MAXIMUM-LIKELIHOOD TRAINING OF PROBABILISTIC NEURAL NETWORKS

A maximum likelihood method is presented for training probabilistic neural networks (PNN's) using a Gaussian kernal, or Parzen window. The proposed training algorithm enables general nonlinear discrimination and is a generalization of Fisher's method for linear discrimination. Important features of maximum likelihood training for PNN's are: 1) it economizes the well known Parzen window estimator while preserving feed-forward NN architecture, 2) it utilizes class pooling to generalize classes represented by small training sets, 3) it gives smooth discriminant boundaries that often are ''piece-wise flat'' for statistical robustness, 4) it is very fast computationally compared to back-propagation, and 5) it is numerically stable. The effectiveness of the proposed maximum likelihood training algorithm is assessed using nonparametric statistical methods to define tolerance intervals on PNN classification performance.