# Federated Learning for Sparse Principal Component Analysis

arXiv: https://arxiv.org/abs/2311.08677 · HTML: https://mlsanity.com/paper/2311.08677/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Federated Learning in Distributed Medical Databases: Meta-Analysis of Large-Scale Subcortical Brain Data](https://mlsanity.com/paper/1810.08553/) (2018)
- [COLA: Decentralized Linear Learning](https://mlsanity.com/paper/1808.04883/) (2018)
- [Helen: Maliciously Secure Coopetitive Learning for Linear Models](https://mlsanity.com/paper/1907.07212/) (2019)

## Abstract (arXiv)

In the rapidly evolving realm of machine learning, algorithm effectiveness often faces limitations due to data quality and availability. Traditional approaches grapple with data sharing due to legal and privacy concerns. The federated learning framework addresses this challenge. Federated learning is a decentralized approach where model training occurs on client sides, preserving privacy by keeping data localized. Instead of sending raw data to a central server, only model updates are exchanged, enhancing data security. We apply this framework to Sparse Principal Component Analysis (SPCA) in this work. SPCA aims to attain sparse component loadings while maximizing data variance for improved interpretability. Beside the L1 norm regularization term in conventional SPCA, we add a smoothing function to facilitate gradient-based optimization methods. Moreover, in order to improve computational efficiency, we introduce a least squares approximation to original SPCA. This enables analytic solutions on the optimization processes, leading to substantial computational improvements. Within the federated framework, we formulate SPCA as a consensus optimization problem, which can be solved using the Alternating Direction Method of Multipliers (ADMM). Our extensive experiments involve both IID and non-IID random features across various data owners. Results on synthetic and public datasets affirm the efficacy of our federated SPCA approach.