# Further Generalizations of the Jaccard Index

arXiv: https://arxiv.org/abs/2110.09619 · HTML: https://mlsanity.com/paper/2110.09619/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 46 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 1 of 1)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)

## Built on by (most cited first, 26 of 26)

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## Abstract (arXiv)

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.