hold A in Figure 3.12(a) is the lowest threshold. Certainly, using

hold, a great proportion of misclassification happens to the left

e consequence is that almost all data points of the right class are

classified. This results in a perfect true positive rate approaching

%. However, the use of this threshold causes a huge

fication rate for the left class. Therefore, almost all data points of

lass have been misclassified as the right class. The consequence

emely high false positive rate approaching to 100% as well. This

he threshold A is approaching to the top-right corner in Figure

The threshold G represents another scenario. Because it is on the

of the horizontal axis shown in Figure 3.12(a), almost all data

the right class are misclassified. The consequence is an almost

positive rate. At the same time, all the data points of the left class

ctly classified. Therefore the false positive rate is also almost 0%.

hy the threshold G is located at the bottom-left corner shown in

12(b) and Figure 3.12(c). Connecting these seven points in this

nsional space finally results in an ROC curve shown in Figure

(a) (b) (c)

The formation of an ROC curve. (a) Two densities of two classes with seven

nts. (b) Seven pairs of two rates in a two-dimensional space. The horizontal axis

e false positive rate. The vertical axis employs the positive rate. (c) Connecting

s leads to an ROC curve.