Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
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Kolda, T.G. & Bader, B.W. | Tensor Decompositions and Applications | 2009 | SIAM Review Vol. 51(3), pp. 455-500 |
article | DOI URL |
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, pp. 122-215 | incollection | |
BibTeX:
@incollection{hl84parafac, author = {Harshman, R. A. and Lundy, M. E.}, title = {The PARAFAC model for three-way factor analysis and multidimensional scaling}, booktitle = {Research methods for multimode data analysis}, publisher = {Praeger}, year = {1984}, pages = {122--215} } |
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