Distributed Principal Component Analysis with Limited Communication

Foivos Alimisis, Peter Davies, Bart Vandereycken, Dan Alistarh

Keywords: Principal Component Analysis, Leading Eigenvector, Bit Complexity, Riemannian Optimization, Sphere

TL;DR: Bit complexity of leading eigenvector computation via quantized Riemannian gradient descent.

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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Code: https://github.com/IST-DASLab/QRGD