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(Dynamic) Subspace Learning from ``Bad`` Data

Event Type
ISE Grad Seminar
103 Transportation Building
Feb 14, 2020   10:00 am  
Namrata Vaswani
Originating Calendar
ISE Seminar Calendar

Principal Components Analysis (PCA), a.k.a. subspace learning, is one of the most widely used noise removal and dimension reduction techniques. It finds applications in a large number of scientific and exploratory data analysis applications. PCA assumes that the clean/true data (``signal``) sequence lies close to a low-dimensional subspace of the ambient space, or, equivalently, that the clean dataset forms a low-rank matrix. This talk will describe our work on practically useful, provably correct and fast solutions to two problems involving subspace learning and tracking from “bad” data – (i) Low Rank Phase Retrieval (Phaseless PCA) and (ii) Robust Subspace Tracking. For the first problem, the term ``bad`` means that the observed data is a phaseless (magnitude-only) function of a linear transformation of the true data; while for the second one it means that the data is incomplete and corrupted by outliers.


Low Rank Phase Retrieval involves recovering an n x q low-rank matrix from a set of m mutually independent magnitude-only linear projections of each of its q columns. An efficient solution to Low Rank PR can enable fast and low-cost imaging of dynamic (time-varying) scenes in a wide variety of phaseless imaging applications. Some examples include astronomical imaging of the sun’s surface properties which gradually change over time, X-ray crystallography, or Fourier ptychographic imaging of live biological specimens. Robust Subspace Tracking is simply understood as the time-varying subspace extension of Robust PCA. It involves tracking sequentially arriving data vectors, that lie in a fixed or slowly changing low-dimensional subspace, while being robust to missing entries and corruption by additive sparse outliers. It occurs in a wide variety of data analytics applications ranging from video foreground-background separation in real-time to recommendation system design.

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