FMeasure

F-measure, also known as the F-score, is a metric that combines precision and recall into a single value to evaluate the accuracy of a classifier. The general form is Fβ = (1 + β^2) · (P · R) / (β^2 · P + R), where P is precision and R is recall. The parameter β determines the relative importance of precision versus recall.

Precision and recall are defined as P = TP / (TP + FP) and R = TP / (TP + FN), using true positives (TP), false positives (FP), and false negatives (FN). For β = 1, the F1 score, or harmonic mean of precision and recall, is F1 = 2PR / (P + R). The F-measure emphasizes a balance between correctly identified positive cases and the completeness of those identifications.

In multiclass and multilabel settings, F-measures are computed using averaging schemes. Micro-averaged F aggregates TP, FP, and FN across all classes to compute a global precision and recall, then derives Fβ from those values. Macro-averaged F computes the Fβ score for each class in a one-vs-rest fashion and then averages the results; weighted macro averaging uses class support as weights.

Applications and interpretation: F-measure is widely used in information retrieval and machine learning for model comparison, especially when class distribution is imbalanced or when precision and recall have different costs. It is threshold-dependent for binary classifiers and does not inherently account for true negatives. While useful for balancing extraction quality, it is one of several metrics and should be considered alongside other measures such as accuracy, AUC, or the precision-recall curve. The F-measure originated in information retrieval, with the F1 score commonly used as a standard benchmark.