Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Global Continuation for Distance Geometry Problems
SIAM Journal on Optimization
Journal of Global Optimization
Convergent Decomposition Techniques for Training RBF Neural Networks
Neural Computation
Real time face and mouth recognition using radial basis function neural networks
Expert Systems with Applications: An International Journal
The WEKA data mining software: an update
ACM SIGKDD Explorations Newsletter
Prediction of Parkinson's disease tremor onset using radial basis function neural networks
Expert Systems with Applications: An International Journal
Information Sciences: an International Journal
A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design
The Journal of Machine Learning Research
Face recognition with radial basis function (RBF) neural networks
IEEE Transactions on Neural Networks
Canonical dual approach to solving the maximum cut problem
Journal of Global Optimization
Hi-index | 0.01 |
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.