An elementary proof of a theorem of Johnson and Lindenstrauss

Authors:
Sanjoy Dasgupta;Anupam Gupta
Affiliations:
AT&T Labs Research, Room A277, Florham Park, New Jersey;Lucent Bell Labs, Room 2C-355, 600 Mountain Avenue, Murray Hill, New Jersey
Venue:
Random Structures & Algorithms
Year:
2003

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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.