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Tensor Decompositions and Applications

Kolda, Tamara G., Bader, Brett W.·2009·SIAM Review
DOI 10.1137/07070111x
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Abstract

Abstract. This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or [Formula: see text]-way array. Decompositions of higher-order tensors (i.e., [Formula: see text]-way arrays with [Formula: see text]) have applications in psychometrics, 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.

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Metadata

Authors
Kolda, T. G., & Bader, B. W.
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2009-08-05
Volume
51
Issue
3
Pages
455-500
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/07070111x
OpenAlex
W2024165284
Cited by
10,301
References
4
FWCI
50.53
Type
journal article
Language
en
Open access
closed

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