On robustness of radial basis function network with input perturbation

In this article, we have proposed a methodology for making a radial basis function network (RBFN) robust with respect to additive and multiplicative input noises. This is achieved by properly selecting the centers and widths for the radial basis function (RBF) units of the hidden layer. For this purpose, firstly, a set of self-organizing map (SOM) networks are trained for center selection. For training a SOM network, random Gaussian noise is injected in the samples of each class of the data set. The number of SOM networks is same as the number of classes present in the data set, and each of the SOM networks is trained separately by the samples belonging to a particular class. The weight vector associated with a unit in the output layer of a particular SOM network corresponding to a class is used as the center of a RBF unit for that class. To determine the widths of the RBF units, p-nearest neighbor algorithm is used class-wise. Proper selection of centers and widths makes the RBFN robust with respect to input perturbation and outliers present in the data set. The weights between the hidden and output layers of RBFN are obtained by pseudo inverse method. To test the robustness of the proposed method in additive and multiplicative noise scenarios, ten standard data sets have been used for classification. Proposed method has been compared with three existing methods, where the centers have been generated in three ways: randomly, using k-means algorithm, and based on SOM network. Simulation results show the superiority of the proposed method compared to those methods. Wilcoxon signed-rank test also shows that the proposed method is statistically better than those methods.