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An elementary proof of a theorem of Johnson and Lindenstrauss
Abstract
A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/ϵ2)‐dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 ± ϵ). In this note, we prove this theorem using elementary probabilistic techniques. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 22: 60–65, 2002
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Approximate nearest neighbors: towards removing the curse of dimensionality
Indyk, P., & Motwani, R. (1998) · Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98 · doi:10.1145/276698.276876 · Cited by 4,188
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“To further reduce coreset selection time, we follow [49], making use of the Johnson-Lindenstrauss theorem [11] to reduce dimensionalities of elements m ∈ M through random linear projections ψ : R → Rd with d∗ < d.”
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Metadata
- Authors
- Dasgupta, S., & Gupta, A.
- Venue
- Random Structures & Algorithms
- Publisher
- Wiley
- Published
- 2002-11-25
- Volume
- 22
- Issue
- 1
- Pages
- 60-65
- ISSN
- 1042-9832 (ISSN-L)
- 1098-2418
- OpenAlex
- W2088658556
- Cited by
- 932
- References
- 1
- FWCI
- 1.34
- Type
- journal article
- Language
- en
- Open access
- closed
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