# Stochastic Optimization of PCA with Capped MSG

arXiv: https://arxiv.org/abs/1307.1674 · HTML: https://mlsanity.com/paper/1307.1674/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2013.

## Built on by (most cited first, 6 of 6)

- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [A Linearly Convergent Algorithm for Distributed Principal Component Analysis](https://mlsanity.com/paper/2101.01300/) (2021)
- [Streaming Kernel PCA Algorithm With Small Space](https://mlsanity.com/paper/2303.04555/) (2023)
- [FedPower: Privacy-Preserving Distributed Eigenspace Estimation](https://mlsanity.com/paper/2103.00704/) (2021)
- [FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis](https://mlsanity.com/paper/2108.12373/) (2021)
- [When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendations](https://mlsanity.com/paper/2310.09687/) (2023)

## Abstract (arXiv)

We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.