On the expected exclusion power of binary partitions for metric search
MetadataShow full item record
The entire history and, we dare say, future of similarity search is governed by the underlying notion of partition. A partition is an equivalence relation defined over the space, therefore each element of the space is contained within precisely one of the equivalence classes of the partition. All attempts to search a finite space efficiently, whether exactly or approximately, rely on some set of principles which imply that if the query is within one equivalence class, then one or more other classes either cannot, or probably do not, contain any of its solutions. In most early research, partitions relied only on the metric postulates, and logarithmic search time could be obtained on low dimensional spaces. In these cases, it was straightforward to identify multiple partitions, each of which gave a relatively high probability of identifying subsets of the space which could not contain solutions. Over time the datasets being searched have become more complex, leading to higher dimensional spaces. It is now understood that even an approximate search in a very high-dimensional space is destined to require O(n) time and space. Almost entirely missing from the research literature however is any analysis of exactly when this effect takes over. In this paper, we make a start on tackling this important issue. Using a quantitative approach, we aim to shed some light on the notion of the exclusion power of partitions, in an attempt to better understand their nature with respect to increasing dimensionality.
Vadicamo , L , Dearle , A & Connor , R 2022 , On the expected exclusion power of binary partitions for metric search . in T Skopal , F Falchi , J Lokoč , M L Sapino , I Bartolini & M Patella (eds) , Similarity search and applications : 15 th International conference, SISAP 2022, Bologna, Italy, October 5–7, 2022, proceedings . Lecture notes in computer science , vol. 13590 , Springer, Cham , Cham , pp. 104-117 , International Conference on Similarity Search and Applications, SISAP 2022 , Bologna , Italy , 5/10/22 . https://doi.org/10.1007/978-3-031-17849-8_9conference
Similarity search and applications
Copyright © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/978-3-031-17849-8_9.
DescriptionFunding: This work was partially funded by AI4Media - A European Excellence Centre for Media, Society, and Democracy (EC, H2020 n. 951911) and by Economic & Social Research Council, ADR UK Programme ES/W010321/1.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.