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Tensor Decompositions and Applications (2009)
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| Venue: | SIAM REVIEW |
| Citations: | 722 - 18 self |
BibTeX
@ARTICLE{Kolda09tensordecompositions,
author = {Tamara G. Kolda and Brett W. Bader},
title = {Tensor Decompositions and Applications},
journal = {SIAM REVIEW},
year = {2009},
volume = {51},
number = {3},
pages = {455--500}
}
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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 ⥠3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decompo- sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal components 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 and Tensor Toolbox, both for MATLAB, and the Multilinear Engine are examples of software packages for working with tensors.
Keyphrases
tensor decomposition way array numerical analysis principal component analysis many tensor decomposition data mining higher-order tensor decomposition candecomp parafac multilinear engine software package computer vision higher-order form particular tensor decomposition n-way toolbox available software signal processing rank-one tensor higher-order extension numerical linear algebra tensor toolbox higher-order tensor nonnegative variant matrix singular value decompo sition tucker decomposition graph analysis
