Abstract:
We study distributed computing of the truncated singular value decomposition (SVD).
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}.
