@article{kolda2009tensor,
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 $N \geq 3$) 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.},
author = {Kolda, Tamara G. and Bader, Brett W.},
doi = {10.1137/07070111X},
interhash = {b30bb2d42e1a05fc41370c50844822ad},
intrahash = {e52e5c7bff59fd01fb6497d3bb620077},
issn = {00361445},
journal = {SIAM Review},
number = 3,
pages = {455--500},
publisher = {SIAM},
title = {Tensor Decompositions and Applications},
url = {http://dx.doi.org/10.1137/07070111X},
volume = 51,
year = 2009
}