Abstract
Our aim is to propose a method for selecting a radial basis functions terms to be included into a neural net model. As it is frequently met in practice, we consider the case of a deficit in the admissible number of observations (learning sequence) in comparison with a much larger number of candidate terms. The proposed approach is based on a random sieve that aims at selecting only necessary RBF’s by a hierarchy of a large number of random mixing of candidate RBF’s and testing their significance. The results of simulations are also reported.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Bazan, M., Skubalska-Rafajłowicz, E.: A new method of centers location in Gaussian RBF interpolation networks. In: Rutkowski, L., et al. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 20–31. Springer, Heidelberg (2013)
Cook, R.D., Weisberg, S.: Partial one-dimensional regression models. Amer. Stat. 58, 110–116 (2004)
Donoho, D., Jin, J.: Higher criticism for detecting sparse heterogeneous mixtures. The Annals of Statistics 32, 962–994 (2004)
Fornberg, B., Larsson, E., Flyer, N.: Stable computations with Gaussian radial basis functions. SIAM J. Sci. Comput. 33(2), 869–892 (2011)
Fu, X., Wang, L.: Data dimensionality reduction with application to simplifying RBF network structure and improving classification performance. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics 33(3), 399–409 (2003)
Hansen, P.C.: Rank-deficient and discrete ill-posed problems. SIAM, Philadelphia (1998)
Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Computation 7(2), 219–269 (1995)
Gyorfi, L., Kohler, M., Krzyżak, A., Walk, H.: A Distribution-free Theory of Nonparametric Regression, ch. 21. Springer, Berlin (2000)
Konishi, S., Kitagawa, G.: Information Criteria and Statistical Modeling, Springer (2008)
Krzyżak, A., Linder, T.: Radial Basis Function Networks and Complexity Regularization in Function Learning. IEEE Trans. Neural Networks 9, 247–256 (1998)
Krzyżak, A., Rafajłowicz, E., Pawlak, M.: Moving average restoration of bandlimited signals from noisy observations. IEEE Transactions on Signal Processing 45, 2967–2976 (1997)
Leonardisa, A., Bischof, H.: An efficient MDL-based construction of RBF networks. Neural Networks 11, 963–973 (1998)
Lewis, S.M., Dean, A.M.: Detection of interactions in experiments on large numbers of factors (with discussion). Journal of the Royal Statistical Society, Series B 63, 633–672 (2001)
Morris, M.D.: An Overview of Group Factor Screening. In: Dean, A.M., Lewis, S.M. (eds.) Screening Methods for Experimentation in Industry, Drug Discovery, and Genetics, ch. 9, pp. 191–207. Springer, New York (2006)
Orr, M.J.: Regularization in the selection of basis function centers. Neural Computation 7(3), 606–623 (1995)
Rafajłowicz, E., Myszka, W.: Optimum experimental design for a regression on a hypercube-generalization of Hoel’s result. Annals of the Institute of Statistical Mathematics 40, 821–827 (1988)
Rafajłowicz, E., Pawlak, M.: Optimization of centers’ positions for RBF nets with generalized kernels. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 253–259. Springer, Heidelberg (2004)
Rafajłowicz, E., Skubalska-Rafajłowicz, E.: RBF nets based on equidistributed points. In: Proceedings of 9th IEEE Int. Conf.: Methods and Models in Automation and Robotics MMAR, pp. 921–926 (2003)
Rafajłowicz, E., Schwabe, R.: Halton and Hammersley sequences in multivariate nonparametric regression. Statistics and Probability Letters 76, 803–812 (2006)
Rutkowski, L.: Adaptive Probabilistic Neural Networks for Pattern Classification in Time-Varying Environment. IEEE Trans. Neural Networks 15(4), 811–827 (2004)
Rutkowski, L.: Generalized Regression Neural Networks in Time-Varying Environment. IEEE Trans. Neural Networks 15(3), 576–596 (2004)
Rutkowski, L.: New Soft Computing Techniques for System Modeling. Pattern Classification and Image Processing. Springer, Heidelberg (2004)
Seber, G.A.F.: Linear regression Analysis. Wiley, New York (1977)
Shaker, A.J., Prendergast, L.A.: Iterative application of dimension reduction methods. Electronic Journal of Statistics 5, 1471–1494 (2011)
Skubalska-Rafajłowicz, E.: Experiments with neural network for modeling of nonlinear dynamical systems: Design problems. Lecture presented at The Newton’s Mathematical Institute, Cambridge, DAE seminar led by D. Uciński (2011), www.newton.ac.uk/programmes/DAE/seminars/072010301.html
Skubalska-Rafajłowicz, E., Rafajłowicz, E.: Random projections in regression model selection and corresponding experiment design problems. To be presented at Model Oriented Data Analysis Conference, Lagów, Poland (June 2013)
Skubalska-Rafajłowicz, E.: Random projection RBF nets for multidimensional density estimation. International Journal of Applied Mathematics and Computer Science 18(4), 455–466 (2008)
Skubalska-Rafajłowicz, E.: Detection and estimation translations of large images using random projections. In: 7th International Workshop Multidimensional (nD) Systems (nDs), September 5-7 (2011)
Skubalska-Rafajłowicz, E.: Neural networks with sigmoidal activation functions–dimension reduction using normal random projection. Nonlinear Anal.: Theory, Methods & Appl. 71, e1255–e1263 (2009)
Skublska-Rafajłowicz, E., Rafajłowicz, E.: Sampling multidimensional signals by a new class of quasi-random sequences. Multidimensional System and Signal Processing 23, 237–253 (2012)
Weisberg S.: Applied Linear Regression. Wiley & Sons, Inc., Hoboken (2005)
Xu, L., Krzyżak, A., Yuille, A.: On radial basis function nets and kernel regression: statistical consistency, convergence, rates and receptive field size. Neural Networks 4, 609–628 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Skubalska-Rafajłowicz, E., Rafajłowicz, E. (2013). Random Sieve Based on Projections for RBF Neural Net Structure Selection. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-38658-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38657-2
Online ISBN: 978-3-642-38658-9
eBook Packages: Computer ScienceComputer Science (R0)