Streaming PCA and Subspace Tracking: The Missing Data Case
Year: 2018
Type: article
Abstract: 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.
Source: Proceedings of the IEEE
Authors: Laura Balzano, Yuejie Chi, Yue M. Lu
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, National Institutes of Health, Defense Advanced Research Projects Agency, Office of Naval Research, National Institute of Biomedical Imaging and Bioengineering, Division of Electrical, Communications and Cyber Systems, Air Force Office of Scientific Research, Army Research Office
Awards: G1523888516, G1717380892, CAREER: Robust Methods for High-Dimensional Signal Processing under Geometric Constraints, G2767619165, G3392305090, CIF: Small: Sampling and Inference Methods for Spatiotemporal Single-Photon Imaging, G4353487559, QuBBD: Geometric Time-Frequency Methods for Multi-modal Physiological Monitoring, G4884717353, G5122771614, G6098521345, G6312778784, G657448715, CIF: Small: High-Dimensional Analysis of Stochastic Iterative Algorithms for Signal Estimation, G7142813775, G7452299184, CIF: Medium: Collaborative Research: Nonconvex Optimization for High-Dimensional Signal Estimation: Theory and Fast Algorithms, Inferring the behavior of distributed energy resources from incomplete measurements, G854152385, G8876996369
OpenAlex ID: W2807786498