Distributed Principal Component Analysis with Limited Communication

Foivos Alimisis; Peter Davies; Bart Vandereycken; Dan Alistarh

NeurIPS 2021poster17 citations

Distributed Principal Component Analysis with Limited Communication

Foivos Alimisis, Peter Davies, Bart Vandereycken, Dan Alistarh

Abstract

We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a new quantized variant of Riemannian gradient descent to solve this problem, and prove that the algorithm converges with high probability under a set of necessary spherical-convexity properties. We give bounds on the number of bits transmitted by the algorithm under common initialization schemes, and investigate the dependency on the problem dimension in each case.

Principal Component AnalysisLeading EigenvectorBit ComplexityRiemannian OptimizationSphere

BibTeX

@inproceedings{
alimisis2021distributed,
title={Distributed Principal Component Analysis with Limited Communication},
author={Foivos Alimisis and Peter Davies and Bart Vandereycken and Dan Alistarh},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=edCFRvlWqV}
}