TY  - JOUR
AU  - Kolda, Tamara G.
AU  - Bader, Brett W.
T1  - Tensor Decompositions and Applications
JO  - SIAM Review
PY  - 2009/
VL  - 51
IS  - 3
SP  - 455
EP  - 500
UR  - http://dx.doi.org/10.1137/07070111X
DO  - 10.1137/07070111X
KW  - decomposition
KW  - hosvd
KW  - parafac
KW  - tensor
KW  - three
KW  - tucker
L1  - 
SN  - 
N1  - 
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AB  - 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.
ER  -

TY  - CHAP
AU  - Harshman, R. A.
AU  - Lundy, M. E.
A2  - Law, H. G.
A2  - Snyder Jr, C. W.
A2  - Hattie, J. A.
A2  - McDonald, R. P.
T1  - The PARAFAC model for three-way factor analysis and multidimensional scaling
T2  - Research methods for multimode data analysis
PB  - Praeger
C1  - New York
PY  - 1984/
VL  - 
IS  - 
SP  - 122
EP  - 215
UR  - 
DO  - 
KW  - mode
KW  - parafac
KW  - three
KW  - 3mode
KW  - analysis
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SN  - 
N1  - 
N1  - 
AB  - 
ER  -