Tensor decompositions and applications

TG Kolda, BW Bader - SIAM review, 2009 - SIAM
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 …

Tensor decompositions, alternating least squares and other tales

P Comon, X Luciani… - Journal of Chemometrics …, 2009 - Wiley Online Library
This work was originally motivated by a classification of tensors proposed by Richard
Harshman. In particular, we focus on simple and multiple 'bottlenecks', and on 'swamps' …

Blind identification of underdetermined mixtures by simultaneous matrix diagonalization

L De Lathauwer, J Castaing - IEEE Transactions on Signal …, 2008 - ieeexplore.ieee.org
In this paper, we study simultaneous matrix diagonalization-based techniques for the
estimation of the mixing matrix in underdetermined independent component analysis (ICA) …

On the non-existence of optimal solutions and the occurrence of “degeneracy” in the Candecomp/Parafac model

WP Krijnen, TK Dijkstra, A Stegeman - Psychometrika, 2008 - Springer
Abstract The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a
prespecified number of R factors and a residual array by minimizing the sum of squares of …

Shift-invariant multilinear decomposition of neuroimaging data

M Mørup, LK Hansen, SM Arnfred, LH Lim, KH Madsen - NeuroImage, 2008 - Elsevier
We present an algorithm for multilinear decomposition that allows for arbitrary shifts along
one modality. The method is applied to neural activity arranged in the three modalities …

Space-time-frequency (STF) MIMO communication systems with blind receiver based on a generalized PARATUCK2 model

ALF de Almeida, G Favier… - IEEE Transactions on …, 2013 - ieeexplore.ieee.org
In this paper, we first propose a generalized fourth-order PARATUCK2 tensor model for
multiple-input multiple-output (MIMO) communication systems with space-time-frequency …

Subtracting a best rank-1 approximation may increase tensor rank

A Stegeman, P Comon - Linear Algebra and its Applications, 2010 - Elsevier
It has been shown that a best rank-R approximation of an order-k tensor may not exist when
R⩾ 2 and k⩾ 3. This poses a serious problem to data analysts using tensor decompositions …

Three-way component analysis using the R package ThreeWay

P Giordani, HAL Kiers, MA Del Ferraro - Journal of Statistical Software, 2014 - jstatsoft.org
The R package ThreeWay is presented and its main features are illustrated. The aim of
ThreeWay is to offer a suit of functions for handling three-way arrays. In particular, the most …

A brief survey of asymmetric MDS and some open problems

N Chino - Behaviormetrika, 2012 - jstage.jst.go.jp
Asymmetric relationships among objects are frequently observed in daily life as well as in
designed experiments. They are diverse in character. One-sided love and hate among …

Exploring dynamic metabolomics data with multiway data analysis: a simulation study

L Li, H Hoefsloot, AA de Graaf, E Acar, AK Smilde - BMC bioinformatics, 2022 - Springer
Background Analysis of dynamic metabolomics data holds the promise to improve our
understanding of underlying mechanisms in metabolism. For example, it may detect …