Constructing RBF network based on interference robust projected gradient

In the radial basis function (RBF) network training, one significant issue is the selection of RBF centers to effectively utilize all available resources. Two additional challenges include handling outlier training samples and weight noise. This paper proposes a robust algorithm that addresses these three issues. The algorithm’s fundamental concept involves formulating the training process as a constrained optimization problem. The objective function consists of two components: one aims to minimize the influence of outlier training samples, while the other addresses the effects of weight noise. Consequently, we can effectively manage and regulate the impact of both outlier noise and weight noise. In the formulation, we incorporate an ${\ell }_0$-norm constraint, which provides explicit control over the number of RBF nodes in the trained network. To solve the optimization problem, we introduce the interference robust projected gradient (IR-PG) algorithm. Furthermore, we present a theoretical analysis that explores the convergence behavior exhibited by the IR-PG algorithm. We then extend the capabilities of the IR-PG algorithm to effectively handle the simultaneous presence of weight noise and weight fault. Through extensive simulations, we demonstrate that our algorithm outperforms several cutting-edge methods in terms of both accuracy and robustness.