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dc.contributor.authorConnor, Richard
dc.contributor.authorDearle, Al
dc.contributor.editorSatoh, Shin'ichi
dc.contributor.editorVadicamo, Lucia
dc.contributor.editorZimek, Arthur
dc.contributor.editorCarrara, Fabio
dc.contributor.editorBartolini, Ilaria
dc.contributor.editorAumüller, Martin
dc.contributor.editorJónsson, Björn Þór
dc.contributor.editorPagh, Rasmus
dc.date.accessioned2020-11-11T15:30:14Z
dc.date.available2020-11-11T15:30:14Z
dc.date.issued2020
dc.identifier270188610
dc.identifier8ef1de29-6808-49e0-ab69-a054cfdd49d3
dc.identifier85093852620
dc.identifier000616694200018
dc.identifier.citationConnor , R & Dearle , A 2020 , Sampled angles in high-dimensional spaces . in S Satoh , L Vadicamo , A Zimek , F Carrara , I Bartolini , M Aumüller , B Þ Jónsson & R Pagh (eds) , Similarity Search and Applications : 13th International Conference, SISAP 2020, Copenhagen, Denmark, September 30–October 2, 2020, Proceedings . Lecture Notes in Computer Science (Information Systems and Applications, incl. Internet/Web, and HCI) , vol. 12440 , Springer , Cham , pp. 233-247 , 13th International Conference on Similarity Search and Applications, SISAP 2020 , 30/09/20 . https://doi.org/10.1007/978-3-030-60936-8_18en
dc.identifier.citationconferenceen
dc.identifier.isbn9783030609351
dc.identifier.isbn9783030609368
dc.identifier.issn0302-9743
dc.identifier.urihttps://hdl.handle.net/10023/20953
dc.description.abstractSimilarity search using metric indexing techniques is largely a solved problem in low-dimensional spaces. However techniques based only on the triangle inequality property start to fail as dimensionality increases. Since proper metric spaces allow a finite projection of any three objects into a 2D Euclidean space, the notion of angle can be validly applied among any three (but no more) objects. High dimensionality is known to have interesting effects on angles in vector spaces, but to our knowledge this has not been studied in more general metric spaces. Here, we consider the use of angles among objects in combination with distances. As dimensionality becomes higher, we show that the variance in sampled angles reduces. Furthermore, sampled angles also become correlated with inter-object distances, giving different distributions between query solutions and non-solutions. We show the theoretical underpinnings of this observation in unbounded high-dimensional Euclidean spaces, and then examine how the pure property is reflected in some real-world high dimensional spaces. Our experiments on both generated and real world datasets demonstrate that these observations can have an important impact on the tractability of search as dimensionality increases.
dc.format.extent1882626
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofSimilarity Search and Applicationsen
dc.relation.ispartofseriesLecture Notes in Computer Science (Information Systems and Applications, incl. Internet/Web, and HCI)en
dc.subjectMetric searchen
dc.subjectHigh dimensional spaceen
dc.subjectQA75 Electronic computers. Computer scienceen
dc.subjectDASen
dc.subjectBDCen
dc.subject.lccQA75en
dc.titleSampled angles in high-dimensional spacesen
dc.typeConference itemen
dc.contributor.institutionUniversity of St Andrews. School of Computer Scienceen
dc.identifier.doi10.1007/978-3-030-60936-8_18
dc.date.embargoedUntil2020-11-11
dc.identifier.urlhttps://www.springer.com/gp/book/9783030609351en


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