Supermetric Search with the Four-Point Property

  • Richard Connor
  • Lucia Vadicamo
  • Franco Alberto Cardillo
  • Fausto Rabitti
Conference paper

DOI: 10.1007/978-3-319-46759-7_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9939)
Cite this paper as:
Connor R., Vadicamo L., Cardillo F.A., Rabitti F. (2016) Supermetric Search with the Four-Point Property. In: Amsaleg L., Houle M., Schubert E. (eds) Similarity Search and Applications. SISAP 2016. Lecture Notes in Computer Science, vol 9939. Springer, Cham

Abstract

Metric indexing research 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 such 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 which is finitely 4-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 supermetricspace as, in terms of metric search, they are significantly more tractable. We show some stronger geometric guarantees deriving from the four-point property which can be used in indexing to great effect, and show results for two of the SISAP benchmark searches that are substantially better than any previously published.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Richard Connor
    • 1
  • Lucia Vadicamo
    • 2
  • Franco Alberto Cardillo
    • 3
  • Fausto Rabitti
    • 2
  1. 1.Department of Computer and Information SciencesUniversity of StrathclydeGlasgowUK
  2. 2.Institute of Information Science and Technologies (ISTI), CNRPisaItaly
  3. 3.Institute of Computational Linguistics (ILC), CNRPisaItaly

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