Tensor decomposition for signal processing and machine learning
Tensors or multiway arrays are functions of three or more indices (i, j, k,...)-similar to matrices
(two-way arrays), which are functions of two indices (r, c) for (row, column). Tensors have a …
(two-way arrays), which are functions of two indices (r, c) for (row, column). Tensors have a …
Overview of constrained PARAFAC models
G Favier, ALF de Almeida - EURASIP Journal on Advances in Signal …, 2014 - Springer
In this paper, we present an overview of constrained parallel factor (PARAFAC) models
where the constraints model linear dependencies among columns of the factor matrices of …
where the constraints model linear dependencies among columns of the factor matrices of …
On the uniqueness of the canonical polyadic decomposition of third-order tensors---Part II: Uniqueness of the overall decomposition
I Domanov, L De Lathauwer - SIAM Journal on Matrix Analysis and …, 2013 - SIAM
Canonical polyadic (also known as Candecomp/Parafac) decomposition (CPD) of a higher-
order tensor is decomposition into a minimal number of rank-1 tensors. In Part I, we gave an …
order tensor is decomposition into a minimal number of rank-1 tensors. In Part I, we gave an …
On the uniqueness of the canonical polyadic decomposition of third-order tensors---Part I: Basic results and uniqueness of one factor matrix
I Domanov, L De Lathauwer - SIAM Journal on Matrix Analysis and …, 2013 - SIAM
Canonical polyadic decomposition (CPD) of a higher-order tensor is decomposition into a
minimal number of rank-1 tensors. We give an overview of existing results concerning …
minimal number of rank-1 tensors. We give an overview of existing results concerning …
Hyperspectral super-resolution with coupled tucker approximation: Recoverability and SVD-based algorithms
We propose a novel approach for hyperspectral super-resolution, that is based on low-rank
tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the …
tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the …
Spectrum cartography via coupled block-term tensor decomposition
Spectrum cartography aims at estimating power propagation patterns over a geographical
region across multiple frequency bands (ie, a radio map)-from limited samples taken …
region across multiple frequency bands (ie, a radio map)-from limited samples taken …
Low complexity damped Gauss--Newton algorithms for CANDECOMP/PARAFAC
The damped Gauss--Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP)
decomposition can handle the challenges of collinearity of factors and different magnitudes …
decomposition can handle the challenges of collinearity of factors and different magnitudes …
DOA estimation for transmit beamspace MIMO radar via tensor decomposition with Vandermonde factor matrix
We address the problem of tensor decomposition in application to direction-of-arrival (DOA)
estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output …
estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output …
[HTML][HTML] Canonical polyadic decomposition of third-order tensors: Relaxed uniqueness conditions and algebraic algorithm
I Domanov, L De Lathauwer - Linear Algebra and its Applications, 2017 - Elsevier
Abstract Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal
decomposition into a sum of rank-1 tensors. We find new mild deterministic conditions for the …
decomposition into a sum of rank-1 tensors. We find new mild deterministic conditions for the …
New uniqueness conditions for the canonical polyadic decomposition of third-order tensors
M Sørensen, L De Lathauwer - SIAM Journal on Matrix Analysis and …, 2015 - SIAM
The uniqueness properties of the canonical polyadic decomposition (CPD) of higher-order
tensors make it an attractive tool for signal separation. However, CPD uniqueness is not yet …
tensors make it an attractive tool for signal separation. However, CPD uniqueness is not yet …