## F1-Score

The F1-Score is the harmonic mean of precision and recall: \[ F_1 = 2 \cdot \frac{precision \cdot recall}{precision + recall} \]
Where

**Precision** is defined as \[ \frac{TP}{TP+FP} \] and

**Recall** is defined as \[ \frac{TP}{TP+FN}
\]
The F1-Score originates from the binary classification background, where we only have two classes that we want to distinguish:

**positive** and

**negative**.
In this scenario there are four possible outcomes:

**TP (True Positive):** The object belongs to class **positive** and we classified it as **positive**,
**FP (False Positive ):** The object belongs to class **negative** and we classified it as **positive**,
**TN (True Negative):** The object belongs to class **negative** and we classified it as **negative**,
**FN (False Negative):** The object belongs to class **positive** but we classified it as **negative**

| | Reality |

| | Positive | Negative |

Prediction | Positive | TP | FP |

Negative | FN | TN |