A constructive algorithm to solve "convex recursive deletion" (CoRD) classification problems via two-layer perceptron networks

A sufficient condition that a region be classifiable by a two-layer feedfor ward neural net (a two-layer perceptron) using threshold activation functio ns is that either it be a convex polytope or that intersected with the comp lement of a convex polytope in its interior, or that intersected with the c omplement of a convex polytope in its interior or,., recursively, These hav e been called convex recursive deletion (CoRD) regions. We give a simple al gorithm for finding the weights and thresholds in both layers for a feedfor ward net that implements such a region. The results of this work help in un derstanding the relationship between the decision region of a perceptron an d its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of Co RD regions (requiring three layers). Therefore this work also helps in unde rstanding how many neurons are needed in the second layer of a general thre e-layer network. In the event that the decision region of a network is know n and is the union of CoRD regions, our results enable the calculation of t he weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations.