### 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 ∈ ℝ^{n × 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 language | English (US) |
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Title of host publication | KDD 2006 |

Subtitle of host publication | Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |

Pages | 287-296 |

Number of pages | 10 |

State | Published - Oct 16 2006 |

Event | KDD 2006: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - Philadelphia, PA, United States Duration: Aug 20 2006 → Aug 23 2006 |

### Publication series

Name | Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |
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Volume | 2006 |

### Other

Other | KDD 2006: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |
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Country | United States |

City | Philadelphia, PA |

Period | 8/20/06 → 8/23/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Information Systems

### Keywords

- Random projections
- Rates of convergence
- Sampling

### Cite this

*KDD 2006: Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining*(pp. 287-296). (Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; Vol. 2006).

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*KDD 2006: Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.*Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, vol. 2006, pp. 287-296, KDD 2006: 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, United States, 8/20/06.

**Very sparse random projections.** / Li, Ping; Hastie, Trevor J.; Church, Kenneth W.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Very sparse random projections

AU - Li, Ping

AU - Hastie, Trevor J.

AU - Church, Kenneth W.

PY - 2006/10/16

Y1 - 2006/10/16

N2 - 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.

AB - 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.

KW - Random projections

KW - Rates of convergence

KW - Sampling

UR - http://www.scopus.com/inward/record.url?scp=33749573641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749573641&partnerID=8YFLogxK

M3 - Conference contribution

SN - 1595933395

SN - 9781595933393

T3 - Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

SP - 287

EP - 296

BT - KDD 2006

ER -