An Empirical Evaluation of the Classification Error of Two Thresholding Methods for Fisher's Classifier

In this paper, we empirically analyze two methods for computing the threshold in Fisher’s classifiers. One of these methods, which we call FC or traditional Fisher’s classifier, obtains the threshold by computing the middle point between the two means in the projected space. The second method, which we call FC, obtains the threshold by computing the optimal classifier in the transformed space. We conduct the analysis in widely used public datasets for cancer detection and protein classification. The empirical results show that FC leads to smaller classification error than FC. The results on Cancer data demonstrate that minimizing the classification error in the transformed space leads to smaller classification error in the original multi-dimensional space. As opposed to this, the results on protein classification show that selecting the theshold that minimizes the error in the transformed space, assuming the data is normally distributed, does not necessarily lead to the best classifier.