F1 score

F1 score

In statistics, the F1 score (also F-score or F-measure) is a measure of a test's accuracy. It considers both the precision "p" and the recall "r" of the test to compute the score: "p" is the number of correct results divided by the number of all returned results and "r" is the number of correct results divided by the number of results that should have been returned. The F1 score can be interpreted as a weighted average of the precision and recall, where an F1 score reaches its best value at 1 and worst score at 0.

The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall:

:F = 2 cdot (mathrm{precision} cdot mathrm{recall}) / (mathrm{precision} + mathrm{recall}).,

The general formula for non-negative real β is::F_eta = (1 + eta^2) cdot (mathrm{precision} cdot mathrm{recall}) / (eta^2 cdot mathrm{precision} + mathrm{recall}).,

The formula in terms of Type I and type II errors::F_eta = frac {(1 + eta^2) cdot mathrm{true positive} }{((1 + eta^2) cdot mathrm{true positive} + eta^2 cdot mathrm{false positive} + mathrm{false negative})}.,

Two other commonly used F measures are the F_{2} measure, which weights recall twice as much as precision, and the F_{0.5} measure, which weights precision twice as much as recall.

The F-measure was derived by van Rijsbergen (1979) so that F_eta "measures the effectiveness of retrieval with respect to a user who attaches β times as much importance to recall as precision". It is based on van Rijsbergen's effectiveness measure E = 1-(1/(alpha/P + (1-alpha)/R)). Their relationship is F_eta = 1 - E where alpha=1/(eta^2+1).

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