Explicit Center Selection and Training for Fault Tolerant RBF Networks

Although some noise tolerant center selection training algorithms for RBF networks have been developed, they usually have some disadvantages. For example, some of them cannot select the RBF centers and train the network simultaneously. Others do not allow us to explicitly define the number of RBF nodes in the resultant network, and we need to go through a time consuming procedure to tune the regularization parameter such that the number of RBF nodes used satisfies our pre-specified value. Therefore, it is important to develop some noise resistant algorithms that allow us to specify the number of RBF nodes in the resultant network. In addition, they should be able to train the network and to select RBF nodes simultaneously. This paper formulates the RBF training problem as a generalized M-sparse problem. We first define a noise tolerant objective function for RBF networks. Afterwards, we formulate the training problem as a generalized M-sparse problem, in which the objective function is the proposed noise tolerant training objective function and the constraint is an l₀-norm of the weight vector. An iterative algorithm is then developed to solve this generalized M-sparse problem. From simulation experiments, the proposed algorithm is superior to the state-of-art noise tolerant algorithms. In addition, the proposed algorithm allows us to explicitly define the number of RBF nodes in the resultant network. We prove that the algorithm converges and that the fixed points of the proposed algorithms are the local minimum of this generalized M-sparse problem.