2017
Journal article  Open Access

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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BibTeX entry
@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}
}