Comparison of Linear Discriminant Functions by K-fold Cross Validation

摘要

To discriminate two classes is essential in the science, technology, and industry. Fisher defined the linear discriminant function (Fisher's LDF) based on the variance-covariance matrices. It was applied for many applications. After Fisher's LDF, several LDFs such as logistic regression and a soft margin support vector machine (S-SVM) are proposed. But, there are serious two problems of the discriminant analysis. First, the numbers of misclassifications (NMs) or error rates by these LDFs may not be correct because these LDFs cannot discriminate cases on the discriminant hyper-plane correctly. Second, these LDFs cannot recognize the linear separable data properly. Only revised optimal LDF by integer programming (Revised IP-OLDF) resolves these problems. In this paper, we compare seven LDFs by 100-fold cross validation using 104 different discriminant models. It is shown that the mean error rates of Revised IP-OLDF are better than other LDFs in the training and validation samples.