A tale of four metrics

Richard Connor*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


There are many contexts where the definition of similarity in multivariate space requires to be based on the correlation, rather than absolute value, of the variables. Examples include classic IR measurements such as TDF/IF and BM25, client similarity measures based on collaborative filtering, feature analysis of chemical molecules, and biodiversity contexts. In such cases, it is almost standard for Cosine similarity to be used. More recently, Jensen-Shannon divergence has appeared in a proper metric form, and a related metric Structural Entropic Distance (SED) has been investigated. A fourth metric, based on a little-known divergence function named as Triangular Divergence, is also assessed here. For these metrics, we study their properties in the context of similarity and metric search. We compare and contrast their semantics and performance. Our conclusion is that, despite Cosine Distance being an almost automatic choice in this context, Triangular Distance is most likely to be the best choice in terms of a compromise between semantics and performance.

Original languageEnglish
Title of host publicationSimilarity Search and Applications - 9th International Conference, SISAP 2016, Proceedings
EditorsErich Schubert, Michael E. Houle, Laurent Amsaleg
Number of pages8
ISBN (Print)9783319467580
Publication statusPublished - 1 Jan 2016
Event9th International Conference on Similarity Search and Applications, SISAP 2016 - Tokyo, Japan
Duration: 24 Oct 201626 Oct 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9939 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Similarity Search and Applications, SISAP 2016


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