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 …
and available software. A tensor is a multidimensional or N-way array. Decompositions of …
Tensor decompositions, alternating least squares and other tales
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' …
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) …
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 …
prespecified number of R factors and a residual array by minimizing the sum of squares of …
Shift-invariant multilinear decomposition of neuroimaging data
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 …
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 …
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 …
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 …
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 …
designed experiments. They are diverse in character. One-sided love and hate among …
Exploring dynamic metabolomics data with multiway data analysis: a simulation study
Background Analysis of dynamic metabolomics data holds the promise to improve our
understanding of underlying mechanisms in metabolism. For example, it may detect …
understanding of underlying mechanisms in metabolism. For example, it may detect …