Canonical dual solutions to nonconvex radial basis neural network optimization problem
- Authors: Latorre, Vittorio , Gao, David
- Date: 2014
- Type: Text , Journal article
- Relation: Neurocomputing Vol. 134, no. Special issue (2014), p. 189-197
- Full Text: false
- Reviewed:
- Description: Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamental difficulties for the traditional optimization theory and methods. This paper presents a generalized canonical duality theory for solving this challenging problem. We demonstrate that by using sequential canonical dual transformations, the nonconvex optimization problem of the RBFNN can be reformulated as a canonical dual problem (without duality gap). Both global optimal solution and local extrema can be classified. Several applications to one of the most used Radial Basis Functions, the Gaussian function, are illustrated. Our results show that even for a one-dimensional case, the global minimizer of the nonconvex problem may not be the best solution to the RBFNNs, and the canonical dual theory is a promising tool for solving general neural networks training problems. © 2014 Elsevier B.V.
Canonical duality for radial basis neural networks
- Authors: Latorre, Vittorio , Gao, David
- Date: 2013
- Type: Text , Journal article
- Relation: Advances in Intelligent Systems and Computing Vol. 212, no. (2013), p. 1189-1197
- Full Text: false
- Reviewed:
- Description: 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. © Springer-Verlag Berlin Heidelberg 2013. Proceedings of the Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013.
- Description: 2003011221