Querying high-dimensional data in single-dimensional space

Querying high-dimensional data in single-dimensional space In this paper, we propose a new tunable index scheme, called iMinMax( $\theta$ ), that maps points in high-dimensional spaces to single-dimensional values determined by their maximum or minimum values among all dimensions. By varying the tuning “knob”, $\theta$ , we can obtain different families of iMinMax structures that are optimized for different distributions of data sets. The transformed data can then be indexed using existing single-dimensional indexing structures such as the B + -trees. Queries in the high-dimensional space have to be transformed into queries in the single-dimensional space and evaluated there. We present efficient algorithms for evaluating window queries as range queries on the single-dimensional space. We conducted an extensive performance study to evaluate the effectiveness of the proposed schemes. Our results show that iMinMax( $\theta$ ) outperforms existing techniques, including the Pyramid scheme and VA-file, by a wide margin. We then describe how iMinMax could be used in approximate K-nearest neighbor (KNN) search, and we present a comparative study against the recently proposed iDistance, a specialized KNN indexing method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The VLDB Journal Springer Journals

Querying high-dimensional data in single-dimensional space

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Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag
Subject
ComputerScience
ISSN
1066-8888
eISSN
0949-877X
D.O.I.
10.1007/s00778-004-0121-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose a new tunable index scheme, called iMinMax( $\theta$ ), that maps points in high-dimensional spaces to single-dimensional values determined by their maximum or minimum values among all dimensions. By varying the tuning “knob”, $\theta$ , we can obtain different families of iMinMax structures that are optimized for different distributions of data sets. The transformed data can then be indexed using existing single-dimensional indexing structures such as the B + -trees. Queries in the high-dimensional space have to be transformed into queries in the single-dimensional space and evaluated there. We present efficient algorithms for evaluating window queries as range queries on the single-dimensional space. We conducted an extensive performance study to evaluate the effectiveness of the proposed schemes. Our results show that iMinMax( $\theta$ ) outperforms existing techniques, including the Pyramid scheme and VA-file, by a wide margin. We then describe how iMinMax could be used in approximate K-nearest neighbor (KNN) search, and we present a comparative study against the recently proposed iDistance, a specialized KNN indexing method.

Journal

The VLDB JournalSpringer Journals

Published: May 1, 2004

References

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