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A measure that combines precision and recall is the harmonic mean of precision and recall, the traditional F-measure or balanced F-score: F = 2 ⋅ p r e c i s i o n ⋅ r e c a l l p r e c i s i o n + r e c a l l {\displaystyle F=2\cdot {\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}}
Macro F1 is a macro-averaged F1 score aiming at a balanced performance measurement. To calculate macro F1, two different averaging-formulas have been used: the F1 score of (arithmetic) class-wise precision and recall means or the arithmetic mean of class-wise F1 scores, where the latter exhibits more desirable properties. [28]
An F-score is a combination of the precision and the recall, providing a single score. There is a one-parameter family of statistics, with parameter β, which determines the relative weights of precision and recall. The traditional or balanced F-score is the harmonic mean of precision and recall:
The F-score combines precision and recall into one number via a choice of weighing, most simply equal weighing, as the balanced F-score . Some metrics come from regression coefficients : the markedness and the informedness , and their geometric mean , the Matthews correlation coefficient .
F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer).
is the true positive rate, also called sensitivity or recall, and is the positive predictive rate, also known as precision. The minimum possible value of the Fowlkes–Mallows index is 0, which corresponds to the worst binary classification possible, where all the elements have been misclassified.
By computing a precision and recall at every position in the ranked sequence of documents, one can plot a precision-recall curve, plotting precision () as a function of recall . Average precision computes the average value of p ( r ) {\displaystyle p(r)} over the interval from r = 0 {\displaystyle r=0} to r = 1 {\displaystyle r=1} : [ 7 ]
The precision of 10 / 10 + 990 = 1% reveals its poor performance. As the classes are so unbalanced, a better metric is the F1 score = 2 × 0.01 × 1 / 0.01 + 1 ≈ 2% (the recall being 10 + 0 / 10 = 1).