# Online Distributed Estimation of Principal Eigenspaces

## TL;DR

This paper introduces an online distributed PCA algorithm that efficiently estimates principal eigenspaces, demonstrating faster computation and maintained accuracy across tasks like low-rank approximation and clustering.

## Contribution

It presents a novel online distributed PCA method with proven convergence rates, linking performance to network size, data rank, and spectral gaps.

## Key findings

- Significant computational speed-up over existing methods
- Maintains high accuracy in eigenspace estimation
- Effective for low-rank approximation and clustering tasks

## Abstract

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further establish its rate of convergence and show how it relates to the number of nodes employed in the distributed computation, the effective rank of the data matrix under consideration, and the gap in the spectrum of the underlying population covariance matrix. The proposed algorithm is illustrated on low-rank approximation and $\boldsymbol{k}$-means clustering tasks. The numerical results show a substantial computational speed-up vis-a-vis standard distributed PCA algorithms, without compromising learning accuracy.