Tensor Decompositions and Applications.
SIAM Review, 51(3):455-500, 2009.
Tamara G. Kolda and Brett W. Bader.
[doi]
[abstract]
[BibTeX]
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.
The PARAFAC model for three-way factor analysis and multidimensional scaling.
In:
H. G. Law, C. W. Snyder Jr, J. A. Hattie and R. P. McDonald, editors,
Research methods for multimode data analysis, pages 122-215.
Praeger, New York, 1984.
R. A. Harshman and M. E. Lundy.
[BibTeX]