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http://www.elsevier.com/locate/jcss Journal of Computer and System Sciences 66 (2003) 671687

Summary: http://www.elsevier.com/locate/jcss
Journal of Computer and System Sciences 66 (2003) 671687
Database-friendly random projections:
Johnson-Lindenstrauss with binary coins
Dimitris Achlioptas
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
Received 28 August 2001; revised 19 July 2002
A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean
space can be embedded into k-dimensional Euclidean space--where k is logarithmic in n and independent
of d--so that all pairwise distances are maintained within an arbitrarily small factor. All known
constructions of such embeddings involve projecting the n points onto a spherically random k-dimensional
hyperplane through the origin. We give two constructions of such embeddings with the property that all
elements of the projection matrix belong in f1; 0; 1g: Such constructions are particularly well suited for
database environments, as the computation of the embedding reduces to evaluating a single aggregate over
k random partitions of the attributes.
r 2003 Elsevier Science (USA). All rights reserved.
1. Introduction
Consider projecting the points of your favorite sculpture first onto the plane and then onto a
single line. The result amply demonstrates the power of dimensionality.


Source: Achlioptas, Dimitris - Department of Computer Engineering, University of California at Santa Cruz


Collections: Computer Technologies and Information Sciences