In this paper we apply an evolving stochastic method to construct simple and effective Artificial Neural Networks,
based on the theory of Tsallis statistical mechanics. Our aim is to establish an automatic process for
building a smaller network with high classification performance. We aim to assess the utility of the method
based on statistical mechanics for the estimation of transparent coating material on security papers and cholesterol
levels in blood samples. Our experimental study verifies that there are indeed improvements in the overall
performance in terms of classification success and at the size of network compared to other efficient backpropagation
learning methods