ASSESSMENT METRICS FOR IMBALANCED LEARNING - Imbalanced Learning: Foundations, Algorithms, and Applications - page 189

amount of actually relevant information from the information assessed as relevant
by f . Precision and recall are defined as follows:

TP
TP + FP

Precision = (8.3)

TP
TP + FN

Recall = (8.4)

Here again, the focus is on the positive class only, meaning that the problems
encountered by multi-class focus metrics in the case of the class imbalance prob-
lem are, once more, avoided. As for sensitivity and specificity, however, the
cost of using precision and recall is that two measures must be considered and
that absolutely no information is given on the performance of f on the negative
class. This information did appear in the form of specificity in the previous pair
of metrics.
We now turn our attention to a couple of ways of combining the components
of the two pairs of single-focus metrics just discussed so as to obtain a single
measure instead of a pair of metrics.

8.3.3 Geometric Mean

The G-mean was introduced by Kubat et al. [7] specifically as a response to the
class imbalance problem and as a response to the fact that a single metric is easier
to manipulate than a pair of metrics. This measure takes into account the relative
balance of the classifier's performance on both the positive and the negative
classes. In order to do so, it is defined as a function of both the sensitivity and
the specificity of the classifier. G-mean is defined in more detail as follows:
G − mean 1 = sensitivity × specificity

(8.5)

Because the two classes are given equal importance in this formulation, the G-
mean, while more sensitive to class imbalances than accuracy, remains close,
in some sense, to the multi-class focus category of metrics. Another version of
the G-mean was, therefore, also suggested, which focuses solely on the positive
class. In order to do so, it replaces the specificity term by the precision term,
yielding

G − mean 2 = sensitivity × precision

(8.6)

8.3.4 F -Measure

The F -measure is another combination metric whose purpose this time is to
combine the values of the precision and recall of a classifier f on a given domain