Gradient-based training of probabilistic neural network with class-feature smoothing

This paper proposes a gradient-based training procedure for probabilistic neural network with class- and feature-dependent smoothing parameters. The parameters are updated using analytically derived gradients defined for the normalized class outputs. Three initialization strategies are considered: class-related feature variance, median pairwise distance, and interquartile range. The method is evaluated on 20 classification datasets using repeated stratified 10-fold cross-validation. The variance-based initialization obtains the best mean rank, although the relative performance of the initialization methods is dataset-dependent. Statistical tests do not indicate significant differences between the considered initialization strategies.