# Single-Pass PCA of Large High-Dimensional Data

arXiv: https://arxiv.org/abs/1704.07669 · HTML: https://mlsanity.com/paper/1704.07669/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2017.

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

- [Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks](https://mlsanity.com/paper/2102.12567/) (2021)
- [Latent State Models of Training Dynamics](https://mlsanity.com/paper/2308.09543/) (2023)
- [Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation](https://mlsanity.com/paper/2305.11495/) (2023)
- [Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation](https://mlsanity.com/paper/2502.17615/) (2025)
- [In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularization](https://mlsanity.com/paper/2511.02659/) (2025)
- [Active Diffusion-Based Inference for Ill-Posed Inverse Problems under Incomplete Priors](https://mlsanity.com/paper/2608.27080/) (2026)

## Abstract (arXiv)

Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant singular values of the data matrix) becomes a challenging task. In this work, a single-pass randomized algorithm is proposed to compute PCA with only one pass over the data. It is suitable for processing extremely large and high-dimensional data stored in slow memory (hard disk) or the data generated in a streaming fashion. Experiments with synthetic and real data validate the algorithm's accuracy, which has orders of magnitude smaller error than an existing single-pass algorithm. For a set of high-dimensional data stored as a 150 GB file, the proposed algorithm is able to compute the first 50 principal components in just 24 minutes on a typical 24-core computer, with less than 1 GB memory cost.