ClustEval clustering evaluation framework
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: