Math @ Duke

Publications [#303201] of Robert Calderbank
Papers Published
 Chi, Y; Eldar, YC; Calderbank, R, PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least
Squares from Partial Observations
(July, 2012) [1207.6353v2], [doi]
(last updated on 2018/03/21)
Abstract: Many real world data sets exhibit an embedding of lowdimensional structure
in a highdimensional manifold. Examples include images, videos and internet
traffic data. It is of great significance to reduce the storage requirements
and computational complexity when the data dimension is high. Therefore we
consider the problem of reconstructing a data stream from a small subset of its
entries, where the data is assumed to lie in a lowdimensional linear subspace,
possibly corrupted by noise. We further consider tracking the change of the
underlying subspace, which can be applied to applications such as video
denoising, network monitoring and anomaly detection. Our problem can be viewed
as a sequential lowrank matrix completion problem in which the subspace is
learned in an online fashion. The proposed algorithm, dubbed Parallel
Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies
the underlying lowdimensional subspace via a recursive procedure for each row
of the subspace matrix in parallel with discounting for previous observations,
and then reconstructs the missing entries via leastsquares estimation if
required. Numerical examples are provided for directionofarrival estimation
and matrix completion, comparing PETRELS with state of the art batch
algorithms.


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