Skip to main content
Top

2013 | OriginalPaper | Chapter

Canonical Duality for Radial Basis Neural Networks

Authors : Vittorio Latorre, David Yang Gao

Published in: Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Radial Basis Function Neural Networks (RBF NN) are a tool largely used for regression problems. The principal drawback of this kind of predictive tool is that the optimization problem solved to train the network can be non-convex. On the other hand Canonical Duality Theory offers a powerful procedure to reformulate general non-convex problems in dual forms so that it is possible to find optimal solutions and to get deep insights into the nature of the challenging problems. By combining the canonical duality theory with the RBF NN, this paper presents a potentially useful method for solving challenging problems in real-world applications.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Haykin S (1999) Neural networks, a comprehensive foundation. Prentice-Hall, PrenticeMATH Haykin S (1999) Neural networks, a comprehensive foundation. Prentice-Hall, PrenticeMATH
2.
go back to reference Buzzi C, Grippo L, Sciandrone M (2001) Convergent decomposition techniques for training RBF neural networks. Neural Comput 13:1891–1920CrossRefMATH Buzzi C, Grippo L, Sciandrone M (2001) Convergent decomposition techniques for training RBF neural networks. Neural Comput 13:1891–1920CrossRefMATH
3.
go back to reference Gao DY (2000) Duality principles in nonconvex systems: theory, methods, and applications. Kluwer Academic Publishers, Dordrecht Nonconvex Optimization and Its ApplicationsCrossRefMATH Gao DY (2000) Duality principles in nonconvex systems: theory, methods, and applications. Kluwer Academic Publishers, Dordrecht Nonconvex Optimization and Its ApplicationsCrossRefMATH
4.
go back to reference Gao DY, Ruan N, Pardalos PM (2011) Canonical dual solutions to sum of fourth-order polynomials minimization problems with applications to sensor network localization. In: Pardalos PM, Boginski V, Commander C (eds) Sensors: theory, algorithms and applications. Springer, New York Gao DY, Ruan N, Pardalos PM (2011) Canonical dual solutions to sum of fourth-order polynomials minimization problems with applications to sensor network localization. In: Pardalos PM, Boginski V, Commander C (eds) Sensors: theory, algorithms and applications. Springer, New York
5.
go back to reference Gao DY, Wu CZ (2012) On the triality theory for a quartic polynomial optimization problem. J Ind Manage Optim 8(1):229–242MathSciNetCrossRef Gao DY, Wu CZ (2012) On the triality theory for a quartic polynomial optimization problem. J Ind Manage Optim 8(1):229–242MathSciNetCrossRef
8.
go back to reference Gao DY (2009) Canonical duality theory: theory, method, and applications in global optimization. Comput Chem 33:1964–1972CrossRef Gao DY (2009) Canonical duality theory: theory, method, and applications in global optimization. Comput Chem 33:1964–1972CrossRef
9.
go back to reference Gao DY, Watson LT, Easterling DR, Thacker WI, Billups SC (2011) Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Optim Methods Softw. doi:10.1080/10556788.2011.641125 MATH Gao DY, Watson LT, Easterling DR, Thacker WI, Billups SC (2011) Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm. Optim Methods Softw. doi:10.​1080/​10556788.​2011.​641125 MATH
Metadata
Title
Canonical Duality for Radial Basis Neural Networks
Authors
Vittorio Latorre
David Yang Gao
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-37502-6_139

Premium Partner