# History PCA: A New Algorithm for Streaming PCA

arXiv: https://arxiv.org/abs/1802.05447 · HTML: https://mlsanity.com/paper/1802.05447/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 9 of 9)

- [Streaming PCA for Markovian Data](https://mlsanity.com/paper/2305.02456/) (2023)
- [Oja's Algorithm for Streaming Sparse PCA](https://mlsanity.com/paper/2402.07240/) (2024)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Beyond Sin-Squared Error: Linear-Time Entrywise Uncertainty Quantification for Streaming PCA](https://mlsanity.com/paper/2506.12655/) (2025)
- [Low-Precision Streaming PCA](https://mlsanity.com/paper/2510.22440/) (2025)
- [Exploring Scalable, Distributed Real-Time Anomaly Detection for Bridge Health Monitoring](https://mlsanity.com/paper/2203.02380/) (2022)
- [DOME: Improving Signal-to-Noise in Stochastic Gradient Descent via Sharp-Direction Subspace Filtering](https://mlsanity.com/paper/2507.03545/) (2025)
- [Temporal Streaming Batch Principal Component Analysis for Time Series Classification](https://mlsanity.com/paper/2410.20820/) (2024)
- [PCA-Driven Adaptive Sensor Triage for Edge AI Inference](https://mlsanity.com/paper/2604.05045/) (2026)

## Abstract (arXiv)

In this paper we propose a new algorithm for streaming principal component analysis. With limited memory, small devices cannot store all the samples in the high-dimensional regime. Streaming principal component analysis aims to find the k-dimensional subspace which can explain the most variation of the d-dimensional data points that come into memory sequentially. In order to deal with large d and large N (number of samples), most streaming PCA algorithms update the current model using only the incoming sample and then dump the information right away to save memory. However the information contained in previously streamed data could be useful. Motivated by this idea, we develop a new streaming PCA algorithm called History PCA that achieves this goal. By using O(Bd) memory with B≈ 10 being the block size, our algorithm converges much faster than existing streaming PCA algorithms. By changing the number of inner iterations, the memory usage can be further reduced to O(d) while maintaining a comparable convergence speed. We provide theoretical guarantees for the convergence of our algorithm along with the rate of convergence. We also demonstrate on synthetic and real world data sets that our algorithm compares favorably with other state-of-the-art streaming PCA methods in terms of the convergence speed and performance.