# Streaming PCA and Subspace Tracking: The Missing Data Case

arXiv: https://arxiv.org/abs/1806.04609 · HTML: https://mlsanity.com/paper/1806.04609/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 19 of 19)

- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [SubTrack++ : Gradient Subspace Tracking for Scalable LLM Training](https://mlsanity.com/paper/2502.01586/) (2025)
- [Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent](https://mlsanity.com/paper/2206.09109/) (2022)
- [Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA](https://mlsanity.com/paper/2303.06198/) (2023)
- [Unlabeled Principal Component Analysis and Matrix Completion](https://mlsanity.com/paper/2101.09446/) (2021)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [One Rank at a Time: Cascading Error Dynamics in Sequential Learning](https://mlsanity.com/paper/2505.22602/) (2025)
- [Learning Low-dimensional Latent Dynamics from High-dimensional Observations: Non-asymptotics and Lower Bounds](https://mlsanity.com/paper/2405.06089/) (2024)
- [Exploring the Precise Dynamics of Single-Layer GAN Models: Leveraging Multi-Feature Discriminators for High-Dimensional Subspace Learning](https://mlsanity.com/paper/2411.00498/) (2024)
- [Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approaches](https://mlsanity.com/paper/2506.01696/) (2025)
- [An Incremental Non-Linear Manifold Approximation Method](https://mlsanity.com/paper/2504.09068/) (2025)
- [Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation](https://mlsanity.com/paper/2505.10882/) (2025)
- [Sliding Window Informative Canonical Correlation Analysis](https://mlsanity.com/paper/2507.17921/) (2025)
- [PCA-VAE: Differentiable Subspace Quantization without Codebook Collapse](https://mlsanity.com/paper/2602.18904/) (2026)
- [PCA-Driven Adaptive Sensor Triage for Edge AI Inference](https://mlsanity.com/paper/2604.05045/) (2026)
- [Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics](https://mlsanity.com/paper/2606.31390/) (2026)
- [In-context learning from self-generated trajectories for adaptive model reduction](https://mlsanity.com/paper/2607.02937/) (2026)
- [AIGS: Adaptive Incremental Gating System for Online Representation Learning in Non-Stationary Data Streams](https://mlsanity.com/paper/2610.02661/) (2026)

## Abstract (arXiv)

For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming Principal Component Analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and non-asymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence of missing data for both well-conditioned and ill-conditioned systems.