Partitioning capabilities of multi-layer perceptrons on nested rectangular decision regions part I: Algorithm

Three papers are presented in a series of articles regarding to the partitioning capabilities on nested rectangular decision regions using multi-layer perceptrons. These articles are based on a constructive algorithm, called the up-down algorithm, to determine the weights in multi-layer perceptrons without any training procedure. The first article introduces the partitioning capabilities and explains how two layer perceptrons form the decision regions. The computational procedure of the algorithm is also depicted in the first paper. 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 article of the series, this paper first discusses the preliminaries and gives the definitions necessary for the up-down algorithm. The paper also proposes the formulas of determining the weights of the second layer and threshold of the output node for a two-layer percptron. Finally, this paper discusses the generalization issues related to the proposed algorithm and demonstrates a conceptual diagram for a hardware implementation of the up-down algorithm.