New developments of the Z-EDM algorithm

In this paper we address some open questions on the recently proposed Zero-Error Density Maximization algorithm for MLP training. We propose a new version of the cost function that solves a training problem encountered in previous work and prove that the use of a nonparametric density estimator preserves the optimal solution. Some experiments are reported comparing this cost function to the usual mean-square error and cross entropy cost functions. also consider a training set with N pattern vectors, such that the nth sample produces an output y(n) which is compared with the corresponding target t(n) to produce the error (or more precisely, the deviation) e(n) = t(n) − y(n), n = 1,...,N. Target vectors are encoded in an one-out-of-C scheme such that t = [−1,...,1,...,−1], where the 1 appears at the kth component, is the target for a pattern from class Ck. One can easily see that the errors belonging to each class lie in disjoint hypercubes with the origin as their unique common point. The three-class case is represented in Figure 1. 1