Skip to main content
SpringerLink
Log in
Book cover

Innovations in Hybrid Intelligent Systems pp 88–95Cite as

Combined Projection and Kernel Basis Functions for Classification in Evolutionary Neural Networks

  • Chapter

  • 1345 Accesses

Part of the book series: Advances in Soft Computing ((AINSC,volume 44))

Abstract

This paper describes a methodology for constructing the hidden layer of a feed forward network using a possible combination of different transfer projection functions (sigmoidal, product) and kernel functions (radial basis functions), where the architecture, weights and node typology is learnt using an evolutionary programming algorithm. The methodology proposed is tested using five benchmark classification problems from well-known machine intelligence problems. We conclude that combined functions are better than pure basis functions for the classification task in several datasets and that the combination of basis functions produces the best models in some other datasets.

This work has been partially subsidized by TIN 2005-08386-C05-02 projects of the Spanish Inter-Ministerial Commission of Science and Technology (MICYT) and FEDER funds. The research of P.A. Gutiérrez and J.C. Fernández has been backed respectively by the FPU a the FPI Predoctoral Programs (Spanish Ministry of Education and Science).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lippmann, R.P.: Pattern classification using neural net. IEEE Com. Mag., 27 (1989) 47–64

    Article  Google Scholar 

  2. Bishop, C.M.: Improving the generalization properties of radial basis function neural networks. Neural Computation, Vol. 3(4) (1991) 579–581

    Article  Google Scholar 

  3. Specht, D.F.: A General Regression Neural Network. IEEE Transactions on Neural Networks, Vol. 2(6) (1991) 568–576

    Article  Google Scholar 

  4. Durbin, R., Rumelhart, D.: Products Units: A computationally powerful and biologically plausible extension to backpropagation networks. Neural Computation, 1 (1989) 133–142

    Article  Google Scholar 

  5. Hervás, C., Martinez, F.J., Gutiérrez, P.A.: Classification by means of Evolutionary Product-Unit Neural Networks. International Joint Conference on Neural Networks (2006), Canada.

    Google Scholar 

  6. Friedman, J.H., Stuetzle, W.: Projection Pursuit Regression. J. Amer. Statist. Assoc., Vol. 76 (1981) 817–823

    Article  MathSciNet  Google Scholar 

  7. Donoho, D.L., Johnstone, I.M.: Projection based in approximation and a duality with kernel methods. Ann. Statist., Vol. 17 (1989) 58–106

    Article  MATH  MathSciNet  Google Scholar 

  8. Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press (1995).

    Google Scholar 

  9. Martínez-Estudillo, A.C., Martínez-Estudillo, F.J., Hervás-Martínez, C., et al.: Evolutionary Product Unit based Neural Networks for Regression, Neural Networks, 19,4 (2006) 477–486

    Article  MATH  Google Scholar 

  10. Coen, S. y Intrator, N.: Global Optimization of RBF Networks. Technical report, School of Computer Science, Tel-Aviv University (2000)

    Google Scholar 

  11. Angeline, P. J., Saunders, G. M., Pollack, J. B.: An evolutionary algorithm that constructs recurrent neural networks. IEEE Transactions on Neural Networks, Vol. 5(1) (1994) 54–65

    Article  Google Scholar 

  12. Miller, R.G.: Simultaneous Statistical Inference. 2nd edn. Wiley, New York (1981)

    MATH  Google Scholar 

  13. Snedecor, G.W., Cochran, W.G.: Statistical Methods. Iowa State University Press (1980)

    Google Scholar 

  14. Miller, R.G.: Beyond ANOVA, Basics of App. Statistics. Chapman & Hall, London (1996)

    Google Scholar 

  15. Levene, H.: In Contributions to Probability and Statistics. Chapter: Essays in Honor of Harold Hotelling. Stanford University Press (1960) 278–292

    Google Scholar 

  16. Tamhane, A.C., Dunlop, D.D.: Statistics and Data Analysis. Prentice Hall (2000)

    Google Scholar 

  17. Landwehr, N., Hall, M. et al.: Logistic Model Trees. Machine Learning, 59 (2005) 161–205

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing and Numerical Analysis of the University of Córdoba, Campus de Rabanales, 14071, Córdoba, Spain

    P. A. Gutiérrez, C. Hervás & J. C. Fernández

  2. Department of Management and Quantitative Methods, ETEA, Escritor Castilla Aguayo 4, 14005, Córdoba, Spain

    M. Carbonero

Authors
  1. P. A. Gutiérrez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Hervás
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Carbonero
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. C. Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Escuela Politécnica Superior Campus Vena, Edifico C, Universidad de Burgos, C/Francisco de Vitoria s/n, 09006, Burgos, Spain

    Emilio Corchado

  2. Departamento de Informática y Automática Facultad de Ciencias, Universidad de Salamanca, Plaza de la Merced S/N, 37008, Salamanca, Spain

    Juan M. Corchado

  3. Centre for Quantifiable Quality of Service in Communication Systems (Q2S) Centre of Excellence, Norwegian University of Science and Technology, O.S. Bragstads plass 2E, 7491, Trondheim, Norway

    Ajith Abraham

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gutiérrez, P.A., Hervás, C., Carbonero, M., Fernández, J.C. (2007). Combined Projection and Kernel Basis Functions for Classification in Evolutionary Neural Networks. In: Corchado, E., Corchado, J.M., Abraham, A. (eds) Innovations in Hybrid Intelligent Systems. Advances in Soft Computing, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74972-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74972-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74971-4

  • Online ISBN: 978-3-540-74972-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation