# A Generalized Mean Approach for Distributed-PCA

arXiv: https://arxiv.org/abs/2410.00397 · HTML: https://mlsanity.com/paper/2410.00397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 2 of 2)

- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [Communication-Efficient Distributed SVD via Local Power Iterations](https://mlsanity.com/paper/2002.08014/) (2020)

## Built on by (most cited first, 2 of 2)

- [Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration](https://mlsanity.com/paper/2507.22170/) (2025)
- [The φ-PCA Framework: A Unified and Efficiency-Preserving Approach with Robust Variants](https://mlsanity.com/paper/2510.13159/) (2025)

## Abstract (arXiv)

Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating results across multiple machines or computing nodes due to computational overhead. Fan et al. (2019) introduced a pioneering DPCA method to estimate the leading rank-r eigenspace, aggregating local rank-r projection matrices by averaging. However, their method does not utilize eigenvalue information. In this article, we propose a novel DPCA method that incorporates eigenvalue information to aggregate local results via the matrix β-mean, which we call β-DPCA. The matrix β-mean offers a flexible and robust aggregation method through the adjustable choice of β values. Notably, for β=1, it corresponds to the arithmetic mean; for β=-1, the harmonic mean; and as β → 0, the geometric mean. Moreover, the matrix β-mean is shown to associate with the matrix β-divergence, a subclass of the Bregman matrix divergence, to support the robustness of β-DPCA. We also study the stability of eigenvector ordering under eigenvalue perturbation for β-DPCA. The performance of our proposal is evaluated through numerical studies.