Radial basis function neural network training using variable projection and fuzzy means

Radial basis function (RBF) neural network training presents a challenging optimization task, necessitating the utilization of advanced algorithms that can fully train the network so as to produce accurate and computationally efficient models. To achieve this goal, this work introduces a new framework where the original RBF training problem is divided into two simpler subproblems; the linear parameters, namely the network weights, are projected out of the problem using variable projection (VP), thus leaving a reduced functional, which depends only on nonlinear parameters, i.e., the RBF centers. The centers are updated using the Levenberg–Marquardt (LM) algorithm, while the optimal values of the synaptic weights are calculated in each iteration of the LM algorithm using linear regression. The proposed VP-LM scheme is coupled with the fuzzy means (FM) algorithm, which helps to select the number of RBF centers and enhances the overall search procedure, thus resulting to a framework that produces parsimonious models with enhanced accuracy in shorter training times. The proposed training scheme is evaluated on 12 both real-world and synthetic benchmark datasets and tested against various RBF training algorithms, as well as different neural network architectures. The experimental results underscore the effectiveness of the VP-FM algorithm in producing neural network models that outperform those generated by alternative methods in many aspects; to be more specific, the proposed approach achieves very competitive model accuracy, while resulting to smaller network sizes and thus lower complexity, which leads to shorter training times.