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_beta = (1 + beta^2) cdot (mathrm{precision} cdot mathrm{recall}) / (beta^2 cdot mathrm{precision} + mathrm{recall}).,

The formula in terms of Type I and type II errors:

F_beta = frac {(1 + beta^2) cdot mathrm{true positive} }{((1 + beta^2) cdot mathrm{true positive} + beta^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_beta "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_beta = 1 - E where alpha=1/(beta^2+1).

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