  In this paper we present a practical solution with performance guarantees to
the problem of dimensionality reduction for very large scale sparse matrices.
We show applications of our approach to computing the low rank approximation
(reduced SVD) of such matrices. Our solution uses coresets, which is a subset
of $O(k/\eps^2)$ scaled rows from the $n\times d$ input matrix, that
approximates the sub of squared distances from its rows to every
$k$-dimensional subspace in $\REAL^d$, up to a factor of $1\pm\eps$. An open
theoretical problem has been whether we can compute such a coreset that is
independent of the input matrix and also a weighted subset of its rows. %An
open practical problem has been whether we can compute a non-trivial
approximation to the reduced SVD of very large databases such as the Wikipedia
document-term matrix in a reasonable time. We answer this question
affirmatively. % and demonstrate an algorithm that efficiently computes a low
rank approximation of the entire English Wikipedia. Our main technical result
is a novel technique for deterministic coreset construction that is based on a
reduction to the problem of $\ell_2$ approximation for item frequencies.
