Title
New relations between similarity measures for vectors based on vector norms New relations between similarity measures for vectors based on vector norms
Author
Faculty/Department
Faculty of Social Sciences. Instructional and Educational Sciences
Publication type
article
Publication
Washington, D.C. ,
Subject
Documentation and information
Computer. Automation
Source (journal)
Journal of the American Society for Information Science and Technology. - Washington, D.C., 2001 - 2013
Volume/pages
60(2009) :2 , p. 232-239
ISSN
1532-2882
1532-2890
ISI
000263136200002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The well-known similarity measures Jaccard, Salton's cosine, Dice, and several related overlap measures for vectors are compared. While general relations are not possible to prove, we study these measures on the trajectories of the form , where a > 0 is a constant and ||·|| denotes the Euclidean norm of a vector. In this case, direct functional relations between these measures are proved. For Jaccard, we prove that it is a convexly increasing function of Salton's cosine measure, but always smaller than or equal to the latter, hereby explaining a curve, experimentally found by Leydesdorff. All the other measures have a linear relation with Salton's cosine, reducing even to equality, in case a = 1. Hence, for equally normed vectors (e.g., for normalized vectors) we, essentially, only have Jaccard's measure and Salton's cosine measure since all the other measures are equal to the latter.
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