Communication-Efficient Distributed SVD via Local Power Iterations

We study the distributed computing of the truncated singular value decomposition (SVD). We develop an algorithm that we call \texttt{LocalPower} for improving the communication efficiency. Specifically, we uniformly partition the dataset among $m$ nodes and alternate between multiple (precisely $p$) local power iterations and one global aggregation. We theoretically show that under certain assumptions, \texttt{LocalPower} lowers the required number of communications by a factor of $p$ to reach a certain accuracy. We also show that the strategy of periodically decaying $p$ helps improve the performance of \texttt{LocalPower}. We conduct experiments to demonstrate the effectiveness of \texttt{LocalPower}.