ASSESSMENT METRICS FOR IMBALANCED LEARNING - Imbalanced Learning: Foundations, Algorithms, and Applications - page 188

The true positive and true negative entries indicate the number of examples
correctly classified by classifier f as positive and negative, respectively.
The false negative entry indicates the number of positive examples wrongly
classified as negative. Conversely, the false positive entry indicates the number
of negative examples wrongly classified as positive. With these quantities
defined, we are now able to define the single-class focus metrics of interest
here as well as the multiple-class focus metrics adapted to the class imbalance
problem.

8.3.1 Sensitivity and Specificity

The sensitivity of a classifier f corresponds to its true positive rate or, in other
words, the proportion of positive examples actually assigned as positive by f .The
complement metric to this is called the specificity of classifier f and corresponds
to the proportion of negative examples that are detected. It is the same quantity,
only it is measured over the negative class. These two metrics are typically used
in the medical context to assess the effectiveness of a clinical test in detecting a
disease. They are defined as follows:

TP
TP + FN

Sensitivity = (8.1)

TN
FP + TN

=

Specificity (8.2)

These measures, together, identify the proportions of the two classes correctly
classified. However, unlike accuracy, they do this separately in the context of
each individual class of instances. As a result, the class imbalance does not
affect these measures. On the other hand, the cost of using these metrics appears
in the form of a metric for each single class, which is more difficult to process
than a single measure. Another issue that is missed by this pair of metrics is the
measure of the proportion of examples assigned to a given class by classifier f
that actually belongs to this class. This aspect is captured by the following pair
of metrics.

8.3.2 Precision and Recall
The precision of a classifier f measures how precise f is when identifying the
examples of a given class. More precisely, it assesses the proportion of examples
assigned a positive classification that are truly positive. This quantity together
with sensitivity, which is commonly called recall when considered together with
precision, is typically used in the information retrieval context where researchers
are interested in the proportion of relevant information identified along with the