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