(a) (b)

The impact of the threshold variation on the misclassification rate variation. (a)

old causes more misclassifications in the left class. (b) The threshold causes

assifications in the right class.

d on the discussion of the example in Figure 3.10, a question arises,

robustness of a classifier. The question is how to determine

a classifier is robust against the threshold variation for the

ation between two classes of data points. In other words, whether

assification rate variation of a classifier can be less dependent on

hold variation. There are two classifiers shown in Figure 3.11,

e classifier is placed in the upper panels and the other classifier

in the lower panels. The densities of two classes are highly

ed shown in the upper panels. Therefore, when a threshold is

a dramatic misclassification rate change will happen. For

the top-left panel shows a much great misclassification rate for

on the left side. The top-right panel shows a much great

fication rate for the class on the right side. However two densities

asses have a light degree of overlap shown in the lower panels.

threshold is changed, little misclassification rate variation may

Therefore the classifier shown in the lower panels is more robust

shown in the upper panels against the threshold variation.

this analysis, it can be seen that if a classifier is robust against the

variation, the overlap between the densities of two classes should

all as possible.