CO\(^2\)RBFN-CS: First Approach Introducing Cost-Sensitivity in the Cooperative-Competitive RBFN Design

  • María Dolores Pérez-Godoy
  • Antonio Jesús Rivera
  • Francisco Charte
  • Maria Jose del Jesus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9094)

Abstract

The interest in dealing with imbalanced datasets has grown in the last years, since they represent many real world scenarios. Different methods that address imbalance problems can be classified into three categories: data sampling, algorithmic modification and cost-sensitive learning. The fundamentals of the last methodology is to assign higher costs to wrong classification classes with the aim of reducing higher cost errors.

In this paper, CO\(^2\)RBFN-CS, a cooperative-competitive Radial Basis Function Network algorithm that implements cost-sensitivity is presented. Specifically, a cost parameter is introduced in the training stage of the algorithm. This parameter modifies the learning rate of the weights taking into account the right (or wrong) classification of the instance, the type of class (majority or minority) and the imbalance ratio of the data set.

Keywords

RBFNs Imbalanced data sets Cost sensitive 

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References

  1. 1.
    Alcalá-Fdez, J., Fernández, A., Luengo, J., Derrac, J., García, S., Sánchez, L., Herrera, F.: Keel data-mining software tool: Data set repository, integration of algorithms and experimental analysis framework. J. of Mult.-Valued Logic & Soft Computing 17, 255–287 (2011)Google Scholar
  2. 2.
    Alexandridis, A., Chondrodima, E., Sarimveis, H.: Radial basis function network training using a nonsymmetric partition of the input space and particle swarm optimization. IEEE Transactions on Neural Networks and Learning Systems 24(2), 219–230 (2013)CrossRefGoogle Scholar
  3. 3.
    Barandela, R., Sánchez, J.S., García, V., Rangel, E.: Strategies for learning in class imbalance problems. Pattern Recognition 36(3), 849–851 (2003)CrossRefGoogle Scholar
  4. 4.
    Bradford, J.P., Kunz, C., Kohavi, R., Brunk, C., Brodley, C.E.: Pruning decision trees with misclassification costs. In: Proceedings of the the 10th European Conference on Machine Learning (ECML 1998), pp. 131–136 (1998)Google Scholar
  5. 5.
    Broomhead, D., Lowe, D.: Multivariable functional interpolation and adaptive networks. Complex Systems 2, 321–355 (1988)MATHMathSciNetGoogle Scholar
  6. 6.
    Buchtala, O., Klimek, M., Sick, B.: Evolutionary optimization of radial basis function classifiers for data mining applications. IEEE Transactions on System, Man, and Cybernetics, B 35(5), 928–947 (2005)CrossRefGoogle Scholar
  7. 7.
    Chawla, N.V., Japkowicz, N., Kolcz, A.: Special issue on learning from imbalanced data sets. SIGKDD Explorations Newsletter 6(1), 1–6 (2004)CrossRefGoogle Scholar
  8. 8.
    Chen, H., Kong, L., Leng, W.: Numerical solution of pdes via integrated radial basis function networks with adaptive training algorithm. Applied Soft Computing 11, 856–860 (2011)Google Scholar
  9. 9.
    Domingos, P.: Metacost: a general method for making classifiers cost sensitive. In: Proceedings of the 5th International Conference on Knowledge Discovery and Data Mining, pp. 155–164 (1999)Google Scholar
  10. 10.
    Du, H., Zhang, N.: Time series prediction using evolving radial basis function networks with new enconding scheme. Neurocomputing 71, 1388–1400 (2008)CrossRefGoogle Scholar
  11. 11.
    Fernández, A., del Jesus, M.J., Herrera, F.: Hierarchical fuzzy rule based classification system with genetic rule selection for imbalanced data-set. International Journal of Approximate Reasoning 50, 561–577 (2009)MATHCrossRefGoogle Scholar
  12. 12.
    Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association 32, 675–701 (1937)CrossRefGoogle Scholar
  13. 13.
    García, S., Fernández, A., Luengo, J., Herrera, F.: Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Information Sciences 180, 2044–2064 (2010)CrossRefGoogle Scholar
  14. 14.
    Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)Google Scholar
  15. 15.
    Harpham, C., Dawson, C.W., Brown, M.R.: A review of genetic algorithms applied to training radial basis function networks. Neural Computing and Applications 13, 193–201 (2004)CrossRefGoogle Scholar
  16. 16.
    He, Z.M.: Cost-sensitive steganalysis with stochastic sensitvity and cost sensitive training error. Proceedings of the International Conference on Machine Learning and Cybernetics 1, 349–354 (2012)Google Scholar
  17. 17.
    Hochberg, Y.: A sharper bonferroni procedure for multiple tests of significance. Biometrika 75(4), 800–802 (1988)MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    C. X. Ling, Q. Yang, J. Wang, and S. Zhang. Decision trees with minimal costs. In: Proceedings of the 21st International Conference on Machine Learning (ICML 2004), vol. 69, pp. 544–551 (2004)Google Scholar
  19. 19.
    López, V., Fernández, A., García, S., Palade, V., Herrera, F.: An insight into classiffcation with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Information Sciences 250, 113–141 (2013)CrossRefGoogle Scholar
  20. 20.
    Mandani, E., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7(1), 1–13 (1975)CrossRefGoogle Scholar
  21. 21.
    Moody, J., Darken, C.J.: Fast learning in networks of locally-tuned processing units. Neural Computation 1, 281–294 (1989)CrossRefGoogle Scholar
  22. 22.
    Niu, H.L., Wang, J.: Financial time series prediction by a random data-time effective RBF neural network. Soft Computing 18(3), 497–508 (2014)CrossRefGoogle Scholar
  23. 23.
    Pérez-Godoy, M.D., Fernández, A., Rivera, A.J., del Jesus, M.J.: Analysis of an evolutionary RBFN design algorithm, CO\(^2\)RBFN, for imbalanced data sets. Pattern Recognition Letters 31(15), 2375–2388 (2010)CrossRefGoogle Scholar
  24. 24.
    Pérez-Godoy, M.D., Rivera, A.J., Carmona, C.J., del Jesus, M.J.: Training algorithms for radial basis function networks to tackle learning processes with imbalanced data-sets. Applied Soft Computing 25, 26–39 (2014)CrossRefGoogle Scholar
  25. 25.
    Pérez-Godoy, M.D., Rivera, A.J., del Jesus, M.J., Berlanga, F.J.: CO\(^2\)RBFN: An evolutionary cooperative-competitive RBFN design algorithm for classification problems. Soft Computing 14(9), 953–971 (2010)CrossRefGoogle Scholar
  26. 26.
    Qasem, S.N., Shamsuddin, S.M.: Memetic elitist pareto differential evolution algorithm based radial basis function networks for classification problems. Applied Soft Computing 11(8), 5565–5581 (2011)CrossRefGoogle Scholar
  27. 27.
    Rojas, I., Valenzuela, O., Prieto, A.: Statistical analysis of the main parameters in the definition of radial basis function networks. LNCS 1240, 882–891 (1997)Google Scholar
  28. 28.
    Tang, Y., Zhang, Y.-Q., Chawla, N.V., Krasser, S.: Svms modeling for highly imbalanced classification. IEEE Transactions on Systems Man and Cybernetics. PART B. Cybernetics 39(1), 281–288 (2009)Google Scholar
  29. 29.
    Ting, K.M.: An instance-weighting method to induce cost-sensitive trees. IEEE Transactions on Knowledge and Data Engineering 14(3), 659–665 (2002)CrossRefGoogle Scholar
  30. 30.
    Turney, P.D.: Cost-sensitive classification: empirical evaluation of a hybrid genetic decision tree induction algorithm. Journal of Artificial Intelligence Research 2, 369–409 (1995)Google Scholar
  31. 31.
    Veropoulos, K., Cristianini, N., Campbell, C.: Controlling the sensitivity of support vector machines. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 55–60 (1999)Google Scholar
  32. 32.
    Whitehead, B., Choate, T.: Cooperative-competitive genetic evolution of radial basis function centers and widths for time series prediction. IEEE Transactions on Neural Networks 7(4), 869–880 (1996)CrossRefGoogle Scholar
  33. 33.
    Widrow, B., Lehr, M.A.: 30 years of adaptive neural networks: perceptron, madaline and backpropagation. Proceedings of the IEEE 78(9), 1415–1442 (1990)CrossRefGoogle Scholar
  34. 34.
    Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics 1, 80–83 (1945)CrossRefGoogle Scholar
  35. 35.
    Zadrozny, B., Langford, J., Abe, N.: Costsensitive learning by costproportionateexample weighting. In: Proceedings of the 3rd IEEE International Conference on Data Mining (ICDM 2003), pp. 435–442 (2003)Google Scholar
  36. 36.
    Zhou, Z.H., Liu, X.Y.: Training cost-sensitive neural networks with methods addressing the class imbalance problem. IEEE Transactions on Knowledge Data Engineering 18(1), 63–77 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • María Dolores Pérez-Godoy
    • 1
  • Antonio Jesús Rivera
    • 1
  • Francisco Charte
    • 2
  • Maria Jose del Jesus
    • 1
  1. 1.Department of Computer ScienceUniversity of JaénJaénSpain
  2. 2.Department of Computer Science and Artificial InteligenceUniversity of GranadaGranadaSpain

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