IMBALANCED DATASETS: FROM SAMPLING TO CLASSIFIERS - Imbalanced Learning: Foundations, Algorithms, and Applications - page 53

1

Strong performance

Weak performance

Random performance

Inverted performance

0 1

False positive rate

Figure 3.2 Examples of ROC curves. Each curve represents the performance of a dif-
ferent classifier on a dataset.

a point in the ROC space at ( 0 , 1 ) , that is, all positive instances are correctly
classified, and no negative instances are misclassified. Alternatively, the classifier
that misclassifies all instances would have a single point at ( 1 , 0 ) .
While ( 0 , 1 ) represents the ideal classifier and ( 1 , 0 ) represents its complement,
in ROC space, the line y = x represents a random classifier, that is, a classifier
that applies a random prediction to each instance. This gives a trivial lower bound
in ROC space for any classifier. An ROC curve is said to “dominate” another
ROC curve if, for each FPR, it offers a higher TPR. By analyzing ROC curves,
one can determine the best classifier for a specific FPR by selecting the classifier
with the best corresponding TPR.
In order to generate an ROC curve, each point is generated by moving the deci-
sion boundary for classification. That is, points nearer to the left in ROC space
are the result of requiring a higher threshold for classifying an instance as positive
instance. This property of ROC curves allows practitioners to choose the deci-
sion threshold that gives the best TPR for an acceptable FPR (Neyman-Pearson
method) [33].
The ROC convex hull can also provide a robust method for identifying poten-
tially optimal classifiers [34]. Given a set of ROC curves, the ROC convex hull
is generated by selecting only the best point for a given FPR . This is advanta-
geous, since, if a line passes through a point on the convex hull, then there is