# Federated singular value decomposition for high dimensional data

arXiv: https://arxiv.org/abs/2205.12109 · HTML: https://mlsanity.com/paper/2205.12109/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 65 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 13 of 13)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [A generic framework for privacy preserving deep learning](https://mlsanity.com/paper/1811.04017/) (2018)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [An Improved Gap-Dependency Analysis of the Noisy Power Method](https://mlsanity.com/paper/1602.07046/) (2016)
- [Practical Lossless Federated Singular Vector Decomposition over Billion-Scale Data](https://mlsanity.com/paper/2105.08925/) (2021)
- [Improved Distributed Principal Component Analysis](https://mlsanity.com/paper/1408.5823/) (2014)
- [Communication-Efficient Distributed SVD via Local Power Iterations](https://mlsanity.com/paper/2002.08014/) (2020)
- [Smooth Sensitivity Based Approach for Differentially Private Principal Component Analysis](https://mlsanity.com/paper/1710.10556/) (2017)
- [Distributed Differentially Private Computation of Functions with Correlated Noise](https://mlsanity.com/paper/1904.10059/) (2019)
- [Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis](https://mlsanity.com/paper/2004.02336/) (2020)
- [The FeatureCloud AI Store for Federated Learning in Biomedicine and Beyond](https://mlsanity.com/paper/2105.05734/) (2021)
- [Privacy Preserving PCA for Multiparty Modeling](https://mlsanity.com/paper/2002.02091/) (2020)

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

- [Privacy of federated QR decomposition using additive secure multiparty computation](https://mlsanity.com/paper/2210.06163/) (2022)
- [A Two-Stage Federated Learning Approach for Industrial Prognostics Using Large-Scale High-Dimensional Signals](https://mlsanity.com/paper/2410.11101/) (2024)

## Abstract (arXiv)

Federated learning (FL) is emerging as a privacy-aware alternative to classical cloud-based machine learning. In FL, the sensitive data remains in data silos and only aggregated parameters are exchanged. Hospitals and research institutions which are not willing to share their data can join a federated study without breaching confidentiality. In addition to the extreme sensitivity of biomedical data, the high dimensionality poses a challenge in the context of federated genome-wide association studies (GWAS). In this article, we present a federated singular value decomposition (SVD) algorithm, suitable for the privacy-related and computational requirements of GWAS. Notably, the algorithm has a transmission cost independent of the number of samples and is only weakly dependent on the number of features, because the singular vectors associated with the samples are never exchanged and the vectors associated with the features only for a fixed number of iterations. Although motivated by GWAS, the algorithm is generically applicable for both horizontally and vertically partitioned data.