The problem we study here is a natural extension of two problems, (i) Subspace Tracking and (ii) (Robust) Matrix Completion. These problem have been extensively studied in the batch setting, but there is a lack of provable online algorithms. We study this problem, and in fact, interpret is as a simplification of the Dynamic RPCA problem.

First, we study the case of subsace tracking from missing data, which can be interpreted as a online version of the matrix completion problem when the subspace changes slowly (we in fact prove that this is necessary). The results for these are shown here.

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Next, as a simple modification, we also study the case when the low-rank data is also corrupted by sparse, arbitrary noise, in addition to missing data. The results for this problem are as follows.

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List of Selected Publications:

  1. Provable Subspace Tracking from Missing Data and Matrix Completion,
    Praneeth Narayanamurthy, Vahid Daneshpajooh, and Namrata Vaswani,
    IEEE Transactions on Signal Processing, June 2019.
    (A part of this paper was the finalist of the best student paper award at SPARS 2019).