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Searching in metric spaces by spatial approximation

Author:

Gonzalo NavarroAuthors Info & Claims

The VLDB Journal — The International Journal on Very Large Data Bases, Volume 11, Issue 1

Pages 28 - 46

https://doi.org/10.1007/s007780200060

Published: 01 August 2002 Publication History

Abstract

We propose a new data structure to search in metric spaces. A metric space is formed by a collection of objects and a distance function defined among them which satisfies the triangle inequality. The goal is, given a set of objects and a query, retrieve those objects close enough to the query. The complexity measure is the number of distances computed to achieve this goal. Our data structure, called sa-tree (“spatial approximation tree”), is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures. We analyze our method and show that the number of distance evaluations to search among n objects is sublinear. We show experimentally that the sa-tree is the best existing technique when the metric space is hard to search or the query has low selectivity. These are the most important unsolved cases in real applications. As a practical advantage, our data structure is one of the few that does not need to tune parameters, which makes it appealing for use by non-experts.

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Searching in metric spaces by spatial approximation

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cover image The VLDB Journal — The International Journal on Very Large Data Bases

The VLDB Journal — The International Journal on Very Large Data Bases Volume 11, Issue 1

August 2002

91 pages

ISSN:1066-8888

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 2002

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Cited By

Patel LKraft PGuestrin CZaharia M(2024)ACORN: Performant and Predicate-Agnostic Search Over Vector Embeddings and Structured DataProceedings of the ACM on Management of Data10.1145/36549232:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654923
Hezel NBarthel KSchall KJung KGurrin CKongkachandra RSchoeffmann KDang-Nguyen DRossetto LSatoh SZhou L(2024)An Exploration Graph with Continuous Refinement for Efficient Multimedia RetrievalProceedings of the 2024 International Conference on Multimedia Retrieval10.1145/3652583.3658117(657-665)Online publication date: 30-May-2024
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Pan JWang JLi G(2024)Survey of vector database management systemsThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-024-00864-x33:5(1591-1615)Online publication date: 1-Sep-2024
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Indyk PXu HOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Worst-case performance of popular approximate nearest neighbor search implementationsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669013(66239-66256)Online publication date: 10-Dec-2023
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Lampropoulos KZardbani FMamoulis NKarras P(2023)Adaptive Indexing in High-Dimensional Metric SpacesProceedings of the VLDB Endowment10.14778/3603581.360359216:10(2525-2537)Online publication date: 1-Jun-2023
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