# Distributed Principal Component Analysis with Limited Communication

arXiv: https://arxiv.org/abs/2110.14391 · HTML: https://mlsanity.com/paper/2110.14391/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2021.

## Built on by (most cited first, 6 of 6)

- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Federated Learning on Riemannian Manifolds](https://mlsanity.com/paper/2206.05668/) (2022)
- [Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data](https://mlsanity.com/paper/2406.08465/) (2024)
- [Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation](https://mlsanity.com/paper/2502.17615/) (2025)
- [Flow-Based Fragment Identification via Binding Site-Specific Latent Representations](https://mlsanity.com/paper/2509.13216/) (2025)
- [Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computation](https://mlsanity.com/paper/2608.04406/) (2026)

## Abstract (arXiv)

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.