A Clustering Based Procedure for Learning the Hidden Unit Parameters in Elliptical Basis Function Networks

  • Marilena Pillati
  • Daniela G. Calò
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Radial basis function (RBF) neural networks can be used for a wide range of applications as they can be regarded as universal approximators and their training is faster than that of multilayer perceptrons. A more general version of these neural networks are referred to as elliptical basis function (EBF) networks. In this paper a robust method for EBF parameter estimation is proposed, based on hyperellipsoidal clustering and on multivariate sign and rank concepts. A simulation study on a classification problem has shown that this method represents a valid learning scheme, particularly in presence of outlying data.


Radial Basis Function Radial Basis Function Network Hide Unit Gaussian Basis Function Spatial Median 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BISHOP, M.C. (1995): Neural Networks for Pattern Recognition, Clarendon Press, Oxford.Google Scholar
  2. CERIOLI, A. (2001): Elliptical Clusters and the K-means Algorithm. In: Book of Short Papers of Cladag 2001, Meeting of the Classification and Data Analysis Group of the Italian Statistical Society.Google Scholar
  3. LAY, S.R. and HWANG, J.N. (1993): Robust construction of Radial Basis Function Networks for classification, IEEE International Conference on Neural Networks, 1859–1864.Google Scholar
  4. MAO, J. and JAIN, A. K., (1996): A Self-Organizing Network for Hyperellipsoidal Clustering (HEC), IEEE Transactions on Neural Networks, 7, 16–29.CrossRefGoogle Scholar
  5. MOODY, J. and DARKEN, C.J. (1989): Fast Learning in Network of Locally-Tuned Processing Units, Neural Computation, 1, 281–294.CrossRefGoogle Scholar
  6. MUSAVI, M., AHMED, W., CHAN, K., FARIS, K. and HUMMELS, D. (1992): On the training of radial basis function classifiers, Neural Networks, 5, 595–603.CrossRefGoogle Scholar
  7. PILLATI, M. and CALO, D.G. (2001): A Robust Clustering Procedure for Centre Location in RBF Networks. In C. Provasi (Ed.): Modelli complessi e metodi computazionali intensivi per la stima e la previsione, Cleup Editrice, Padova.Google Scholar
  8. POGGIO, T. and GIROSI, F. (1990): Networks for approximation and learning, Proceeding of the IEEE, 78, 1481–1497.CrossRefGoogle Scholar
  9. RIPLEY, B.D. (1996): Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  10. SUNG, K. and POGGIO, T. (1998): Example-Based Learning for View-Based Human Face Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 39–51.CrossRefGoogle Scholar
  11. VISURI, S., KOIVUNEN, V. and OJA, H. (2000): Sign and Rank Covariance Matrices, Journal of Statistical Planning and Inference, 19, 557–575.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marilena Pillati
    • 1
  • Daniela G. Calò
    • 1
  1. 1.Dipartimento di Scienze statisticheUniversità di BolognaBolognaItaly

Personalised recommendations