## Jaccard Index (R)

The Jaccard Index neglects the true negatives (TN) and relates the true positives to the number of pairs that either belong to the same class or are in the same cluster. This measure estimates a likelihood of an element being positive, if it is not correctly classified a negative element. This measure is based on the pairwise approach to calculate TP,TN,FP and FN.
\[ J = \frac{TP}{TP+FP+FN} \]
In the binary classification background we 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 |