LCA based RBF training algorithm for the concurrent fault situation

In the construction of a radial basis function (RBF) network, one of the most important issues is the selection of RBF centers. However, many selection methods are designed for the fault free situation only. This paper first assumes that all the training samples are used for constructing a fault tolerant RBF network. We then add an l1 norm regularizer into the fault tolerant objective function. According to the nature of the l1 norm regularizer, some unnecessary RBF nodes are removed automatically during training. Based on the local competition algorithm (LCA) concept, we propose an analog method, namely fault tolerant LCA (FTLCA), to minimize the fault tolerant objective function. We prove that the proposed fault tolerant objective function has a unique optimal solution, and that the FTLCA converges to the global optimal solution. Simulation results show that the FTLCA is better than the orthogonal least square approach and the support vector regression approach.