Radial basis function networks in nonparametric classification and function learning

In this paper we apply normalized radial basis function networks to function learning and in nonparametric classification. A simple parameter learning technique is proposed and convergence and the rates of convergence of the empirically trained networks are studied theoretically and in computer experiments.

[1]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[2]  A. Barron.  Approximation and Estimation Bounds for Artificial Neural Networks , 1991, COLT '91.

[3]  中澤 真,et al.  Devroye, L., Gyorfi, L. and Lugosi, G. : A Probabilistic Theory of Pattern Recognition, Springer (1996). , 1997 .

[4]  Adam Krzyzak,et al.  Radial Basis Function Networks and Complexity Regularization in Function Learning , 2022 .

[5]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[6]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[7]  A. Krzyżak,et al.  On Radial Basis Function Net and Kernel Regression: Approximation Ability, Convergence Rate and Receptive Field Size , 1993, Proceedings. IEEE International Symposium on Information Theory.

[8]  J. Simonoff.  Smoothing Methods in Statistics , 1998 .

[9]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[10]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[11]  Adam Krzyzak,et al.  Nonparametric estimation and classification using radial basis function nets and empirical risk minimization , 1996, IEEE Trans. Neural Networks.

[12]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[13]  Tomaso A. Poggio,et al.  Regularization Theory and Neural Networks Architectures , 1995, Neural Computation.

[14]  Federico Girosi,et al.  On the Relationship between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions , 1996, Neural Computation.

[15]  Kurt Hornik,et al.  FEED FORWARD NETWORKS ARE UNIVERSAL APPROXIMATORS , 1989 .

[16]  John Fox,et al.  What Is Nonparametric Regression , 2000 .

[17]  Jooyoung Park,et al.  Approximation and Radial-Basis-Function Networks , 1993, Neural Computation.

[18]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[19]  Adam Krzyzak,et al.  On radial basis function nets and kernel regression: Statistical consistency, convergence rates, and receptive field size , 1994, Neural Networks.

[20]  Richard J. Mammone,et al.  Artificial neural networks for speech and vision , 1994 .