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Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.
Étude comparative de la distribution florale dans une portion des Alpes et du Jura
P. Jaccard · 1901
Earlier work this paper cites.
On a certain distance of sets and the corresponding distance of functions
E. Marczewski, H. Steinhaus · 1958
Earlier work this paper cites.
An elementary mathematical theory of classification and prediction
T. T. Tanimoto · 1958
Earlier work this paper cites.
Distance between sets
M. Levandowsky, D. Winter · 1971
Earlier work this paper cites.
Distance between sets
G. Gilbert · 1972
Earlier work this paper cites.
Minimizing a submodular function on a lattice
D. M. Topkis · 1978
Earlier work this paper cites.
A proof of the triangle inequality for the Tanimoto distance
A. H. Lipkus · 1999
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Similarity Estimation Techniques from Rounding Algorithms
M. S. Charikar · 2002
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Combinatorial Optimization
A. Schrijver · 2003
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Metrics for Mining Multisets
W. A. Kosters, J. F. J. Laros · 2007
Cited alongside, same era.
Similarity, Dissimilarity and Distance, Measures of
J. C. Gower · 2008
Cited alongside, same era.
Mathematical Tools for Data Mining
D. A. Simovici, C. Djeraba · 2008
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Encyclopedia of Distances
M. M. Deza, E. Deza · 2009
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Metrics based on average distance between sets
O. Fujita · 2013
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Measuring Distance Between Unordered Sets of Different Sizes
A. Gardner, J. Kanno, C. A. Duncan, R. Selmic · 2014
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Submodular Hamming Metrics
J. Gillenwater, R. Iyer, B. Lusch, R. Kidambi, J. A. Bilmes · 2015
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