On Implementation of Nested Rectangular Decision Regions by Multi-layer Perceptrons I: Algorithm

There are three papers in a series of discussions related to the partitioning capabilities on nested rectangular decision regions using multi-layer perceptrons. We propose a constructive algorithm, called the up-down algorithm, to realize the nested rectangular decision regions. The algorithm determines the weights easily and can be generalized to solve other decision regions with the properties of similarity and dissimilarity. The first article gives preliminaries and describes the algorithm. The second one presents the properties of the algorithm and proves the feasibility. The last one discusses the applications of the algorithm using the properties of similarity and dissimilarity. As the first part of the series, this paper first discusses the partition capability of multi-layer perceptrons and then explains how two-layer perceptrons form the decision regions. The paper presents the formulas of determining the weights of the second layer and threshold of the output node for a two-layer percptron and demonstrates examples. Finally the paper discusses the generalization issues related to the proposed algorithm. Key-Words: Classification; Multi-layer perceptron; Nested decision region.