Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/27669
Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Hilbert exclusion: Improved metric search through finite isometric embeddings
Author(s): Connor, Richard
Cardillo, Franco Alberto
Vadicamo, Lucia
Rabitti, Fausto
Contact Email: richard.connor@stir.ac.uk
Issue Date: 9-Jun-2017
Citation: Connor R, Cardillo FA, Vadicamo L & Rabitti F (2017) Hilbert exclusion: Improved metric search through finite isometric embeddings. ACM Transactions on Information Systems, 35 (3), Art. No.: 17. https://doi.org/10.1145/3001583
Abstract: Most research into similarity search in metric spaces relies on the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common metric spaces, notably including those using Euclidean and Jensen-Shannon distances, also have a stronger property, sometimes called the four-point property: In essence, these spaces allow an isometric embedding of any four points in three-dimensional Euclidean space, as well as any three points in two-dimensional Euclidean space. In fact, we show that any space that is isometrically embeddable in Hilbert space has the stronger property. This property gives stronger geometric guarantees, and one in particular, which we name the Hilbert Exclusion property, allows any indexing mechanism which uses hyperplane partitioning to perform better. One outcome of this observation is that a number of state-of-the-art indexing mechanisms over high-dimensional spaces can be easily refined to give a significant increase in performance; furthermore, the improvement given is greater in higher dimensions. This therefore leads to a significant improvement in the cost of metric search in these spaces.
DOI Link: 10.1145/3001583
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