A NEURAL NETWORK MODEL FOR MINIMUM SPANNING CIRCLE: ITS CONVERGENCE, ARCHITECTURE DESIGN AND APPLICATIONS

Abstract

A self-organizing neural network model that computes the smallest circle (also called minimum spanning circle) enclosing a finite set of given points was proposed by Datta.3 In the article,3 the algorithm is stated and it is demonstrated by simulation that the center of the smallest circle can be achieved with a given level of accuracy. No rigorous proof was given in support of the simulation results. In this paper, we make a rigorous analysis of the model and mathematically prove that the model converges to the desired center of the minimum spanning circle. A suitable neural network architecture is also designed for parallel implementation of the proposed model. Time complexity of the algorithm is worked out under the proposed architecture. Extension of the proposed model to higher dimensions is discussed and demonstrated with some applications.