Fmeas

F-measure, commonly referred to as the F1 score in its standard form, is a performance metric used to evaluate binary (and multi-class) classification tasks. It combines precision and recall into a single value, the harmonic mean of the two, which helps to balance the trade-off between correctly identifying positives and avoiding false positives.

Precision measures the proportion of predicted positives that are true positives, while recall measures the proportion of actual positives that are retrieved. They are defined from the confusion matrix as follows: precision = TP / (TP + FP) and recall = TP / (TP + FN), where TP is true positives, FP false positives, and FN false negatives.

The general F-measure with a beta parameter is defined as F_beta = (1 + beta^2) * precision * recall / (beta^2 * precision + recall). Equivalently, in terms of TP, FP, FN: F_beta = (1 + beta^2) * TP / [ (1 + beta^2) * TP + beta^2 * FP + FN ]. The F1 score uses beta = 1, yielding F1 = 2 * precision * recall / (precision + recall) = 2TP / (2TP + FP + FN).

F-measure ranges from 0 to 1, with 1 indicating perfect precision and recall. It is widely used in information retrieval, natural language processing, and computer vision, and can be averaged across classes using macro, micro, or weighted methods for multi-class evaluation. Limitations include sensitivity to class distribution and the fact that F-measure provides a single summary that may obscure distinct errors; choosing beta allows different emphasis on precision versus recall depending on the application.