# Communication-Efficient Distributed SVD via Local Power Iterations

arXiv: https://arxiv.org/abs/2002.08014 · HTML: https://mlsanity.com/paper/2002.08014/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 12 of 12)

- [Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces](https://mlsanity.com/paper/2209.10526/) (2022)
- [Vertical Federated Principal Component Analysis and Its Kernel Extension on Feature-wise Distributed Data](https://mlsanity.com/paper/2203.01752/) (2022)
- [FedPower: Privacy-Preserving Distributed Eigenspace Estimation](https://mlsanity.com/paper/2103.00704/) (2021)
- [Federated singular value decomposition for high dimensional data](https://mlsanity.com/paper/2205.12109/) (2022)
- [Privacy-Preserving Community Detection for Locally Distributed Multiple Networks](https://mlsanity.com/paper/2306.15709/) (2023)
- [In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting](https://mlsanity.com/paper/2409.08771/) (2024)
- [A Generalized Mean Approach for Distributed-PCA](https://mlsanity.com/paper/2410.00397/) (2024)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation](https://mlsanity.com/paper/2502.17615/) (2025)
- [Collaborative Compressors in Distributed Mean Estimation with Limited Communication Budget](https://mlsanity.com/paper/2601.18950/) (2026)
- [Statistical Analysis of Karcher Means for Random Restricted PSD Matrices](https://mlsanity.com/paper/2302.12426/) (2023)
- [Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computation](https://mlsanity.com/paper/2608.04406/) (2026)

## Abstract (arXiv)

We study distributed computing of the truncated singular value decomposition problem. We develop an algorithm that we call textttLocalPower for improving communication efficiency. Specifically, we uniformly partition the dataset among m nodes and alternate between multiple (precisely p) local power iterations and one global aggregation. In the aggregation, we propose to weight each local eigenvector matrix with orthogonal Procrustes transformation (OPT). As a practical surrogate of OPT, sign-fixing, which uses a diagonal matrix with ± 1 entries as weights, has better computation complexity and stability in experiments. We theoretically show that under certain assumptions textttLocalPower lowers the required number of communications by a factor of p to reach a constant accuracy. We also show that the strategy of periodically decaying p helps obtain high-precision solutions. We conduct experiments to demonstrate the effectiveness of textttLocalPower.