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Distance between Sets

Abstract

DISTANCE functions expressing the degree of dissimilarity of sets have found use in physical anthropology1, psychology2, numerical taxonomy3, ecology3 and elsewhere. During an ecological study by one of us, it was noticed that the similarity coefficient of Jaccard6, used in ecology, gives rise to a metric function satisfying the triangle inequality. For two non-empty finite sets X, Y, the Jaccard coefficient is the number of elements in the intersection XY of X and Y. This coefficient (we use absolute value signs to indicate number of elements) has a heuristic interpretation. It measures the probability that an element of at least one of two sets is an element of both, and thus is a reasonable measure of similarity or “overlap” between the two. The one-complement may then be considered a measure of the dissimilarity of the two sets.

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References

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LEVANDOWSKY, M., WINTER, D. Distance between Sets. Nature 234, 34–35 (1971). https://doi.org/10.1038/234034a0

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  • DOI: https://doi.org/10.1038/234034a0

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