Robust Iterative Hard Thresholding Algorithm for Fault Tolerant RBF Network

In the construction of a radial basis function (RBF) network, there are three crucial issues. The first one is to select RBF nodes from training samples. Two additional vital issues are addressing the realization of imperfections and mitigating the impact of outlier training samples. This paper considers that training data contain some outlier samples and that there is weight noise in the RBF weights in the implementation. We formulate the construction of an RBF network as a constrained optimization problem in which the objective function consists of two terms. The first term is designed to suppress the effect of outlier samples, while the second term handles the effect of weight noise. Our formulation has an \(\ell _0\) -norm constraint whose role is to select the training samples for constructing RBF nodes. We then develop the robust iterative hard thresholding algorithm (R-IHT) to solve the optimization problem based on the projected gradient concept. We theoretically study the convergence properties of the R-IHT. We use several benchmark datasets to verify the effectiveness of the proposed algorithm. The performance of our algorithm is superior to a number of state-of-the-art methods.