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:
The general formula for non-negative real β is:
The formula in terms of Type I and type II errors:
Two other commonly used F measures are the F2 measure, which weights recall twice as much as precision, and the F0.5 measure, which weights precision twice as much as recall.
The F-measure was derived so that Fβ "measures the effectiveness of retrieval with respect to a user who attaches β times as much importance to recall as precision" [1]. It is based on van Rijsbergen's effectiveness measure E = 1 − (1 / (α / P + (1 − α) / R)). Their relationship is Fβ = 1 − E where α = 1 / (β2 + 1).
Information Retrieval
The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance [2]. 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 [3] and so Fβ is seen in wide application.
References
- ^ van Rijsbergen, C. J. (1979). Information Retrieval (2nd ed.). Butterworth.
- ^ Steven M. Beitzel. (2006). On Understanding and Classifying Web Queries. Phd Thesis. http://ir.iit.edu/~steve/beitzel_phd_thesis.pdf.
- ^ X. Li, Y.-Y. Wang, and A. Acero (July 2008). "Learning query intent from regularized click graphs". Proceedings of the 31st SIGIR Conference.
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