Hilbert exclusion: improved metric search through finite isometric embeddings
Connor R., Cardillo F. A., Vadicamo L., Rabitti F.
H. Information systems. Retrieval models and ranking Metric space Management and Accounting Information Systems F. Theory of computation. Random projections and metric embeddings Similarity search Metric indexing Four-point property Information Retrieval (cs.IR) Computer Science - Information Retrieval FOS: Computer and information sciences Computer Science Applications H. Information systems. Proximity search H. Information systems. Database query processing General Business Information systems. Retrieval efficiency H. Information systems. Multimedia information systems Hilbert embedding H. Information systems. Multidimensional range search H.3.3 H. Information systems. Data structures
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.
Source: ACM transactions on information systems 35 (2017): 17–27. doi:10.1145/3001583
Publisher: Association for Computing Machinery,, New York, NY , Stati Uniti d'America
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Data Set euc 6 euc 8 euc 10 euc 12 euc 14 tri 6 tri 8 tri 10 tri 12 tri 14 jsd 6 jsd 8 jsd 10 jsd 12 jsd 14
Metrics
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@article{oai:it.cnr:prodotti:363052,
title = {Hilbert exclusion: improved metric search through finite isometric embeddings},
author = {Connor R. and Cardillo F. A. and Vadicamo L. and Rabitti F.},
publisher = {Association for Computing Machinery,, New York, NY , Stati Uniti d'America},
doi = {10.1145/3001583 and 10.48550/arxiv.1604.08640},
journal = {ACM transactions on information systems},
volume = {35},
pages = {17–27},
year = {2017}
}
0000-0003-0940-4768ISTI Repository
DOI
10.1145/3001583
10.48550/arxiv.1604.08640
arXiv.org e-Print Archive
ACM Transactions on Information Systems
doi.acm.org