Integrated probabilistic simplified fuzzy ARTMAP

Abstract

The integrated probabilistic simplified fuzzy ARTMAP (IPSFAM) neural network is described. The primary objectives were to develop a network which determines the class of a test vector as that class which possesses the highest estimated Bayes posterior probability, can be trained with one iteration of training data, offers extendable training without retraining (i.e. incremental training), is suitable for online use, and contains fewer nodes than the probabilistic neural network (PNN). The IPSFAM is a hybrid simplified fuzzy ARTMAP (SFAM) and PNN, which develops its own architecture. To reduce the number of one-to-many mappings which occur, the input vectors are not individually normalised, as is the case in the PNN. The two outputs are the classes predicted by the highest estimated Bayes posterior probability and by the SFAM. Comparison of the two offers the possibility of novelty detection. Extensive testing using statistically generated data, and medical and electronic data was performed. The Bayes classification accuracy of the IPSFAM was generally less than that of the probabilistic simplified fuzzy ARTMAP (PSFAM), but its testing time was considerably shorter. The incorporated nodal choice parameter sometimes increased the classification accuracy, while that of the incorporated frequency counter sometimes decreased it, depending on the training vectors. A formula for the local smoothing parameters of the Parzen windows formula is introduced. Polynomial approximations to this formula are impractical when the global smoothing parameter <1.