An average predictive accuracy of the nearest neighbor classifier

Abstract

The definition of similarity between cases is a key issue on case-based reasoning. The nearest neighbor method represents a basic mechanism for defining the similarity in the case-based reasoning system. In this paper, we perform an average-case analysis of the nearest neighbor classifier for conjunctive classes. We formally compute the predictive accuracy of the nearest neighbor classifier. The predictive accuracy is represented as a function of the number of training cases and the numbers of relevant attributes for classes. We also plot the predictive behavior of the classifier by substituting actual values into the parameters of the accuracy function. The graphs by plotting the predictive behavior help us to understand the relationships between the parameters of the accuracy function and the predictive accuracy of the nearest neighbor classifier. Our investigation focuses on how the numbers of relevant attributes for classes affect the predictive accuracy.