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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 61; no. 23; pp. 5947 - 5959
Main Authors: Yuejie Chi, Eldar, Yonina C., Calderbank, Robert
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2013.2282910