Introduction to Probabilistic Neural Networks

Abstract

Probabilistic neural networks (PNN), introduced by Specht [255] – [258], have their predecessors in the theory of statistical pattern classification. In the fifties and sixties problems of statistical pattern classification in the stationary case were accomplished by means of parametric methods, using the available apparatus of statistical mathematics (e.g. [35], [75], [89], [90], [293]). The knowledge of the probability density to an accuracy of unknown parameters was assumed and the parameters were estimated based on the learning sequence. Typical techniques included maximum likelihood and Bayesian approaches. Having observed tendencies present in literature within the last twenty years we should say that these methods have been almost completely replaced by the non-parametric approach (see e.g. [67], [70], [71], [79], [80], [81], [104], [105], [113], [114], [122], [175], [191], [195], [272], [296], [297]). In the non-parametric approach it is assumed that a functional form of probability ensities is unknown. The latter are estimated by non-parametric estimators.