Kolda, T. G. & Bader, B. W.
(2009):
Tensor Decompositions and Applications.
In: SIAM Review,
Ausgabe/Number: 3,
Vol. 51,
Verlag/Publisher: SIAM.
Erscheinungsjahr/Year: 2009.
Seiten/Pages: 455-500.
[Volltext] [Kurzfassung] [BibTeX]
[Endnote]
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N geq3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
@article{kolda2009tensor,
author = {Kolda, Tamara G. and Bader, Brett W.},
title = {Tensor Decompositions and Applications},
journal = {SIAM Review},
publisher = {SIAM},
year = {2009},
volume = {51},
number = {3},
pages = {455--500},
url = {http://dx.doi.org/10.1137/07070111X},
doi = {10.1137/07070111X},
issn = {00361445},
keywords = {decomposition, hosvd, parafac, tensor, three, tucker},
abstract = {This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N geq3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.}
}
%0 = article
%A = Kolda, Tamara G. and Bader, Brett W.
%D = 2009
%I = SIAM
%T = Tensor Decompositions and Applications
%U = http://dx.doi.org/10.1137/07070111X
Harshman, R. A. & Lundy, M. E.
(1984):
The PARAFAC model for three-way factor analysis and multidimensional scaling.
In: Research methods for multimode data analysis.
Hrsg./Editors: Law, H. G.; Snyder Jr, C. W.; Hattie, J. A. & McDonald, R. P.
Verlag/Publisher: Praeger,
New York.
Erscheinungsjahr/Year: 1984.
Seiten/Pages: 122-215.
[BibTeX]
[Endnote]
@incollection{hl84parafac,
author = {Harshman, R. A. and Lundy, M. E.},
title = {The PARAFAC model for three-way factor analysis and multidimensional scaling},
editor = {Law, H. G. and Snyder Jr, C. W. and Hattie, J. A. and McDonald, R. P.},
booktitle = {Research methods for multimode data analysis},
publisher = {Praeger},
address = {New York},
year = {1984},
pages = {122--215},
keywords = {mode, parafac, three, 3mode, analysis}
}
%0 = incollection
%A = Harshman, R. A. and Lundy, M. E.
%B = Research methods for multimode data analysis
%C = New York
%D = 1984
%I = Praeger
%T = The PARAFAC model for three-way factor analysis and multidimensional scaling