Extraction of underlying rules by projection pursuit learning networks with M-apoptosis structural learning algorithm

In order to extract simple rules from observed samples, we introduce the PPLN with RBF to represent the relationship between inputs and outputs in a low-dimensional projected space, and propose a structural learning method for the PPLN. We consider three kinds of penalty terms to eliminate the dimensionality, the input variables and hidden units of PPLN. In our method, Minkowski norms of the first order derivatives of the network with respect to input variables, the elements of projection vectors and the weight parameters, are used as the penalty terms. Simple rules are extracted from the PPLN by eliminating the unnecessary links and units.