Abstract
Neural networks with radial basis activation functions are typically trained in two different phases: the first consists in the construction of the hidden layer, while the second consists in finding the output layer weights. Constructing the hidden layer involves defining the number of units in it, as well as their centers and widths. The training process of the output layer can be done using least squares methods, usually setting a regularization term. This work proposes an approach for building the whole network using information extracted directly from the projected training data in the space formed by the likelihoods functions. One can, then, train RBF networks for pattern classification with minimal external intervention.
Thanks to funding agencies CNPq, CAPES and FAPEMIG.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bartlett, P.L.: For valid generalization the size of the weights is more important than the size of the network. In: Advances in Neural Information Processing Systems, pp. 134–140 (1997)
Boser, B.E., Guyon, I.M., Vapnik, V.N.: A training algorithm for optimal margin classifiers. In: Proceedings of the Fifth Annual Workshop on Computational Learning Theory, COLT 1992, pp. 144–152. ACM, New York (1992). http://doi.acm.org/10.1145/130385.130401
Chen, S., Cowan, C.F., Grant, P.M.: Orthogonal least squares learning algorithm for radial basis function networks. EEE Trans. Neural Netw. 2(2), 302–309 (1991)
Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)
Demšar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7(Jan), 1–30 (2006)
Geman, S., Bienenstock, E., Doursat, R.: Neural networks and the bias/variance dilemma. Neural Comput. 4(1), 1–58 (1992)
Hess, K.R., et al.: Pharmacogenomic predictor of sensitivity to preoperative chemotherapy with paclitaxel and fluorouracil, doxorubicin, and cyclophosphamide in breast cancer. J. Clin. Oncol. 24(26), 4236–4244 (2006)
James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning, vol. 112. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4614-7138-7
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, pp. 281–297. University of California Press, Berkeley (1967)
Mao, K.: RBF neural network center selection based on fisher ratio class separability measure. IEEE Trans. Neural Netw. 13(5), 1211–1217 (2002)
Menezes, M., Torres, L., Braga, A.: Otimização da largura de kernels rbf para máquinas de vetores de suporte: Uma abordagem baseada em estimativa de densidades. In: XIII Congresso Brasileiro de Inteligência Computacional (2017)
Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Wiley, Hoboken (2010)
Oh, S.K., Kim, W.D., Pedrycz, W., Joo, S.C.: Design of K-means clustering-based polynomial radial basis function neural networks (pRBF NNs) realized with the aid of particle swarm optimization and differential evolution. Neurocomputing 78(1), 121–132 (2012)
Rosenblatt, M.: Remarks on some nonparametric estimates of a density function. Ann. Math. Stat. 27, 832–837 (1956)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis, vol. 26. CRC Press, Boca Raton (1986)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4757-3264-1
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Menezes, M., Torres, L.C.B., Braga, A.P. (2019). Learning Regularization Parameters of Radial Basis Functions in Embedded Likelihoods Space. In: Moura Oliveira, P., Novais, P., Reis, L. (eds) Progress in Artificial Intelligence. EPIA 2019. Lecture Notes in Computer Science(), vol 11805. Springer, Cham. https://doi.org/10.1007/978-3-030-30244-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-030-30244-3_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30243-6
Online ISBN: 978-3-030-30244-3
eBook Packages: Computer ScienceComputer Science (R0)