The Bayesian ARTMAP

In this paper, we modify the fuzzy ARTMAP (FA) neural network (NN) using the Bayesian framework in order to improve its classification accuracy while simultaneously reduce its category proliferation. The proposed algorithm, called Bayesian ARTMAP (BA), preserves the FA advantages and also enhances its performance by the following: (1) representing a category using a multidimensional Gaussian distribution, (2) allowing a category to grow or shrink, (3) limiting a category hypervolume, (4) using Bayes´ decision theory for learning and inference, and (5) employing the probabilistic association between every category and a class in order to predict the class. In addition, the BA estimates the class posterior probability and thereby enables the introduction of loss and classification according to the minimum expected loss. Based on these characteristics and using synthetic and 20 real-world databases, we show that the BA outperformes the FA, either trained for one epoch or until completion, with respect to classification accuracy, sensitivity to statistical overlapping, learning curves, expected loss, and category proliferation.