Provable Dynamic Robust PCA or Robust Subspace Tracking
By Praneeth Narayanamurthy, Namrata Vaswani. 2017
59 citations recorded by the source corpus.
Dynamic robust principal component analysis (PCA) refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lie in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this changing subspace over time in the presence of sparse outliers. We develop and study a novel algorithm, which we call simple-ReProCS, based on the recently introduced Recursive Projected Compressive Sensing (ReProCS) framework. This paper provides the first guarantee for dynamic RPCA that holds under weakened versions of standard RPCA assumptions, slow subspace change, and a lower bound assumption on most outlier magnitudes. Our result is significant because: 1) it removes the strong assumptions needed by the two previous complete guarantees for ReProCS-based algorithms; 2) it shows that it is possible to achieve significantly improved outlier tolerance, compared with all existing RPCA or dynamic RPCA solutions by exploiting the above-mentioned two simple extra assumptions; and 3) it proves that simple-ReProCS is online (after initialization), fast, and, has near-optimal memory complexity.
Subfields: Computational Mechanics, Computer Networks and Communications, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Thierry Bouwmans
- Sajid Javed
- René Vidal
- Paris V. Giampouras
- Liangzu Peng
- Praneeth Narayanamurthy
- Namrata Vaswani
- Ehsan Elhamifar
In Computer Networks and Communications
In Statistics and Probability
- Thierry Bouwmans
- Sajid Javed
- Namrata Vaswani
- Praneeth Narayanamurthy
- René Vidal
- Paris V. Giampouras
- Liangzu Peng
Citations in the corpus
- The Ideal Continual Learner: An Agent That Never Forgets (2023, background): “For example, St could be slowly rotated, or keep static for a sufficiently long time until changing (Narayanamurthy & Vaswani, 2018).”
- Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery (2017, methodology): “This last limitation can be removed by using the ReProCS approach to detecting subspace change [9], [29].”