  We study distributed computing of the truncated singular value decomposition
problem. We develop an algorithm that we call \texttt{LocalPower} for improving
communication efficiency. Specifically, we uniformly partition the dataset
among $m$ nodes and alternate between multiple (precisely $p$) local power
iterations and one global aggregation. In the aggregation, we propose to weight
each local eigenvector matrix with orthogonal Procrustes transformation (OPT).
As a practical surrogate of OPT, sign-fixing, which uses a diagonal matrix with
$\pm 1$ entries as weights, has better computation complexity and stability in
experiments. We theoretically show that under certain assumptions
\texttt{LocalPower} lowers the required number of communications by a factor of
$p$ to reach a constant accuracy. We also show that the strategy of
periodically decaying $p$ helps obtain high-precision solutions. We conduct
experiments to demonstrate the effectiveness of \texttt{LocalPower}.

Machine Learning;Machine Learning;Optimization and Control