Further Generalizations of the Jaccard Index
- URL: http://arxiv.org/abs/2110.09619v2
- Date: Wed, 20 Oct 2021 10:12:15 GMT
- Title: Further Generalizations of the Jaccard Index
- Authors: Luciano da F. Costa
- Abstract summary: Quantifying the similarity between two sets constitutes a particularly interesting and useful operation in several theoretical and applied problems involving set theory.
The Jaccard index has been extensively used in the most diverse types of problems, also motivating respective generalizations.
It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities.
- Score: 1.0152838128195467
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Quantifying the similarity between two sets constitutes a particularly
interesting and useful operation in several theoretical and applied problems
involving set theory. Aimed at quantifying the similarity between two sets, the
Jaccard index has been extensively used in the most diverse types of problems,
also motivating respective generalizations. The present work addressew further
generalizations of this index, including its modification into a coincidence
index capable of accounting also for the level of interiority of the sets, an
extension for sets in continuous vector spaces, the consideration of weights
associated to the involved set elements, the generalization to multiset
addition, densities and generic scalar fields, as well as a means to quantify
the joint interdependence between random variables. The also interesting
possibility to take into account more than two sets was also addressed,
including the description of an index capable of quantifying the level of
chaining between three sets. Several of the described and suggested
generalizations 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.
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