In general, algorithms for order-3 CANDECOMP/PARAFAC (CP), also coined canonical
polyadic decomposition (CPD), are easy to implement and can be extended to higher order …

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult
scenarios, especially, when the rank exceeds the tensor dimension, or when the loading …

Tensor Probabilistic Independent Component Analysis (TPICA) is a popular tool for
analyzing multi-subject fMRI data (voxels× time× subjects) because of TPICA's supposed …

This paper presents a Cramér-Rao lower bound (CRLB) on the variance of unbiased
estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) …

The Schmidt--Eckart--Young theorem for matrices states that the optimal rank-r
approximation of a matrix is obtained by retaining the first r terms from the singular value …

Abstract Three-way Candecomp/Parafac (CP) is a three-way generalization of principal
component analysis (PCA) for matrices. Contrary to PCA, a CP decomposition is rotationally …

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal
form through multiplying the tensor by non-orthogonal invertible matrices along selected …

In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of
polynomial equations with simple roots. We extend this framework to incorporate multiple …

A best rank-R approximation of an order-3 tensor or three-way array may not exist due to the
fact that the set of three-way arrays with rank at most R is not closed. In this case, we are …

A three-mode covariance matrix contains covariances of N observations (eg, subject scores)
on J variables for K different occasions or conditions. We model such an JK× JK covariance …