# Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?

arXiv: https://arxiv.org/abs/1511.03688 · HTML: https://mlsanity.com/paper/1511.03688/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2015.

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

- [Spatiotemporal Covariance Neural Networks](https://mlsanity.com/paper/2409.10068/) (2024)
- [DeepWeightFlow: Re-Basined Flow Matching for Generating Neural Network Weights](https://mlsanity.com/paper/2601.05052/) (2026)
- [Meta Learning in Bandits within Shared Affine Subspaces](https://mlsanity.com/paper/2404.00688/) (2024)
- [Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series](https://mlsanity.com/paper/2304.03069/) (2023)
- [Manifold learning and optimization using tangent space proxies](https://mlsanity.com/paper/2501.12678/) (2025)
- [Dynamic Orthogonal Continual Fine-tuning for Mitigating Catastrophic Forgettings](https://mlsanity.com/paper/2509.23893/) (2025)
- [Online Kernel Sliced Inverse Regression](https://mlsanity.com/paper/2301.09516/) (2023)
- [Reward Dimension Reduction for Scalable Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2502.20957/) (2025)
- [Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamics](https://mlsanity.com/paper/2512.01231/) (2025)
- [RENs: Relevance Encoding Networks](https://mlsanity.com/paper/2205.13061/) (2022)
- [Online Nonparametric Supervised Learning for Massive Data](https://mlsanity.com/paper/2405.19486/) (2024)
- [High-dimensional Adaptive MCMC with Reduced Computational Complexity](https://mlsanity.com/paper/2604.09286/) (2026)

## Abstract (arXiv)

In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with each new observation have been studied in various fields of research and found wide applications in industrial monitoring, computer vision, astronomy, and latent semantic indexing, among others. This work provides guidance for selecting an online PCA algorithm in practice. We present the main approaches to online PCA, namely, perturbation techniques, incremental methods, and stochastic optimization, and compare their statistical accuracy, computation time, and memory requirements using artificial and real data. Extensions to missing data and to functional data are discussed. All studied algorithms are available in the R package onlinePCA on CRAN.