154 citations · 637 across the 17 of their papers we have counts for
20 papers
Sparse Approximation via Polynomial Equations
Matija Tomić, Raphaël Widdershoven, Lieven De Lathauwer
We consider the problem of finding sparse solutions of an underdetermined linear system . In contrast to conventional approaches based on greedy algorithms or convex relaxati…
A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography
Shakir Showkat Sofi, Charlotte Vermeylen, Fatemeh Mohammadi +1
Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantu…
Least-squares methods for nonnegative matrix factorization over rational functions
Cécile Hautecoeur, Lieven De Lathauwer, Nicolas Gillis +1
Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in N…
Canonical Polyadic Decomposition via the generalized Schur decomposition
Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) is a fundamental tensor decomposition which expresses a tensor as a sum of rank one tensors. In stark contrast to the matrix case, with l…
A recursive eigenspace computation for the Canonical Polyadic decomposition
Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is compu…
Guarantees for existence of a best canonical polyadic approximation of a noisy low-rank tensor
Eric Evert, Lieven De Lathauwer
The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. How…
Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors: A Unified Nonconvex Optimization Perspective
Xiao Fu, Nico Vervliet, Lieven De Lathauwer +2
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly fo…
A quadratically convergent proximal algorithm for nonnegative tensor decomposition
Nico Vervliet, Andreas Themelis, Panagiotis Patrinos +1
The decomposition of tensors into simple rank-1 terms is key in a variety of applications in signal processing, data analysis and machine learning. While this canonical polyadic de…
Equivalent Polyadic Decompositions of Matrix Multiplication Tensors
Guillaume O. Berger, P. -A. Absil, Lieven De Lathauwer +2
Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present a…
Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation
Xiao-Feng Gong, Qiu-Hua Lin, Feng-Yu Cong +1
Joint blind source separation (J-BSS) is an emerging data-driven technique for multi-set data-fusion. In this paper, J-BSS is addressed from a tensorial perspective. We show how, b…
On the largest multilinear singular values of higher-order tensors
Ignat Domanov, Alwin Stegeman, Lieven De Lathauwer
Let denote the largest mode- multilinear singular value of an tensor . We prove that $$ σ_1^2+\dots+σ_{n-1}^2+σ_{n+1}^2+\dots+σ_{N}…
Generic uniqueness of a structured matrix factorization and applications in blind source separation
Ignat Domanov, Lieven DeLathauwer
Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Gen…
Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank- tensors. We find new mild deterministic conditions for the uniquene…
Generic uniqueness conditions for the canonical polyadic decomposition and INDSCAL
Ignat Domanov, Lieven De Lathauwer
We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank- tensors (canonical polyadic decomposition (CPD)) is unique up…
Canonical polyadic decomposition of third-order tensors: reduction to generalized eigenvalue decomposition
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a third-order tensor is decomposition in a minimal number of rank- tensors. We call an algorithm algebraic if it is guaranteed to find…
Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties
Marco Signoretto, Lieven De Lathauwer, Johan A. K. Suykens
We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable f…
On the Uniqueness of the Canonical Polyadic Decomposition of third-order tensors --- Part II: Uniqueness of the overall decomposition
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic (also known as Candecomp/Parafac) Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. In Part I, we gave an over…
On the Uniqueness of the Canonical Polyadic Decomposition of third-order tensors --- Part I: Basic Results and Uniqueness of One Factor Matrix
Ignat Domanov, Lieven De Lathauwer
Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniquenes…
Are diverging CP components always nearly proportional?
Alwin Stegeman, Lieven De Lathauwer
Fitting a Candecomp/Parafac (CP) decomposition (also known as Canonical Polyadic decomposition) to a multi-way array or higher-order tensor, is equivalent to finding a best low-ran…
A geometric Newton method for Oja's vector field
P. -A. Absil, M. Ishteva, L. De Lathauwer +1
Newton's method for solving the matrix equation runs up against the fact that its zeros are not isolated. This is due to a symmetry of by the action of…