PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least Squares From Partial Observations

Many real world datasets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to estimate and track the low-dimensional structure with small storage requirements and computational comp...

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Vydáno v:	IEEE transactions on signal processing Ročník 61; číslo 23; s. 5947 - 5959
Hlavní autoři:	Yuejie Chi, Eldar, Yonina C., Calderbank, Robert
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.12.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Approximation algorithms Convergence Detection, estimation, filtering, equalization, prediction Estimation Exact sciences and technology Information, signal and communications theory Internet Least squares approximations Least squares method Matrix completion Networks Noise reduction online algorithms partial observations Recursive recursive least squares Signal and communications theory Signal processing algorithms Signal, noise Sparse matrices subspace identification and tracking Subspaces Telecommunications and information theory Tracking Vectors Parameter estimation Direction-of-arrival estimation State of the art partial observations Noise reduction Signal estimation Video signal recursive least squares Remote sensing Least squares method Matrix completion Target tracking subspace identification and tracking Subspace method Video technique Algorithm Computational complexity online algorithms Videocommunication Batch process On line processing Recursive method Signal processing Numerical simulation Internet Remote supervision
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	Many real world datasets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to estimate and track the low-dimensional structure with small 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 low-dimensional 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 setting can be viewed as a sequential low-rank 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 low-dimensional subspace, and then reconstructs the missing entries via least-squares estimation if required. Subspace identification is performed via a recursive procedure for each row of the subspace matrix in parallel with discounting for previous observations. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2013.2282910