Abstract
Given a set S of n data points in some metric space. Given a query point q in this space, a nearest neighbor query asks for the nearest point of S to q. Throughout we will assume that the space is real d-dimensional space Rd, and the metric is Euclidean distance. The goal is to preprocess S into a data structure so that such queries can be answered efficiently. Nearest neighbor searching has applications in many areas, including data mining [7], pattern classification [5], data compression [10].
The support of the National Science Foundation under grant CCR-9712379 is gratefully acknowledged.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Wu. An optimal algorithm for approximate nearest neighbor searching. In Proc. 5th ACM-SIAM Sympos. Discrete Algorithms, pages 573–582, 1994.
P. Ciaccia and M. Patella. Using the distance distribution for approximate similarity queries in high-dimensional metric spaces. In Proc. 10th Workshop Database and Expert Systems Applications, pages 200–205, 1999.
K. L. Clarkson. An algorithm for approximate closest-point queries. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 160–164, 1994.
M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, 1997.
R. O. Duda and P. E. Hart. Pattern Classification and Scene Analysis. John Wiley & Sons, New York, NY, 1973.
C. Faloutsos and I. Kamel. Beyond uniformity and independence: Analysis of R-trees using the concept of fractal dimension. In Proc. Annu. ACM Sympos. Principles Database Syst., pages 4–13, 1994.
U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy. Advances in Knowledge Discovery and Data Mining. AAAI Press/Mit Press, 1996.
J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Trans. Math. Software, 3(3):209–226, 1977.
K. Fukunaga. Introduction to Statistical Pattern Recognition. Academic Press, 2nd edition, 1990.
A. Gersho and R. M. Gray. Vector Quantization and Signal Compression. Kluwer Academic, Boston, MA, 1992.
P. Indyk and R. Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. In Proc. 30th Annu. ACM Sympos. Theory Comput., pages 604–613, 1998.
S. Maneewongvatana and D. Mount. An empirical study of a new approach to nearest nearbor searching. In ALENEX, 2001.
V. Vapnik. Statistical Learning Theory. John Wiley & Sons, New York, NY, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maneewongvatana, S., Mount, D.M. (2001). The Analysis of a Probabilistic Approach to Nearest Neighbor Searching. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_26
Download citation
DOI: https://doi.org/10.1007/3-540-44634-6_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42423-9
Online ISBN: 978-3-540-44634-7
eBook Packages: Springer Book Archive