Introducing an inequalities index from the simple perceptron pattern in ANN: An unemployment inequalities application in regional economics

Abstract

This article introduces a new inequalities index, which was inspired from the simple perceptron's pattern in the artificial neural networks (ANN) scientific field and nominated by the authors Modulus Perceptron Inequalities Index (MPII). The structural similarities of this ANN pattern with a binary logic gate, in the Digital Electronics Theory (DET), lead to deal with the existence of operational similarities between these two models. The introduced index aroused while examining the potentials of the simple perceptron to solve the non-linear separable "exclusive disjunction" (XOR) problem, by using techniques of the Theory of Numbers in Mathematics. Since the XOR architecture is considered by the DET an inequality detector, due to its ability to result to the same outcome in the same input values, the solution of the XOR problem for a simple perceptron authorizes the ANN and DET XOR models to be considered identical, in the extend that inequalities is regarded. The above XOR models utility appears to operate satisfactory in Regional Science's inequalities research. The examination of MPII's behavior in comparison with the Theil index, concluded to be almost identical in the extend that slope conservation is regarded and more capable on cases that the Theil's index cannot operate. © 2012 Kavala Institute of Technology.