F-Measure

Synonyms

Harmonic mean of recall and precision

Definition

Assume an information retrieval (IR) system has recall R and precision P on a test document collection and an information need. The F-measure of the system is defined as the weighted harmonic mean of its precision and recall, that is, $F=\frac{1}{\alpha \frac{1}{P}+\left(1-\alpha \right)\frac{1}{R}}$, where the weight α ∈ [0,1]. The balanced F-measure, commonly denoted as F₁ or just F, equally weighs precision and recall, which means α = 1∕2. The F₁ measure can be written as ${F}_1=\frac{2PR}{P+R}$.

Key Points

The F-measure can be viewed as a compromise between recall and precision. It is high only when both recall and precision are high. It is equivalent to recall when α = 0 and precision when α = 1. The F-measure assumes values in the interval [0,1]. It is 0 when no relevant documents have been retrieved, and is 1 if all retrieved documents are relevant and all relevant documents have been retrieved.

Cross-References

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