 
Summary: Fast Computation of Low Rank Matrix Approximations
Dimitris Achlioptas
Department of Computer Science
University of California at Santa Cruz
Santa Cruz, CA 95060
optas@cs.ucsc.edu
Frank McSherry
Microsoft Research
1065 La Avenida
Mountain View, CA 94043
mcsherry@microsoft.com
Abstract
Given a matrix A, it is often desirable to find a good approximation to A that has low rank.
We introduce a simple technique for accelerating the computation of such approximations when
A has strong spectral features, i.e., when the singular values of interest are significantly greater
than those of a random matrix with size and entries similar to A. Our technique amounts to
independently sampling and/or quantizing the entries of A, thus speeding up computation by
reducing the number of nonzero entries and/or the length of their representation. Our analysis
is based on observing that the acts of sampling and quantization can be viewed as adding a
random matrix N to A, whose entries are independent random variables with zeromean and
