Adaptive Learning Algorithm for RBF Neural Networks in Kernel Spaces

An adaptive learning algorithm for Radial Basis Functions Neural Networks, RBFNNs, is provided. In recent years, RBFs have been subject to extensive areas of interests. But the setting up of RBFs in a network architecture can be time consuming, computationally deficient and unstable. Thus we have developed an efficient adaptive algorithm in a feedforward neural architecture in which the hidden neurons are Newton bases. These bases are derived from the RBFs on optimal center points. Unlike the RBFs, the Newton bases are stable and orthonormal in the kernel space. The algorithm is implemented on variably scaled RBFs that simultaneously adjust the shape parameter. The procedure of the training is computationally efficient, accurate and stable in the kernel spaces specially for noisy data set. Numerical modeling for time series shows that our proposed algorithm has very promising performance in compare to some recent approaches.