Block clustering based on difference of convex functions (DC) programming and DC algorithms

Neural Computation

Volumn 25, Issue 10, 2013, Pages 2776-2807

  Le, Hoai Minh ^a   Thi, Hoai An Le ^a   Dinh, Tao Pham ^b   Huynh, Van Ngai ^c  

^a UNIVERSITÉ DE LORRAINE   (France)

^b Avenue de l Université 76801 Saint Etienne du Rouvray   (France)

^c UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; BRAIN TUMOR; CLUSTER ANALYSIS; COMPUTER PROGRAM; COMPUTER SIMULATION; FACTUAL DATABASE; FUZZY LOGIC; HUMAN; LUNG TUMOR; NEOPLASM; PATHOLOGY; PROBLEM SOLVING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BRAIN NEOPLASMS; CLUSTER ANALYSIS; COMPUTER SIMULATION; DATABASES, FACTUAL; FUZZY LOGIC; HUMANS; LUNG NEOPLASMS; NEOPLASMS; PROBLEM SOLVING; SOFTWARE;

EID: 84887377768     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00490     Document Type: Article

References (37)

1. Banfield, J. D., & Raftery, A. E. (1993). Model-based gaussian and non gaussian clustering. Biometrics, 49, 803-821.
2. Bezdek, J. C. (1973). Fuzzy mathematics in pattern classification. Unpublished doctoral dissertation, Cornell University, Ithaca, NY.
3. Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithm. New York: Plenum Press.
4. Bhattacharjee, A., Richards, W. G., Staunton, J., Li, C., Monti, S., Vasa, P., et al. (2001). Classification of human lung carcinomas by mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proc. Natl. Acad. Sci. USA, 98(24), 13790-13795.
5. Bradley, B. S., & Mangasarian, O. L. (1998). Feature selection via concave minimization and support vector machines. In J. Shavlik (Ed.), Machine Learning Proceedings of the Fifteenth International Conferences (pp. 82-90). San Francisco: Morgan Kaufmann.
6. Celeux, G., & Govaert, G. (1992). A classification EM algorithm for clustering and two stochastic versions. Comput. Statist. Data Anal., 14(3), 315-332.
7. Celeux, G., & Govaert, G. (1993). Comparison of the mixture and the classification maximum likelihood in cluster analysis. J. Stat. Comput. Simul., 47, 127-146.
8. Collobert, R., Sinz, F., Weston, J., & Bottou, L. (2006). Trading convexity for scalability. In Proceedings of the 23rd International Conference on Machine Learning. NewYork: ACM.
9. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39(1), 1-38.
10. Govaert, G., & Nadif, M. (2003). Clustering with block mixture models. Pattern Recognition, 36, 463-473.
11. Govaert, G., & Nadif, M. (2008). Block clustering with Bernoulli mixture models: Comparison of different approaches. Computational Statistics and Data Analysis, 52, 3233-3245.
12. Hartigan, J. A. (1975). Clustering algorithms. NewYork: Wiley.
13. Krause, N., & Singer, Y. (2004). Leveraging the margin more carefully. In Proceedings of the International Conference on Machine Learning ICML'04. San Mateo, CA: Morgan Kaufmann.
14. Le Thi, H. A. (N.d.). DC Programming and DCA. http://lita.sciences.univ-metz.fr/lethi.
15. Le Thi, H. A. (1997). Contributiona l'optimisation non convexe et l'optimisation globale: Théorie, algorithmes et applications. Habilitationa Diriger des Recherches, Universite de Rouen.
16. Le Thi, H. A., Belghiti, T., & Pham Dinh, T. (2006). A new efficient algorithm based on DC programming and DCA for clustering. Journal of Global Optimization, 37, 593-608.
17. Le Thi, H. A., Le, H. M., Nguyen, V. V., & Pham Dinh, T. (2008). A DC programming approach for feature selection in support vector machine learning. Journal of Advances in Data Analysis and Classification, 2(3), 259-278.
18. Le Thi, H. A., Le, H. M., & Pham Dinh, T. (2006). Optimization based DC programming andDCAfor hierarchical clustering. European Journal ofOperational Research, 183, 1067-1085.
19. Le Thi, H. A., Le, H. M., & Pham Dinh, T. (2007). Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms. Journal of Advances in Data Analysis and Classification, 2, 1-20.
20. Le Thi, H. A., Nguyen, V. V., & Ouchani, S. (2008). Gene selection for cancer classification using DCA. In Proceedings of the 4th International Conference on Advanced Data Mining and Classification (pp. 62-72). New York: Springer-Verlag.
21. Le Thi, H. A., & Pham Dinh, T. (1997). Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. Journal of Global Optimization, 11(3), 253-285.
22. Le Thi, H. A., & Pham Dinh, T. (2005). The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research, 133, 23-46.
23. Le Thi, H. A., Pham Dinh, T., & Huynh, V. N. (2012). Exact penalty techniques in DC programming. Journal of Global Optimization, 52(3), 509-535.
24. Liu, Y., & Shen, X. (2006). Multicategory ψ-learning. Journal of the American Statistical Association, 101, 500-509.
25. Liu, Y., Shen, X., & Doss, H. (2005). Multicategory ψ-learning and support vector machine: Computational tools. Journal of Computational and Graphical Statistics, 14, 219-236.
26. Mechelen, V., Bock, H. H., & De Boeck, P. (2004). Two-mode clustering methods: A structured overview. Statistical Methods in Medical Research, 13, 363-394.
27. Neumann, J., Schnörr, C., & Steidl, G. (2004). SVM-based feature selection by direct objective minimisation. In Proc. of 26th DAGM Symposium (pp. 212-219). New York: Springer-Verlag.
28. Nutt, C. L., Mani, D. R., Betensky, R. A., Tamayo, P., Cairncross, J. G., Ladd, C., et al. (2003). Gene expression-based classification ofmalignant gliomas correlates better with survival than histological classification. Cancer Res., 63(7), 1602-1607.
29. Ong, C. S., & Le Thi, H. A. (2011). Learning with sparsity by difference of convex functions algorithm. J. Optimization Methods and Software. doi:10.1080/10556788.2011.652630
30. Pham Dinh, T., & Le Thi, H. A. (1998). DC optimization algorithms for solving the trust region subproblem. SIAM J. Optimization, 8, 476-505.
31. Pomeroy, S. L., Tamayo, P., Gaasenbeek, M., Sturla, L. M, Angelo, M., McLaughlin, M. E., et al. (2002). Prediction of central nervous system embryonal tumour outcome based on gene expression. Nature, 415, 436-442.
32. Ramaswamy, S., Tamayo, P., Rifkin, R., Mukherjee, S., Yeang, C. H., Angelo, M., et al. (2001). Multiclass cancer diagnosis using tumor gene expression signatures. Proc. Natl. Acad. Sci. USA, 98, 15149-15154.
33. Rosmalen, J. V., Groenen, P. J. F., Trejos, J., & Castillo, W. (2005). Global optimization strategies for two-mode clustering (Rep., EI-2005-33). Econometric Institute.
34. Shen, X., Tseng, G. C., Zhang, X., & Wong, W. H. (2003). ψ-learning. Journal of American Statistical Association, 98, 724-734.
35. Symons, M. J. (1981). Clustering criteria and multivariate normal mixtures. Biometrics, 37, 35-43.
36. Weber, S., Schüle, T., & Schnörr, C. (2005). Prior learning and convex-concave regularization of binary tomography. Electr. Notes in Discr. Math., 20, 313-327.
37. Yuille, A. L., & Rangarajan, A. (2002). The convex concave procedure (CCCP). In T. G. Dietterich, S. Becker, & Z. Ghahramani (Eds.), Advances in neural information processing systems, 14. Cambridge, MA: MIT Press.