F₁-Measure

The F₁-measure is used to evaluate the accuracy of predictions in two-class (binary) classification problems. It originates in the field of information retrieval and is often used to evaluate document classification models and algorithms. It is defined as the harmonic mean of precision (i.e., the ratio of true positives to all instances predicted as positive) and recall (i.e., the ratio of true positives to all instances that are actually positive). As such, it lies between precision and recall, but is closer to the smaller of these two values. Therefore a system with high F₁ has both good precision and good recall. The F₁-measure is a special case of the more general family of evaluation measures:

$$\displaystyle\begin{array}{rcl} F_{\beta }& =& (\beta ^{2} + 1)precisionrecall/ {}\\ & & (\beta ^{2}precision + recall) {}\\ \end{array}$$

Thus using β > increases the influence of precision on the overall measure, while using β< 1 increases the influence of recall. Some authors use an...