Improved Distributed Principal Component Analysis

TL;DR

This paper presents new algorithms for distributed PCA that significantly reduce communication and computational costs, enabling faster and more efficient analysis of large distributed datasets with minimal loss in accuracy.

Contribution

The authors develop improved distributed PCA algorithms with better communication and computational efficiency, and introduce techniques for high success probability subspace embeddings.

Findings

Order of magnitude speedup in empirical tests

Negligible degradation in solution quality

Enhanced algorithms for k-means clustering

Abstract

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA), in which the servers would like to compute a low dimensional subspace capturing as much of the variance of the union of their point sets as possible. Given a procedure for approximate PCA, one can use it to approximately solve $\ell_2$-error fitting problems such as $k$-means clustering and subspace clustering. The essential properties of an approximate distributed PCA algorithm are its communication cost and computational efficiency for a given desired accuracy in downstream applications. We give new algorithms and analyses for distributed PCA which lead to improved communication and computational costs for $k$-means clustering and related problems. Our empirical study on real world data shows a speedup of orders of magnitude, preserving communication with only a negligible degradation in solution quality. Some of these techniques we develop, such as a general transformation from a constant success probability subspace embedding to a high success probability subspace embedding with a dimension and sparsity independent of the success probability, may be of independent interest.