Abstract
A variety of clustering algorithms have been applied to determine the internal structure of Radial Basis Function Neural Networks (RBFNNs). k-means algorithm is one of the most common choice for this task, although, like many other clustering algorithms, it needs to receive the number of prototypes a priori. This is a nontrivial procedure, mainly for real-world applications. An alternative is to use algorithms that automatically determine the number of prototypes. In this paper, we performed a multiobjective analysis involving three of these algorithms, which are: Adaptive Radius Immune Algorithm (ARIA), Affinity Propagation (AP), and Growing Neural Gas (GNG). For each one, the parameters that most influence the resulting number of prototypes composed the decision space, while the RBFNN RMSE and the number of prototypes formed the objective space. The experiments found that ARIA solutions achieved the best results for the multiobjective metrics adopted in this paper.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Guillén, A., Pomares, H., Rojas, I., González, J., Herrera, L.J., Rojas, F., Valenzuela, O.: Studying possibility in a clustering algorithm for RBFNN design for function approximation. Neural Computing and Applications 17 (1), 75–89 (2008)
MacQueen, J.B.: Some methods of classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
Yeung, D., Ng, W., Wang, D., Tsang, E., Wang, X.Z.: Localized Generalization Error Model and Its Application to Architecture Selection for Radial Basis Function Neural Network. IEEE Trans. on Neural Networks 18(5), 1294–1305 (2007)
Bezerra, G.B., Barra, T.V., de Castro, L.N., Von Zuben, F.J.: Adaptive Radius Immune Algorithm for Data Clustering. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 290–303. Springer, Heidelberg (2005)
Frey, B.J., Dueck, D.: Clustering by passing messages between data points. Science 315, 972–976 (2007)
Fritzke, B., et al.: A growing neural gas network learns topologies. In: Advances in Neural Information Processing Systems, vol. 7, pp. 625–632 (1995)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Violato, R.P.V., Azzolini, A.G., Von Zuben, F.J.: Antibodies with Adaptive Radius as Prototypes of High-Dimensional Datasets. In: Hart, E., McEwan, C., Timmis, J., Hone, A. (eds.) ICARIS 2010. LNCS, vol. 6209, pp. 158–170. Springer, Heidelberg (2010)
Martinetz, T.: Competitive hebbian learning rule forms perfectly topology preserving maps. In: Proceedings of Int. Conf. on Artificial Neural Networks, pp. 427–434. Springer (1993)
Frank, A., Asuncion, A.: UCI machine learning repository (2010)
StatLib–datasets archive, http://lib.stat.cmu.edu/datasets/ (downloaded in: March 22, 2012)
Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice-Hall, New York (1999)
Moore, D.S., Mccabe, G.P., Craig, B.A.: Introduction to the Practice of Statistics, 6th edn. W.H. Freeman & Company (2007)
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation), 2nd edn. Springer (September 2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Veroneze, R., Gonçalves, A.R., Von Zuben, F.J. (2012). A Multiobjective Analysis of Adaptive Clustering Algorithms for the Definition of RBF Neural Network Centers in Regression Problems. In: Yin, H., Costa, J.A.F., Barreto, G. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2012. IDEAL 2012. Lecture Notes in Computer Science, vol 7435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32639-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-32639-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32638-7
Online ISBN: 978-3-642-32639-4
eBook Packages: Computer ScienceComputer Science (R0)