Convex Hull Metrics and Neural Network Classifies, Part1

摘要

This paper explores error estimation in feed-forward neural network classifiers from a geometrical perspective. Metrics, expressed as functions of the convex hull, are introduced and developed to capture the geometrical constraints across the single neuron classifier. An upper error bound is found as a function of convex hull jointedness and the underlying conditional probability distributions. A lower bound of the upper error bound is shown to be only a function of n, the number of samples used to form the convex hull.