An analysis on the relationship between uncertainty and misclassification rate of classifiers

This paper provides new insight into the analysis on the relationship between uncertainty and misclassification of a classifier. We formulate the relationship explicitly by taking entropy as a measurement of uncertainty and by analyzing the misclassification rate based on the membership degree difference. Focusing on binary classification problems, this study theoretically and experimentally validates that the misclassification rate will definitely be upgrading with the increase of uncertainty if two conditions are satisfied: (1) the distributions of two classes based on membership degree difference are unimodal, and (2) these two distributions attain peaks when the membership degree difference is less and larger than zero, respectively. This work aims to provide some practical guidelines for improving classifier performance through clearly expressing and understanding the relationship between uncertainty and misclassification of a classifier.