Is it correct to define the F-measure as the harmonic mean of specificity and sensitivity in such a way?
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09-12-2020 - |
문제
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:
해결책
The one is general formula the other you get for Beta=1:
The beta value greater than 1 means we want our model to pay more attention to the model Recall as compared to Precision. On the other, a value of less than 1 puts more emphasis on Precision. So you just want to generalise, and punish certain mistakes more.
So to conclude: Correct in mathematical sense is always to generalise and derive special cases, in that sense the first one is preferable since setting beta to one you get the 'standard' F-1-harmonic-mean-formula.
http://scikit-learn.org/stable/modules/generated/sklearn.metrics.fbeta_score.html
다른 팁
Yes, as they are effectively synonyms of one another. See for instance this link
If you pay attention, the first formula is the (weighted) harmonic mean of the recall and precision.