A novel clustering approach and prediction of optimal number of clusters: Global optimum search with enhanced positioning

Journal of Global Optimization

Volumn 39, Issue 3, 2007, Pages 323-346

  Tan, Meng Piao ^a   Broach, James R ^b   Floudas, Christodoulos A ^a  

^a Princeton University   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Clustering; Microarray data; Optimization

Indexed keywords

ALGORITHMS; DATA STRUCTURES; DNA; GLOBAL OPTIMIZATION; INTEGER PROGRAMMING; MICROARRAYS; SEARCH ENGINES; YEAST;

DNA MICROARRAY HYBRIDIZATION; GENERALIZED BENDERS DECOMPOSITION; LINEAR PROGRAMMING PROBLEM; MIXED-INTEGER LINEAR PROGRAMMING PROBLEM;

CLUSTER ANALYSIS;

EID: 35148890644     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-007-9140-6     Document Type: Article

References (68)

1. Adams W.P. and Sherali H.D. (1990). Linearization strategies for a class of zero-one mixed integer programming problems. Operat. Res. 38(2): 217-226
2. Aggarwal A. and Floudas C.A. (1990). Synthesis of general separation sequences - nonsharp separations. Comput. Chem. Eng 14: 631-653
3. Beer M. and Tavazoie S. (2004). Predicting gene expression from sequence. Cell 117: 185-198
4. Bezdek J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York
5. Brooke A., Kendrick D. and Meeraus A. (1988). GAMS: A User's Guide. The Scientific Press, San Francisco, CA
6. Carpenter G. and Grossberg S. (1990). ART3: hierarchical search using chemical transmitters in self-organizing patterns recognition architectures. Neural Networks 3: 129-152
7. Ciric A.R. and Floudas C.A. (1989). A retrofit approach of heat exchanger networks. Comput. Chem. Eng 13: 703-715
8. Claverie J. (1999). Computational methods for the identification of differential and coordinated gene expression. Human Mol. Genet. 8: 1821-1832
9. Davis D.L. and Bouldin D.W. (1979). A cluster separation measure. IEEE Trans. Pattern Anal. Machine Intell. 1(4): 224-227
10. Dempster A.P., Laird N.M. and Rudin D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B. 39(1): 1-38
11. DeRisi J.L., Iyer V.R. and Brown P.O. (1997). Exploring the metabolic and genetic control of gene expression on a genomic scale. Science 278: 680-686
12. Dhillon, I.S., Guan, Y.: Information theoretic clustering of sparse co-occurrence data. Proceedings of the Third IEEE International Conference on Data Mining (ICDM) (2003)
13. Dunn J.C. (1973). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybernet. 3: 32-57
14. Dunn J.C. (1974). Well separated clusters and optimal fuzzy partitions. J. Cybernet. 4: 95-104
15. Duran M.A. and Odell P.L. (1974). Cluster Analysis: A Survey. Springer Verlag, New York
16. Eisen M.B., Spellman P.T., Brown P.O. and Botstein D. (1998). Cluster analysis and display of genome-wide expression patterns. Proc. Nat. Acad. Sci. U.S.A. 95(25): 14863-14868
17. Floudas C.A., Akrotirianakis I.G., Caratzoulas S., Meyer C.A. and Kallrath J. (2005). Global optimization in the 21st Century: advances and challenges. Comput. Chem. Eng. 29: 1185-2002
18. Floudas, C.A. Deterministic Global Optimization: Theory, Algorithms, and Applications. Kluwer Academic Publishers (2000)
19. Floudas, C.A.: Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press (1995)
20. Floudas C.A., Aggarwal A. and Ciric A.R. (1989). Global optimum search for non convex NLP and MINLP problems. Comp. Chem. Eng. 13(10): 1117-1132
21. Floudas C.A. and Anastasiadis S.H. (1988). Synthesis of general distillation sequences with several multicomponent feeds and products. Chem. Eng. Sci. 43: 2407-2419
22. Floudas C.A. and Grossmann I.E. (1987). Synthesis of flexible heat exchanger networks with uncertain flow rates and temperatures. Comput. Chem. Eng 11: 319-336
23. Geoffrion A.M. (1973). Generalized benders decomposition. J. Optim. Theory Appl. 10(4): 237
24. Goodman L. and Kruskal W. (1954). Measures of associations for cross-validations. J. Am. Stat. Assoc. 49: 732-764
25. Gower J.C. and Ross G.J.S. (1969). Minimum spanning trees and single-linkage cluster analysis. Appl. Stat. 18: 54-64
26. Halkidi M., Batistakis Y. and Vazirgiannis M. (2002). Cluster validity methods: Part 1. SIGMOD record 31(2): 40-45
27. Hansen P. and Jaumard B. (1997). Cluster analysis and mathematical programming. Math. Program. 79: 191-215
28. Hartigan J.A. (1975). Clustering Algorithms. John Wiley & Sons, New York
29. Hartigan J.A. and Wong M.A. (1979). Algorithm AS 136: a K-means clustering algorithm. Appl. Stat. J. Roy. St. C. 28: 100-108
30. Herrero J., Valencia A. and Dopazo J. (2001). A hierarchical unsupervised growing neural network for clustering gene expression patterns. Bioinformatics 17(2): 126-136
31. Heyer L.J., Kruglyak S. and Yooseph S. (1999). Exploring expression data: identification and analysis of co-expressed genes. Genome Res. 9: 1106-1115
32. Hubert L. and Schultz J. (1976). Quadratic assignment as a general data-analysis strategy. Br. J. Math. Stat. Psychol. 29: 190-241
33. Jaccard P. (1912). The distribution of flora in the alpine zone. New Phytol. 11: 37-50
34. Jain A.K., Murty M.N. and Flynn P.J. (1999). Data clustering: a review. ACM Comput. Surv. 31(3): 264-323
35. Jain A.K. and Dubes R.C. (1988). Algorithms for Clustering Data. Prentice-Hall Advanced Reference Series, Prentice-Hall, Inc., Englewood Cliffs, New Jersey
36. Johnson, R.E.: The role of cluster analysis in assessing comparability under the US transfer pricing regulations. Business Economics (April 2001)
37. Jung Y., Park H., Du D. and Drake B.L. (2003). A decision criterion for the optimal number of clusters in hierarchical clustering. J. Global Optimiz. 25: 91-111
38. Kirkpatrick S., Gelatt C.D. and Vecchi M.P. (1983). Optimization by simulated annealing. Science 220(4598): 671-680
39. Kohonen T. (1984). Self Organization and Associative Memory. Springer Information Science Series, Springer Verlag, Berlin, Heidelberg, New York
40. Kohonen T. (1997). Self-Organizing Maps. Springer Verlag, Berlin
41. Kokossis A.C. and Floudas C.A. (1994). Optimization of complex reactor networks - II. Nonisothermal operation. Chem. Eng. Sci 49: 1037-1051
42. Leisch, F., Weingessel, A., Dimitriadou, E.: Competitive learning for binary valued data. In: Niklasson L., Bod'en M., Ziemke T. (eds.) Proceedings of the 8th International Conference on Artificial Neural Networks (ICANN 98), vol. 2, pp. 779-784. Skovde, Sweden, Springer (1998)
43. Likas A., Vlassis N. and Vebeek J.L. (2003). The global K-means clustering algorithm. Pattern Recogn. 36: 451-461
44. Lin X., Floudas C., Wang Y. and Broach J.R. (2003). Theoretical and computational studies of the glucose signaling pathways in yeast using global gene expression data. Biotechnol. Bioeng. 84(7): 864-886
45. Lukashin A.V. and Fuchs R. (2001). Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters. Bioinformatics 17(5): 405-414
46. McQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281-297 (1967)
47. Metropolis N., Rosenbluth A., Rosenbluth M., Teller A. and Teller E.J. (1953). Equations of State calculations by fast computing machines. J. Chem. Phys. 21: 1087-1091
48. Paules G.E. IV. and Floudas C.A. (1989). APROS: Algorithmic development methodology for discrete-continuous optimization problems. Oper. Res. J. 37: 902-915
49. Pauwels E.J. and Frederix G. (1999). Finding salient regions in images: non-parametric clustering for image segmentation and grouping. Comput. Vision Image Understand. 75: 73-85
50. Pipenbacher P., Schliep A., Schneckener S., Schonhuth A., Schomburg D. and Schrader R. (2002). ProClust: improved clustering of protein sequences with an extended graph-based approach. Bioinformatics 18(Suppl 2): S182-S191
51. Rand W.M. (1971). Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336): 846-850
52. Rousseeuw P.J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comp. App. Math 20: 53-65
53. Ruspini E.H. (1969). A new approach to clustering. Inf. Control 15: 22-32
54. Schneper L., Düvel K. and Broach J.R. (2004). Sense and sensibility: nutritional response and signal integration in yeast. Curr. Opin. Microbiol. 7(6): 624-630
55. Sherali H.D. and Desai J. (2005a). A global optimization RLT-based approach for solving the hard clustering problem. J. Global Optimiz. 32(2): 281-306
56. Sherali H.D. and Desai J. (2005b). A global optimization RLT-based approach for solving the fuzzy clustering approach. J. Global Optimiz. 33(4): 597-615
57. Slonim N., Atwal G.S., Tkačik G. and Bialek W. (2005). Information based clustering. Proc. Nat. Acad. Sci. U.S.A. 102(51): 18297-18302
58. Sokal R.R. and Michener C.D. (1958). A statistical method for evaluating systematic relationships. Univ. Kans. Sci. Bull. 38: 1409-1438
59. Sorlie T., Tibshirani R., Parker J., Hastie T., Marron J.S., Nobel A., Deng S., Johnsen H., Pesich R., Geisler S., Demeter J., Perou C.M., Lonning P.E., Brown P.O., Borresen-Dala A.L. and Botstein D. (2003). Repeated observations of breast tumor subtypes in independent gene expression data sets. Proc. Nat. Acad. Sci. U.S.A. 100: 8418-8423
60. Tishby, N., Pereira, F., Bialek, W.: The information bottleneck method; proceedings of the 37th annual allerton conference on communication. Control Comput. 368-377 (1999)
61. Troyanskaya O.G., Dolinski K., Owen A.B., Altman R.B. and Botstein D. (2003). A Bayesian framework for combining heterogeneous data sources for gene function prediction (in Saccharomyces cerevisiae). Proc. Nat. Acad. Sci. U.S.A. 100: 8348-8353
62. Wang Y., Pierce M., Schneper L., Guldal C.G., Zhang X., Tavazoie S. and Broach J.R. (2004). Ras and Gpa2 mediate one branch of a redundant glucose signaling pathway in yeast. Plos Biol. 2(5): 610-622
63. Weiler J., Gausepohl H., Hauser N., Jensen O.N. and Hoheisel J.D. (1997). Hybridization-based DNA screening on peptide nucleic acid (PNA) oligomer arrays. Nuclei Acids Res. 25: 2792-2799
64. Wu Z. and Leahy R. (1993). An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Trans. Pattern Recogn. Mach. Intell. 15(11): 1101-1113
65. Xu R. and Wunsch D. (2005). Survey of clustering algorithms. IEEE Trans. Neural Networks 16(3): 645-678
66. Zahn C.T. (1971). Graph theoretical methods for detecting and describing gestalt systems. IEEE Trans. Comput. C- 20: 68-86
67. Zhang, B., Hsu, M., Dayal, U.: K-Harmonic Means - A Data Clustering Algorithm. Hewlett-Packard Research Laboratory Technical Report (June 1999)
68. Zhang, B.: Generalized K-Harmonic Means: Boosting in Unsupervised Learning. Hewlett-Packard Research Laboratory Technical Report (October 2000)