| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Kolda, T. G. & Bader, B. W. | Tensor Decompositions and Applications | 2009 | SIAM Review | article | DOIURL |
| 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. | |||||
BibTeX:
@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 = {http://dx.doi.org/10.1137/07070111X}
}
|
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| Harshman, R. A. & Lundy, M. E. | The PARAFAC model for three-way factor analysis and multidimensional scaling [BibTeX] |
1984 | Research methods for multimode data analysis | incollection | |
BibTeX:
@incollection{hl84parafac,
author = {Harshman, R. A. and Lundy, M. E.},
title = {{T}he {P}{A}{R}{A}{F}{A}{C} model for three-way factor analysis and multidimensional scaling},
booktitle = {{R}esearch methods for multimode data analysis},
publisher = {Praeger},
year = {1984},
pages = {122--215}
}
|
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