The area under the ROC curve can be thought of as a single scalar representation of the ROC curve itself. The AUC of a classifier has the property of being equivalent to the probability that the classifier will rank a randomly chosen positive data point higher than a randomly chosen negative data point.
The area under the ROC curve can be thought of as a single scalar representation of the ROC curve itself. Since this value represents part of the area of a 1x1 square, the AUC is a value between 0.0 and 1.0. However, since a classifier should always perform better than random, the realistic domain of the AUC values should be 0.5 to 1.0. The AUC of a classifier has the property of being equivalent to the probability that the classifier will rank a randomly chosen positive data point higher than a randomly chosen negative data point [Fawcett, 2006]. It can be shown that the AUC is related to the Gini coefficient [Hand et al, 2001]. The AUC can be estimated using trapezoidal approximation by considering the interval between consecutive points [Hand et al, 2001]
Fawcett, Tom. 2006. “An Introduction to ROC Analysis.” Pattern Recognition Letters 27 (8) (June): 861–874. doi:10.1016/j.patrec.2005.10.010.
Hand, David J, and Robert J Till. 2001. “A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems.” Machine Learning 45 (2) (January 1): 171–186. doi:10.1023/A:1010920819831.
