Abstract
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques in a variety of scientific and data science applications. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work nicely defined outliers as additive sparse corruptions, and with this, the RPCA problem becomes one of decomposing a given data matrix into the sum of a low-rank matrix (true data) and a sparse matrix (outliers). The column space of the low-rank matrix then gives the PCA solution. For long data sequences, e.g., long surveillance videos, if one tries to use a single subspace to represent the entire sequence, the required subspace dimension may be too large. For such data, a better model is to assume that the data subspace changes with time, albeit gradually. This problem of tracking data lying in a (slowly) changing subspace while being robust to additive sparse outliers is referred to as “robust subspace tracking (RST)” or “dynamic RPCA”. While the RPCA problem has received a lot of attention in the last decade, its dynamic version was largely open until recently. In a recent body of work, we have introduced the first provably correct, fast, and practically usable solution framework for dynamic RPCA or RST that we call Recursive Projected Compressive Sensing (ReProCS).

Our most recent work (ICML 2018) shows that a simple ReProCS-based algorithm called ReProCS-NORST provides an online, fast, and provably nearly (delay and memory) optimal RST solution under mild assumptions: weakened standard RPCA assumptions, slow subspace change, and a lower bound on (most) outlier magnitudes. ReProCS-NORST also has a significantly improved worst-case outlier tolerance compared with all previous robust PCA or RST methods; without requiring any model on how the outlier support is generated. For the video application this implies that the foreground moving objects could be slow moving or even occasionally static, and the ReProCS algorithm will still work. We demonstrate this practical advantage via extensive experimental comparisons for two computer vision applications: video layering and video denoising/enhancement.

Bio
Namrata Vaswani is a Professor of Electrical and Computer Engineering, and (by courtesy) of Mathematics, at Iowa State University. She received a Ph.D. in 2004 from the University of Maryland, College Park and a B.Tech. from Indian Institute of Technology (IIT-Delhi) in India in 1999. Her research interests lie at the intersection of statistical machine learning and data science, computer vision, and signal processing. Her recent work has developed provably correct and practically useful online algorithms for various dynamic structured high-dimensional (big) data recovery problems -- dynamic compressive sensing (CS), dynamic robust principal component analysis (RPCA), and phase retrieval (ongoing work). Vaswani is an Area Editor for IEEE Signal Processing Magazine, has served twice as an Associate Editor for IEEE Transactions on Signal Processing, and is the Lead Guest Editor for a Proceedings IEEE Special Issue on Rethinking PCA for Modern Datasets that will appear in August 2018. She is also the Chair of the Women in Signal Processing (WiSP) Committee and a steering committee member of SPS's Data Science Initiative. In 2014, Prof. Vaswani received the IEEE Signal Processing Society (SPS) Best Paper Award for her Modified-CS work that was co-authored with her graduate student Lu in the IEEE Transactions on Signal Processing in 2010.