Distributed Principal Component Analysis with Limited Communication

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.

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Cite

Text

Alimisis et al. "Distributed Principal Component Analysis with Limited Communication." Neural Information Processing Systems, 2021.

Markdown

[Alimisis et al. "Distributed Principal Component Analysis with Limited Communication." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/alimisis2021neurips-distributed/)

BibTeX

@inproceedings{alimisis2021neurips-distributed,
  title     = {{Distributed Principal Component Analysis with Limited Communication}},
  author    = {Alimisis, Foivos and Davies, Peter and Vandereycken, Bart and Alistarh, Dan},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/alimisis2021neurips-distributed/}
}