F-Score

Table of contents

1. Confusion matrix
2. Precision and Recall
   1. Precision
   2. Recall
3. F1-score

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Confusion matrix

Actual\Prediction	Positive	Negative
Positive	True Positive	False Negative
Negative	False Positive	True Negative

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Precision and Recall

Walber, CC BY-SA 4.0, via Wikimedia Commons

Precision

Also called the positive predict value (PPV),

$$precision=\frac{TP}{TP+FP}$$

Recall

Also called the sensitivity,

$$recall=\frac{TP}{TP+FN}$$

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F1-score

An F-score is a measure of a binary classification’s accuracy.

There exists a general F-score of $F_{\beta }$, where the $\beta$ acts as a weight of importance for recall.

However, the balanced F-score (or $F_1$ score), where precision and recall are considered equally, is the harmonic mean of precision and recall:

$$F_1=\frac{2}{recal{l}^{-1}+precisio{n}^{-1}}=2\cdot \frac{precision\cdot recall}{precision+recall}=\frac{TP}{TP+\frac{1}{2}(FP+FN)}$$

Where $0\le F_1\le 1$.

$F_1$ of $1.0$ means perfect precision and recall, while $0$ means either one of them was $0$.

Always remeber that F1 score (and the whole TP, TN …) is dependent on which threshold was selected (by examining ROC, etc.).
Low F1 score does not represent the performance of the entire model, but the performance at a certain classification threshold.