Radial basis function networks provides a more flexible model and gives a very good performance over a wide range of applications. However, in the modeling process, care is taken not to choose the number of the basis functions and the positions of the centres, the regularization parameter and the smoothing parameter as appropriate according to the model complexity, they often gives poor generalization performance.
In this paper, we develop a new model building procedure based on radial basis function networks; positioning the centres with k-means clustering for the conditional distribution Pr(x|y) and estimating the weights by maximum penalized likelihood with Lasso penalty. We present an information criterion for choosing the regularization and smoothing parameters in the models. The proposed procedure determines the proper number and location of the centres automatically. The simulation result shows that the proposed method performs very well.