On the application of convex transforms to metric search
Abstract
Scalable similarity search in metric spaces relies on using the mathematical properties of the space in order to allow efficient querying. Most important in this context is the triangle inequality property, which can allow the majority of individual similarity comparisons to be avoided for a given query. However many important metric spaces, typically those with high dimensionality, are not amenable to such techniques. In the past convex transforms have been studied as a pragmatic mechanism which can overcome this effect; however the problem with this approach is that the metric properties may be lost, leading to loss of accuracy. Here, we study the underlying properties of such transforms and their effect on metric indexing mechanisms. We show there are some spaces where certain transforms may be applied without loss of accuracy, and further spaces where we can understand the engineering tradeoffs between accuracy and efficiency. We back these observations with experimental analysis. To highlight the value of the approach, we show three large spaces deriving from practical domains whose dimensionality prevents normal indexing techniques, but where the transforms applied give scalable access with a relatively small loss of accuracy.
Citation
Connor , R , Dearle , A , Mic , V & Zezula , P 2020 , ' On the application of convex transforms to metric search ' , Pattern Recognition Letters , vol. 138 , pp. 563-570 . https://doi.org/10.1016/j.patrec.2020.08.008
Publication
Pattern Recognition Letters
Status
Peer reviewed
ISSN
0167-8655Type
Journal article
Description
Funding: This research was supported by ERDF “CyberSecurity, CyberCrime and Critical Information Infrastructures Center of Excellence” (No.CZ.02.1.01/0.0/0.0/16 019/0000822) and by ESRC “Administrative Data Research Centres 2018” (No. ES/S007407/1).Collections
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