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It is common to define the F-measure as a function of precision and recall, as mentioned in [1]:

$F_{\beta}=\frac{(1+\beta^2)PR}{\beta^2 P+R}$

However I came across some other cases, another definition is used [2] (without weights):

$F = H(sensitivity, 1- specificity)$

Where H is harmonic mean.

Reference: