  To recover a low rank structure from a noisy matrix, truncated singular value
decomposition has been extensively used and studied. Recent studies suggested
that the signal can be better estimated by shrinking the singular values. We
pursue this line of research and propose a new estimator offering a continuum
of thresholding and shrinking functions. To avoid an unstable and costly
cross-validation search, we propose new rules to select two thresholding and
shrinking parameters from the data. In particular we propose a generalized
Stein unbiased risk estimation criterion that does not require knowledge of the
variance of the noise and that is computationally fast. A Monte Carlo
simulation reveals that our estimator outperforms the tested methods in terms
of mean squared error on both low-rank and general signal matrices across
different signal to noise ratio regimes. In addition, it accurately estimates
the rank of the signal when it is detectable.
