F-score
In statistical analysis of binary classification, the F-score or F-measure is a measure of a test's accuracy. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all positive results, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. Precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the lowest possible value is 0, if either precision or recall are zero. Etymology The name F-measure is believed to be named after a different F function in Van Rijsbergen's book, when introduced to the Fourth Message Understanding Conference (MUC-4, 1992). Definition The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall: . Fβ score A more general F score, , that uses a positive real factor , where is chosen such that recall is considered times as important as precision, is: . In terms of Type I and type II errors this becomes: . Two commonly used values for are 2, which weighs recall higher than precision, and 0.5, which weighs recall lower than precision. The F-measure was derived so that "measures the effectiveness of retrieval with respect to a user who attaches times as much importance to recall as precision". It is based on Van Rijsbergen's effectiveness measure . Their relationship is where . Diagnostic testing This is related to the field of binary classification where recall is often termed "sensitivity". Dependence of the F-score on class imbalance Precision-recall curve, and thus the score, explicitly depends on the ratio of positive to negative test cases. This means that comparison of the F-score across different problems with differing class ratios is problematic. One way to address this issue (see e.g., Siblini et al, 2020 ) is to use a standard class ratio when making such comparisons. 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 is seen in wide application. The F-score is also used in machine learning. However, the F-measures do not take true negatives into account, hence measures such as the Matthews correlation coefficient, Informedness or Cohen's kappa may be preferred to assess the performance of a binary classifier. The F-score has been widely used in the natural language