Abstract
Neural networks are intended to be robust to noise and tolerant to failures in their architecture. Therefore, these systems are particularly interesting to be integrated in hardware and to be operating under noisy environment. In this work, measurements are introduced which can decrease the sensitivity of Radial Basis Function networks to noise without any degradation in their approximation capability. For this purpose, pareto-optimal solutions are determined for the parameters of the network.
This work was supported by the Graduate College 776 – Automatic Configuration in Open Systems- funded by the German Research Foundation (DFG).
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References
Haykin, S.: Neural Networks. A Comprehensive Foundation, 2nd edn. Prentice Hall, New Jersey (1999)
Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Computation 7(2), 219–269 (1995)
Bernier, J.L., Diáz, A.F., Fernández, F.J., Cañas, A., González, J., Martín-Smith, P., Ortega, J.: Assessing the noise immunity and generalization of radial basis function networks. Neural Processing Letters 18(1), 35–48 (2003)
Rudin, W.: Principles of Mathematical Analysis. International Series in Pure and Applied Mathematics. McGraw-Hill (1976)
Eickhoff, R., Rückert, U.: Robustness of Radial Basis Functions. Neurocomputing (2006) (in press)
Bronstein, I.N., Semendyayev, K.A.: Handbook of Mathematics, 3rd edn. Springer, Heidelberg (1997)
Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)
Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies (Decision Engineering). Springer, Heidelberg (2004)
Gonzalez, J., Rojas, I., Ortega, J., Pomares, H., Fernandez, F., Diaz, A.: Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE Transactions on Neural Networks 14(6), 1478–1495 (2003)
Pohlheim, H.: GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab. Online resource (2005), http://www.geatbx.com
Köster, M., Grauel, A., Klene, G., Convey, H.J.: A new paradigm of optimisation by using artificial immune reactions. In: 7th International Conference on Knowledge-Based Intelligent Information & Engineering Systems, pp. 287–292 (2003)
Nabney, I.: NETLAB: algorithms for pattern recognitions. Advances in pattern recognition. pub-SV, New York (2002)
Verleysen, M., François, D.: The Curse of Dimensionality in Data Mining and Time Series Prediction. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 758–770. Springer, Heidelberg (2005)
Dellnitz, M., Schütze, O., Hestermeyer, T.: Covering Pareto sets by multilevel subdivision techniques. J. Optim. Theory Appl. 124(1), 113–136 (2005)
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Eickhoff, R., Rückert, U. (2006). Pareto-optimal Noise and Approximation Properties of RBF Networks. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840817_103
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DOI: https://doi.org/10.1007/11840817_103
Publisher Name: Springer, Berlin, Heidelberg
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