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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Supermetric search
Author(s): Connor, Richard
Vadicamo, Lucia
Cardillo, Franco Alberto
Rabitti, Fausto
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Keywords: similarity search
metric space
supermetric space
metric indexing
four-point property
Hilbert exclusion
Issue Date: 28-Feb-2019
Citation: Connor R, Vadicamo L, Cardillo FA & Rabitti F (2019) Supermetric search. Information Systems, 80, pp. 108-123.
Abstract: Metric search is concerned with the efficient evaluation of queries in metric spaces. In general, a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space that is finitely four-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property. All spaces with the four-point property are metric spaces, but they also have some stronger geometric guarantees. We coin the term supermetric space as, in terms of metric search, they are significantly more tractable. Supermetric spaces include all those governed by Euclidean, Cosine, Jensen–Shannon and Triangular distances, and are thus commonly used within many domains. In previous work we have given a generic mathematical basis for the supermetric property and shown how it can improve indexing performance for a given exact search structure. Here we present a full investigation into its use within a variety of different hyperplane partition indexing structures, and go on to show some more of its flexibility by examining a search structure whose partition and exclusion conditions are tailored, at each node, to suit the individual reference points and data set present there. Among the results given, we show a new best performance for exact search using a well-known benchmark.
DOI Link: 10.1016/
Rights: Accepted refereed manuscript of: Connor R, Vadicamo L, Cardillo FA & Rabitti F (2019) Supermetric search. Information Systems, 80, pp. 108-123. DOI: © 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
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