Moment tensor decompositions revisited

Decompositions of moment tensors

Canonical Tensor Decompositions

The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the tensor rank. Important basic questions are raised in this short paper, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a ...

Orthogonal Tensor Decompositions

We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebr...

Tensor Decompositions and Applications

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, grap...

Topic Moment tensor inversion and moment tensor interpretation

page