An efficient multi-objective learning algorithm for RBF neural network

Neurocomputing

Volumn 73, Issue 16-18, 2010, Pages 2799-2808

  Kokshenev, Illya ^a   Padua Braga, Antonio ^a  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Model selection; Multi objective learning; Pareto optimality; Radial basis functions; Regularization

Indexed keywords

MODEL SELECTION; MULTI OBJECTIVE; PARETO-OPTIMALITY; RADIAL BASIS FUNCTIONS; REGULARIZATION;

LEARNING ALGORITHMS; LEARNING SYSTEMS; NEURAL NETWORKS; PARETO PRINCIPLE; RADIAL BASIS FUNCTION NETWORKS;

MULTIOBJECTIVE OPTIMIZATION;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BAYESIAN LEARNING; CLASSIFICATION ALGORITHM; CRITERION RELATED VALIDITY; KERNEL METHOD; LEARNING ALGORITHM; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONLINEAR SYSTEM; PREDICTION; PRIORITY JOURNAL; PROCESS OPTIMIZATION; QUALITY CONTROL; RADIAL BASED FUNCTION; VALIDATION PROCESS;

EID: 78649974166     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.06.022     Document Type: Article

References (40)

1. Vapnik V.N. The Nature of Statistical Learning Theory 1995, Springer Verlag, New York.
2. Geman S., Bienenstock E., Doursat R. Neural network and the bias/variance dilemma. Neural Computation 1992, 4:1-58.
3. Vapnik V.N., Chervonenkis A.Y. Theory of Pattern Recognition 1974, Nauka, Moscow, (in Russian).
4. Y. Jin (Ed.), Multi-Objective Machine Learning, Series: Studies in Computational Intelligence, vol. 16, Springer Verlag, Heidelberg, 2006.
5. Fonseca C.M., Fleming P.J. An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation 1995, 3(1):1-16.
6. T. Hanne, Global multiobjective optimization using evolutionary algorithms, Journal of Heuristics 6 (3) (2000) 347-360.
7. Jin Y., Sendhoff B. Pareto-based multi-objective machine learning: an overview and case studies. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 2008, 38(3):397-415.
8. Liu G., Kadirkamanathan V. Learning with multi-objective criteria. Fourth International Conference on Artificial Neural Networks 1995, 53-58.
9. Jin Y., Okabe T., Sendhoff B. Neural network regularization and ensembling using multi-objective evolutionary algorithms. Evolutionary Computation, CEC2004 2004, 1:1-8.
10. Yen G.G. Multi-objective evolutionary algorithm for radial basis function neural network design. Multi-Objective Machine Learning, Studies in Computational Intelligence 2006, vol. 16:221-239. Springer.
11. V. Bevilacqua, G. Mastronardi, F. Menolascina, P. Pannarale, A. Pedone, A novel multi-objective genetic algorithm approach to artificial neural network topology optimisation: the breast cancer classification problem, in: International Joint Conference on Neural Networks (IJCNN'06), Vancouver, 2006, pp. 1958-1965.
12. Kondo N., Hatanaka T., Uosaki K. Pattern classification via multi-objective evolutionary RBF networks ensemble. International Joint Conference on SICE-ICASE 2006 2006, 137-142. DOI: 10.1109/SICE.2006.315388.
13. Teixeira R.A., Braga A.P., Takahashi R.H.C., Saldanha R.R. Improving generalization of MLPs with multi-objective optimization. Neurocomputing 2000, 35:189-194.
14. Costa M.A., Braga A., Menezes B.R., Teixeira R.A., Parma G.G. Training neural networks with a multi-objective sliding mode control algorithm. Neurocomputing 2003, 51:467-473.
15. Braga A.P., Takahashi R.H.C., Costa M.A., Teixeira R.A. Multi-objective algorithms for neural-networks learning. Multi-Objective Machine Learning, Series: Studies in Computational Intelligence 2006, vol. 16:151-171. Springer Verlag, Heidelberg.
16. Kokshenev I., Braga A.P. A multi-objective approach to RBF network learning. Neurocomputing 2008, 71(7-9):1203-1209.
17. Chankong V., Haimes Y. Multiobjective Decision Making: Theory and Methodology 1983, Elsevier Science, New York.
18. Ehrgott M. Multicriteria Optimization 2005, Springer, Berlin, Heidelberg.
19. Geoffrion A. Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications 1968, 22:618-630.
20. Tikhonov A.N., Arsenin V.Y. Solutions of Ill-Posed Problems 1977, Wiley, New York.
21. Girosi F., Jones M., Poggio T. Regularization theory and neural networks architectures. Neural Computation 1995, 7(2):219-269.
22. Buhmann M.D., Powell M.J.D. Radial basis function interpolation on an infinite regular grid. Algorithms for Approximation II 1988, 146-169. Clarendon Press, Oxford. M. Cox, J. Mason (Eds.).
23. Poggio T., Girosi F. Networks for approximation and learning. Proceedings of the IEEE 1990.
24. Tibshirani R. Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society 1996, 58(1):267-288.
25. Efron B., Hastie T., Johnstone I., Tibshirani R. Least angle regression. Annals of Statistics 2004, 32:407-499.
26. Park M.Y., Hastie T. L1-regularization path algorithm for generalized linear models. Journal of the Royal Statistical Society 2007, 69(1):659-677.
27. Bjorck A. Numerical Methods for Least Squares Problems 1996, SIAM.
28. J. Handl, J. Knowles, Exploiting the tradeoff-the benefits of multiple objectives in data clustering, in: Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 3410, Springer-Verlag, New York, 2005, pp. 547-560.
29. Gonzalez J., Rojas I., Ortega J., H., Fernandez F.J., Diaz A.F. Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE Transactions on Neural Networks 2003, 14(6):1478-1495.
30. S. Forrest (Ed.), Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization, 1993.
31. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 1974, 19(6):716-723.
32. G. Schwarz, Estimating the dimension of a model, Annals of Statistics 6 (1978) 461-464.
33. Burnham K.P., Anderson R.D. Model Selection and Inference: A Practical Information Theoretic Approach 1998, Springer-Verlag, New York.
34. Zou H., Hastie T., Tibshirani R. On the "degrees of freedom" of the LASSO. Annals of Statistics 2007, 35(5):2173-2192.
35. Lang K., Witbrock M. Learning to tell two spirals apart. Proceedings of the Connectionist Models Summer School 1988, Morgan Kaufmann.
36. M.J.L. Orr, Recent advances in radial basis function networks, Technical Report Institute for Adaptive and Neural Computation, 1999. http://www.ed.ac.uk/mjo/papers/recad.ps.
37. A. Asuncion, D. Newman, UCI machine learning repository, URL: 2007. http://www.ics.uci.edu/~mlearn/MLRepository.html.
38. L. Prechelt, Proben1: A set of neural network benchmark problems and benchmarking rules, Technical Report 21/94, URL: 1994. http://citeseer.ist.psu.edu/prechelt94proben.html.
39. Meyer D., Leisch F., Hornik K. The support vector machine under test. Neurocomputing 2003, 55(1-2):169-186.
40. C.-C. Chang, C.-J. Lin, LIBSVM: a library for support vector machines, Software available at: 2001. http://www.csie.ntu.edu.tw/cjlin/libsvm.