Tensor Decompositions and Applications by Tamara G. Kolda and Brett W. Bader.
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 ≥ 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.
At forty-five pages and two hundred and forty-five (245) references, this is a broad survey of tensor decompostion with numerous pointers to other survey and more specialized works.
I found this shortly after discovering the post I cover in: Tensors and Their Applications…
As I said in the earlier post, this has a lot of promise.
Although it isn’t yet clear to me how you would compare/contrast tensors with different dimensions and perhaps even a different number of dimensions.
Still, a lot of reading to do so perhaps I haven’t reached that point yet.