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Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm
Sept. 2012 (vol. 34 no. 9)
pp. 1681-1690
ASCII Text
x 
 
A. Eriksson, A. van den Hengel, "Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 9, pp. 1681-1690, Sept., 2012.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2012.116,
author = {A. Eriksson and A. van den Hengel},
title = {Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {34},
number = {9},
issn = {0162-8828},
year = {2012},
pages = {1681-1690},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2012.116},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm
IS - 9
SN - 0162-8828
SP1681
EP1690
EPD - 1681-1690
A1 - A. Eriksson,
A1 - A. van den Hengel,
PY - 2012
KW - singular value decomposition
KW - approximation theory
KW - computer vision
KW - optimisation
KW - synthetic data
KW - robust weighted low-rank matrix approximations
KW - L<sub>1</sub> norm
KW - computer vision
KW - singular value decomposition
KW - missing data elements
KW - Wiberg algorithm
KW - rank-constrained factorization
KW - linear programs
KW - optimization software
KW - real data
KW - Robustness
KW - Approximation algorithms
KW - Equations
KW - Least squares approximation
KW - Computational efficiency
KW - Optimization
KW - L_{{1}}-minimization.
KW - Low-rank matrix approximation
VL - 34
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
A. Eriksson, Dept. of Comput. Sci., Univ. of Adelaide, North Terrace, SA, Australia
A. van den Hengel, Dept. of Comput. Sci., Univ. of Adelaide, North Terrace, SA, Australia
The calculation of a low-rank approximation to a matrix is fundamental to many algorithms in computer vision and other fields. One of the primary tools used for calculating such low-rank approximations is the Singular Value Decomposition, but this method is not applicable in the case where there are outliers or missing elements in the data. Unfortunately, this is often the case in practice. We present a method for low-rank matrix approximation which is a generalization of the Wiberg algorithm. Our method calculates the rank-constrained factorization, which minimizes the L1 norm and does so in the presence of missing data. This is achieved by exploiting the differentiability of linear programs, and results in an algorithm can be efficiently implemented using existing optimization software. We show the results of experiments on synthetic and real data.

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Index Terms:
singular value decomposition,approximation theory,computer vision,optimisation,synthetic data,robust weighted low-rank matrix approximations,L<sub>1</sub> norm,computer vision,singular value decomposition,missing data elements,Wiberg algorithm,rank-constrained factorization,linear programs,optimization software,real data,Robustness,Approximation algorithms,Equations,Least squares approximation,Computational efficiency,Optimization,L_{{1}}-minimization.,Low-rank matrix approximation
Citation:
A. Eriksson, A. van den Hengel, "Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 9, pp. 1681-1690, Sept. 2012, doi:10.1109/TPAMI.2012.116
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