AN ALGORITHM TO DETERMINE THE FEASIBILITIES AND WEIGHTS OF TWO-LAYER PERCEPTRONS FOR PARTITIONING AND CLASSIFICATION

摘要

Necessary and sufficient conditions for implementing classification problems by two-layer perceptrons have been presented in the viewpoints of mathematics and geometry. [Zwietering, Arts and Wessels, Int. J. Neural Systems 3(2), 143–156 (1992)]. This paper, in an engineering viewpoint, provides an algorithm, called the Weight Deletion/Selection Algorithm, to examine the feasibility of implementation of a decision region by two-layer perceptrons, and to select the weights of the second layer in a two-layer perceptron without any training process if a decision region is implementable for two-layer perceptrons. For the purpose of visualization, we explain the algorithm by the examples of two-input-two-class cases, and then discuss the generalization to multi-input-multi-class cases. Finally we present a three-class classification example with four features selected as the inputs.