Learning without Local Minima in Radial Basis Function Networks

Learning from examples plays a central role in artificial neural networks. The success of many learning schemes is not guaranteed, however, since algorithms like backpropagation may get stuck in local minima, thus providing suboptimal solutions. For feedforward networks, the theoretical results reported in past literature show that optimal learning can be achieved provided that certain conditions on the network and the learning environment are met. A similar investigation is put forward in this paper for the case of networks using radial basis functions (RBF). The analysis proposed in for multilayer networks is extended naturally under the assumption that the patterns of the learning environment are separable by hyperspheres. In that case, we prove that the attached cost function is local minima free with respect to all the weights. This provides us with some theoretical foundations for a massive application of RBF in pattern recognition.