Theoretical performance of genetic pattern classifier

An investigation is carried out to formulate some theoretical results regarding the behavior of a genetic-algorithm-based pattern classification methodology, for an infinitely large number of training data points n, in an N-dimensional space RN. It is proved that for n→∞, and for a sufficiently large number of iterations, the performance of this classifier (when hyperplanes are considered to generate class boundaries) approaches that of the Bayes classifier, which is the optimal classifier when the class distributions and the a priori probabilities are known. It is shown that the optimum number of hyperplanes generated by the proposed classifier is equal to that required to model the Bayes decision boundary when there exists only one partition of the feature space that provides the Bayes error probability. Extensive experimental results on overlapping data sets following triangular and normal distributions with both linear and non-linear class boundaries are provided that conform to these claims. The claims also hold good when circular surfaces are considered as constituting elements/segments of boundaries. It is also shown experimentally that the variation of recognition score with a priori class probability for both the classifiers is similar.