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Tensor Decompositions and Applications
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Journal Article
Tensor Decompositions and Applications
2009
Overview
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 ≥ 3) have applications in psychometrics, 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.
Publisher
Society for Industrial and Applied Mathematics
Subject
/ Arrays
/ Computer science; control theory; systems
/ Exact sciences and technology
/ Linear and multilinear algebra, matrix theory
/ Matrices
/ Matrix
/ Methods of scientific computing (including symbolic computation, algebraic computation)
/ Modeling
/ Numerical analysis. Scientific computation
/ Principal components analysis
/ Sciences and techniques of general use
/ Software
/ Studies
/ Tensors
