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In a classification task, the precision for a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of elements labelled as belonging to the positive class (i.e. the sum of true positives and false positives, which are items incorrectly labelled as belonging to the class).
Precision and recall. In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. 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 samples predicted to be positive, including those not identified correctly ...
An F-score is a combination of the precision and the recall, providing a single score. There is a one-parameter family of statistics, with parameter β, which determines the relative weights of precision and recall. The traditional or balanced F-score is the harmonic mean of precision and recall:
The F-score combines precision and recall into one number via a choice of weighing, most simply equal weighing, as the balanced F-score . Some metrics come from regression coefficients : the markedness and the informedness , and their geometric mean , the Matthews correlation coefficient .
Two other commonly used F measures are the measure, which weights recall twice as much as precision, and the measure, which weights precision twice as much as recall. The F-measure was derived by van Rijsbergen (1979) so that F β {\displaystyle F_{\beta }} "measures the effectiveness of retrieval with respect to a user who attaches β ...
The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications.
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The precision of 10 / 10 + 990 = 1% reveals its poor performance. As the classes are so unbalanced, a better metric is the F1 score = 2 × 0.01 × 1 / 0.01 + 1 ≈ 2% (the recall being 10 + 0 / 10 = 1).