## Tensor Decompositions and Applications (2009)

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Venue: | SIAM REVIEW |

Citations: | 225 - 14 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 â¥ 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.