 26 (4), 717-733 (1975)
20. Alpert, C. J., Kahng, A. B.: Splitting an ordering into a partition to minimize diameter. J. Classif. 14, 51-74 (1997)
21. Climer, S., Zhang, W.: Rearrangement clustering: pitfalls, remedies, and applications. J. Mach. Learn. Res. 7, 919-943 (2006)
22. Turner, H. L., Bailey, T. C., Krzanowski, W. J., Hemingway, C. A.: Biclustering models for structured microarray data. IEEE/ACM Trans. Comput. Biol. Bioinform. 2 (4), 316-329 (2005)
23. Cheng, Y., Church, G. M.: Biclustering of expression data. In: Proc. ISMB 2000, pp. 93-103 (2000)
24. Reiss, D. J., Baliga, N. S., Bonneau, R.: Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks. BMC Bioinform. 7, 280-302 (2006)
25. Kluger, Y., Basri, R., Chang, J. T., Gerstein, M.: Spectral biclustering of microarray data: coclustering genes and conditions. Genome Res. 13, 703-716 (2003)
26. Prelic, A., Bleuler, S., Zimmermann, P., Wille, A., Buhlmann, P., Gruissem, W., Hennig, L., Thiele, L., Zitzler, E.: A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics 22 (9), 1122-1129 (2006)
27. Tanay, A., Sharan, R., Shamir, R.: Discovering statistically significant biclusters in gene expression data. Bioinformatics 18, S136-S144 (2002)
28. Yoon, S., Nardini, C., Benini, L., De Micheli, G.: Discovering coherent biclusters from gene expression data using zero-suppressed binary decision diagrams. IEEE/ACM Trans. Comput. Biol. Bioinform. 2 (4), 339-354 (2005)
29. Bleuler, S., Prelic, A., Zitzler, E.: An EA framework for biclustering of gene expression data. In: IEEE Congress on Evolutionary Computation, pp. 166-173 (2004)
30. Divina, F., Aguilar, J.: Biclustering of expression data with evolutionary computation. Trans. Knowl. Data Eng. 18 (5), 590-602 (2006)
31. 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) (Pubitemid 41205694)
32. Ford, L. R., Fulkerson, D. R.: Flows in Networks. Princeton University Press, Princeton (1962)
33. Floudas, C. A., Grossmann, I. E.: Synthesis of flexible heat exchanger networks with uncertain flowrates and temperatures. Comput. Chem. Eng. 11 (4), 319-336 (1987)
34. Ciric, A. R., Floudas, C. A.: A retrofit approach for heat-exchanger networks. Comput. Chem. Eng. 13 (6), 703-715 (1989)
35. Floudas, C. A., Anastasiadis, S. H.: Synthesis of distillation sequences with several multicomponent feed and product streams. Chem. Eng. Sci. 43 (9), 2407-2419 (1988)
36. Kokossis, A. C., Floudas, C. A.: Optimization of complex reactor networks-II: nonisothermal operation. Chem. Eng. Sci. 49 (7), 1037-1051 (1994)
37. Aggarwal, A., Floudas, C. A.: Synthesis of general separation sequences-nonsharp separations. Comput. Chem. Eng. 14 (6), 631-653 (1990)
38. CPLEX.: ILOG CPLEX 9.0 User's Manual (2005)
39. Applegate, D. L., Bixby, R. E., Chvatal, V., Cook, W. J.: The traveling salesman problem: a computational study. Princeton University Press, Princeton (2007)
40. Brauer, M. J., Yuan, J., Bennett, B., Lu, W., Kimball, E., Bostein, D., Rabinowitz, J. D.: Conservation of the metabolomic response to starvation across two divergent microbes. Proc. Natl. Acad. Sci. USA 103, 19302-19307 (2006)
41. Ihmels, J., Friedlander, G., Bergmann, S., Sarig, O., Ziv, Y., Barkai, N.: Revealing modular organization in the yeast transcriptional network. Nat. Genet. 31, 370-377 (2002)
42. Ben-Dor, A., Chor, B., Karp, R., Yakhini, Z.: Discovering local structure in gene expression data: the order-preserving submatrix problem. In: Proceedings of the Sixth Annual International Conference on Computational Biology (RECOMB 2002), Washington, DC, USA, pp. 49-57 (2002)
43. Grothaus, G. A., Mufti, A., Murali, T. M.: Automatic layout and visualization of biclusters. Algorithms Mol. Biol. 1, 1-15 (2006)
44. Androulakis, I. P., Maranas, C. D., Floudas, C. A.: Prediction of oligopeptide conformations via deterministic global optimization. J. Glob. Optim. 11, 1-34 (1997)
45. Klepeis, J. L., Floudas, C. A.: Free energy calculations for peptides via deterministic global optimization. J. Chem. Phys. 110, 7491-7512 (1999)
46. Klepeis, J. L., Floudas, C. A., Morikis, D., Lambris, J. D.: Predicting peptide structures using NMR data and deterministic global optimization. J. Comput. Chem. 20 (13), 1354-1370 (1999)
47. Klepeis, J. L., Floudas, C. A.: Ab initio tertiary structure prediction of proteins. J. Glob. Optim. 25, 113-140 (2003)
48. Klepeis, J. L., Floudas, C. A.: ASTRO-FOLD: a combinatorial and global optimization framework for ab initio prediction of three-dimensional structures of proteins from the amino acid sequence. Biophys. J. 85, 2119-2146 (2003)
49. Klepeis, J. L., Floudas, C. A., Morikis, D., Tsokos, C. G., Argyropoulos, E., Spruce, L., Lambris, J. D.: Integrated computational and experimental approach for lead optimization and design of compstatin variants with improved activity. J. Am. Chem. Soc. 125 (28), 8422-8423 (2003)
50. Fung, H. K., Floudas, C. A., Taylor, M. S., Zhang, L., Morikis, D.: Towards full sequence de novo protein design with flexible templates for human beta-defensin-2. Biophys. J. 94, 584-599 (2008)
51. Lin, X., Floudas, C. A.: Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation. Comput. Chem. Eng. 25, 665-674 (2001)
52. Janak, S. L., Lin, X., Floudas, C. A.: Enhanced continuous-time unit-specific event based formulation for short-term scheduling of multipurpose batch processes: resource constraints and mixed storage policies. Ind. Eng. Chem. Res. 43, 2516-2533 (2004)