F-score measure

Classification results can be presented as a confusion matrix:

An example for cancer:

Then we can compute different metrics:

• Sensitivity or Recall: $Recall=\frac{TP}{TP+FN}$
• Specificity: $Specificity=\frac{TN}{TN+FP}$
• Precision: $Precision=\frac{TP}{TP+FP}$
• Accuracy: $Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$

We can visualize them nicely with this schema:

Two interesting metrics are Recall and Precision: we often want to maximize both, but they are often opposed (if we increase one, the other is decreased). To solve this paradox, we can use a metric that combine both of them: this is the F1-score.

$$F_1=\frac{2}{\frac{1}{Recall}+\frac{1}{Precision}}=\frac{2\cdot TP}{2\cdot TP + FP + FN}$$

We can then make it more general by pondering the Recall and the Precision with a coefficient $\beta$:

Resources

F-score