Communication-Efficient Distributed Svd Via Local Power Iterations

We study distributed computing of the truncated singular value decomposition problem. We develop an algorithm that we call Local Power 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 +/- 1 entries as weights, has better computation complexity and stability in experiments. We theoretically show that under certain assumptions Local Power 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 Local Power.