# FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis

arXiv: https://arxiv.org/abs/2108.12373 · HTML: https://mlsanity.com/paper/2108.12373/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 27 Aug 2021.

## Builds on (most cited first, 14 of 14)

- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [Decentralized Riemannian Gradient Descent on the Stiefel Manifold](https://mlsanity.com/paper/2102.07091/) (2021)
- [Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery](https://mlsanity.com/paper/1711.09492/) (2017)
- [DeEPCA: Decentralized Exact PCA with Linear Convergence Rate](https://mlsanity.com/paper/2102.03990/) (2021)
- [Cloud K-SVD: A Collaborative Dictionary Learning Algorithm for Big, Distributed Data](https://mlsanity.com/paper/1412.7839/) (2014)
- [The Fast Convergence of Incremental PCA](https://mlsanity.com/paper/1501.03796/) (2015)
- [Exponentially convergent stochastic k-PCA without variance reduction](https://mlsanity.com/paper/1904.01750/) (2019)
- [A Linearly Convergent Algorithm for Distributed Principal Component Analysis](https://mlsanity.com/paper/2101.01300/) (2021)
- [Distributed Differentially-Private Algorithms for Matrix and Tensor Factorization](https://mlsanity.com/paper/1804.10299/) (2018)
- [Stochastic Optimization of PCA with Capped MSG](https://mlsanity.com/paper/1307.1674/) (2013)
- [Distributed Principal Subspace Analysis for Partitioned Big Data: Algorithms, Analysis, and Implementation](https://mlsanity.com/paper/2103.06406/) (2021)
- [On the performance overhead tradeoff of distributed principal component analysis via data partitioning](https://mlsanity.com/paper/1512.05172/) (2015)
- [Online Distributed Estimation of Principal Eigenspaces](https://mlsanity.com/paper/1905.07389/) (2019)

## Built on by (most cited first, 3 of 3)

- [Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function](https://mlsanity.com/paper/2112.14949/) (2021)
- [Optimizing Predictive Maintenance in Intelligent Manufacturing: An Integrated FNO-DAE-GNN-PPO MDP Framework](https://mlsanity.com/paper/2511.05594/) (2025)
- [Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA](https://mlsanity.com/paper/2602.03682/) (2026)

## Abstract (arXiv)

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction and uncorrelated feature learning. Furthermore, the enormity of the dimensions and sample size in the modern day datasets have rendered the centralized PCA solutions unusable. In that vein, this paper reconsiders the problem of PCA when data samples are distributed across nodes in an arbitrarily connected network. While a few solutions for distributed PCA exist, those either overlook the uncorrelated feature learning aspect of the PCA, tend to have high communication overhead that makes them inefficient and/or lack `exact' or `global' convergence guarantees. To overcome these aforementioned issues, this paper proposes a distributed PCA algorithm termed FAST-PCA (Fast and exAct diSTributed PCA). The proposed algorithm is efficient in terms of communication and is proven to converge linearly and exactly to the principal components, leading to dimension reduction as well as uncorrelated features. The claims are further supported by experimental results.