ABSTRACT
This chapter investigates theoretical results regarding the behavior of a genetic algorithm-based pattern classification methodology, for an infinitely large number of sample points n, in an N dimensional space RN. It shows that for n → ∞ and for a sufficiently large number of iterations, the performance of this classifier approaches that of the Bayes classifier. Experimental results, for a triangular distribution of points, are also included that conform to this claim. The chapter attempts to show theoretically that the decision surfaces generated by the aforesaid GA-based classifier will approach the Bayes decision surfaces for a large number of training sample points (n) and will consequently provide the optimal decision boundary in terms of the number of misclassified samples. It gives a brief outline of the GA-based classifier. The chapter provides the theoretical treatment to find a relationship between this classifier and the Bayes classifier in terms of classification accuracy.
