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:

$F = 2 \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{\mathrm{precision} + \mathrm{recall}}$.

The general formula for positive real β is:

$F_\beta = (1 + \beta^2) \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{(\beta^2 \cdot \mathrm{precision}) + \mathrm{recall}}$.

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

$F_\beta = \frac {(1 + \beta^2) \cdot \mathrm{true\ positive} }{((1 + \beta^2) \cdot \mathrm{true\ positive} + \beta^2 \cdot \mathrm{false\ negative} + \mathrm{false\ positive})}\,$.

Two other commonly used F measures are the $F_{2}$ measure, which weights recall higher than precision, and the $F_{0.5}$ measure, which puts more emphasis on precision than recall.

The F-measure was derived 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

$E = 1 - \left(\frac{\alpha}{P} + \frac{1-\alpha}{R}\right)^{-1}$.

Their relationship is $F_\beta = 1 - E$ where $\alpha=\frac{1}{1 + \beta^2}$.

Applications

The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance. Earlier works focused primarily on the F₁ score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall and so $F_\beta$ is seen in wide application.

The F-score is also used in machine learning. Note, however, that the F-measures do not take the true negative rate into account, and that measures such as the Matthews correlation coefficient may be preferable to assess the performance of a binary classifier.^{[citation needed]}

See also

• Precision and recall
• BLEU
• NIST (metric)
• METEOR
• ROUGE (metric)
• Word Error Rate (WER)
• Noun phrase chunking
• Receiver operating characteristic
• Matthews correlation coefficient