Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

By Namrata Vaswani, Thierry Bouwmans, Sajid Javed, Praneeth Narayanamurthy. 2017

315 citations recorded by the source corpus.

Principal component analysis (PCA) is one of the most widely used dimension reduction techniques. A related easier problem is termed subspace learning or subspace estimation. Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning (RSL) or robust PCA (RPCA). For long data sequences, if one tries to use a single lower-dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of RSL and tracking.

Subfields: Aerospace Engineering, Civil and Structural Engineering, Computational Mechanics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Belmar García García
2. René Vidal
3. Thierry Bouwmans
4. Yuxin Chen

In Civil and Structural Engineering

1. Belmar García García
2. René Vidal
3. Thierry Bouwmans

In Computational Mechanics

1. René Vidal
2. Paris V. Giampouras
3. Liangzu Peng
4. Belmar García García
5. Yuxin Chen
6. Yuejie Chi
7. Yue M. Lu
8. Thierry Bouwmans

Citations in the corpus

• The Ideal Continual Learner: An Agent That Never Forgets (2023, methodology): “While we refer the reader to Balzano et al. (2018) and Vaswani et al. (2018) for comprehensive reviews, we discuss several related methods here, aiming at highlighting their connections to continual learning.”
• Background Subtraction in Real Applications: Challenges, Current Models and Future Directions (2019, methodology): “[367][366] provided a full study of robust subspace learning methods for background subtraction in terms of detection and algorithms’s properties.”
• Provable Dynamic Robust PCA or Robust Subspace Tracking (2017, unknown): “As explained in [19] and [29], this can also be understood as solving a Robust Regression problem.”
• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview (2018, background): “This problem is also known as robust principal component analysis [7], [8], [51], since we can think of it as recovering the low-rank factors of M when the observed entries are corrupted by sparse outliers (modeled by S ).”