  We present a new computational approach to approximating a large, noisy data
table by a low-rank matrix with sparse singular vectors. The approximation is
obtained from thresholded subspace iterations that produce the singular vectors
simultaneously, rather than successively as in competing proposals. We
introduce novel ways to estimate thresholding parameters which obviate the need
for computationally expensive cross-validation. We also introduce a way to
sparsely initialize the algorithm for computational savings that allow our
algorithm to outperform the vanilla SVD on the full data table when the signal
is sparse. A comparison with two existing sparse SVD methods suggests that our
algorithm is computationally always faster and statistically always at least
comparable to the better of the two competing algorithms.
