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.

本文提供了对分类器不确定性和分类错误之间关系的分析的新见解。我们通过将熵作为不确定性的度量，并根据隶属度差异分析误分类率，来明确地表达关系。针对二元分类问题，本研究从理论和实验上验证了如果满足两个条件，则分类错误率肯定会随着不确定性的增加而提高：（1）基于隶属度差异的两类分布是单峰的，和（2 ）当隶属度差异小于和大于零时，这两个分布分别达到峰值。