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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8489

Title: New relations between similarity measures for vectors based on vector norms
Authors: EGGHE, Leo
Issue Date: 2009
Publisher: JOHN WILEY & SONS INC
Citation: JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, 60(2). p. 232-239
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 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 . 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.
URI: http://hdl.handle.net/1942/8489
DOI: 10.1002/asi.20949
ISI #: 000263136200002
ISSN: 1532-2882
Category: A1
Type: Journal Contribution
Validation: ecoom, 2010
Appears in Collections: Research publications

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