Definition
The curse of dimensionality is a term introduced by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to Euclidean space (Bellman 1957).
For example, 100 evenly-spaced sample points suffice to sample a unit interval with no more than 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a grid with a spacing of 0.01 between adjacent points would require 1020 sample points: thus, in some sense, the 10D hypercube can be said to be a factor of 1018 “larger” than the unit interval.
Informally, the phrase curse of dimensionality is often used to simply refer to the fact that one’s intuitions about how data structures, similarity measures, and algorithms behave in low dimensions do typically generalize well to higher dimensions.
Background
Another way to envisage the vastness of high-dimensional Euclidean space is to compare the size of the unit sphere with the unit cube as...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsRecommended Reading
Aggarwal CC, Hinneburg A, Keim DA (2001) On the surprising behavior of distance metrics in high dimensional spaces. In: ICDT, London, pp 420–434
Bellman RE (1957) Dynamic programming. Princeton University Press, Princeton
Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. In: Proceedings of the VLDB endowment, Auckland, vol 1, pp 1542–1552
The major database (SIGMOD, VLDB, PODS), data mining (SIGKDD, ICDM, SDM), and machine learning (ICML, NIPS) conferences typically feature several papers which explicitly address the curse of dimensionality each year
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media New York
About this entry
Cite this entry
Keogh, E., Mueen, A. (2017). Curse of Dimensionality. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_192
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7687-1_192
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7685-7
Online ISBN: 978-1-4899-7687-1
eBook Packages: Computer ScienceReference Module Computer Science and Engineering