Publication
Title
New relations between similarity measures for vectors based on vector norms
Author
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.
Language
English
Source (journal)
Journal of the American Society for Information Science and Technology. - Washington, D.C., 2001 - 2013
Publication
Washington, D.C. : 2009
ISSN
1532-2882 [print]
1532-2890 [online]
Volume/pages
60:2(2009), p. 232-239
ISI
000263136200002
Full text (Publishers DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 06.05.2009
Last edited 31.03.2017
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