Very sparse random projections

Ping Li, Trevor J. Hastie, Kenneth W. Church

Research output: Chapter in Book/Report/Conference proceedingConference contribution

363 Scopus citations

Abstract

There has been considerable interest in random projections, an approximate algorithm for estimating distances between pairs of points in a high-dimensional vector space. Let A ∈ ℝn × D be our n points in D dimensions. The method multiplies A by a random matrix R ∈ ℝ D × k, reducing the D dimensions down to just k for speeding up the computation. R typically consists of entries of standard normal N(0, 1). It is well known that random projections preserve pairwise distances (in the expectation). Achlioptas proposed sparse random projections by replacing the N(0, 1) entries in R with entries in {-1, 0, 1} with probabilities {1/6, 2/3, 1/6}, achieving a threefold speedup in processing time. We recommend using R of entries in {-1, 0, 1} with probabilities {1/2√D, 1 - 1/√D, 1/2√D} for achieving a significant √D-fold speedup, with little loss in accuracy.

Original languageEnglish (US)
Title of host publicationKDD 2006
Subtitle of host publicationProceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery (ACM)
Pages287-296
Number of pages10
ISBN (Print)1595933395, 9781595933393
DOIs
StatePublished - 2006
Externally publishedYes
EventKDD 2006: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - Philadelphia, PA, United States
Duration: Aug 20 2006Aug 23 2006

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Volume2006

Other

OtherKDD 2006: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Country/TerritoryUnited States
CityPhiladelphia, PA
Period8/20/068/23/06

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems

Keywords

  • Random projections
  • Rates of convergence
  • Sampling

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