F1Wert

The F1-Wert (German for “F1‑value”) is a statistical measure that evaluates the accuracy of binary classification models in machine learning and information retrieval. It is defined as the harmonic mean of precision and recall, two key performance metrics. Precision is the ratio of correctly predicted positive instances to all instances predicted as positive, while recall is the ratio of correctly predicted positive instances to all actual positive instances.

The F1‑Wert is calculated by the formula:

\[F1 = \frac{2 \times \text{precision} \times \text{recall}}{\text{precision} + \text{recall}}\]

This value ranges from 0 to 1, where 0 indicates the worst possible performance and 1 denotes perfect precision and recall simultaneously. The harmonic mean penalizes extreme values, so a high F1‑Wert requires both high precision and high recall.

The metric is especially useful for imbalanced datasets because it does not consider true negatives, focusing only on the positive class. It is widely applied in tasks such as text classification, spam filtering, and medical diagnosis. For multi‑class problems, micro‑averaging aggregates contributions of all classes before computing precision and recall, while macro‑averaging averages the F1‑Werte of each class independently.

The F1‑Wert is related to the Dice coefficient and the Jaccard index; the Dice coefficient is twice the F1‑Wert divided by one plus the F1‑Wert. Limitations include its insensitivity to true negatives and its potential to mask poor performance in one of the metrics if the other is high. Nonetheless, it remains a standard measure for balancing precision and recall in classification evaluation.