Enhanced Solutions for the Block-Term Decomposition in Rank- Terms

L Khamidullina, G Seidl, IA Podkurkov… - IEEE Transactions …, 2023 - ieeexplore.ieee.org
The block-term decompositions (BTD) represent tensors as a linear combination of low
multilinear rank terms and can be explicitly related to the Canonical Polyadic decomposition …

Computing large-scale matrix and tensor decomposition with structured factors: A unified nonconvex optimization perspective

X Fu, N Vervliet, L De Lathauwer… - IEEE Signal …, 2020 - ieeexplore.ieee.org
During the past 20 years, low-rank tensor and matrix decomposition models (LRDMs) have
become indispensable tools for signal processing, machine learning, and data science …

Nonlinear algebra and applications

P Breiding, TÖ Çelik, T Duff, A Heaton, A Maraj… - arXiv preprint arXiv …, 2021 - arxiv.org
We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …

A recursive eigenspace computation for the canonical polyadic decomposition

E Evert, M Vandecappelle, L De Lathauwer - SIAM Journal on Matrix Analysis …, 2022 - SIAM
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 …

[PDF][PDF] Subspace power method for symmetric tensor decomposition and generalized PCA

J Kileel, JM Pereira - arXiv preprint arXiv:1912.04007, 2019 - academia.edu
Abstract We introduce the Subspace Power Method (SPM) for calculating the CP
decomposition of low-rank even-order real symmetric tensors. This algorithm applies the …

Guarantees for existence of a best canonical polyadic approximation of a noisy low-rank tensor

E Evert, L De Lathauwer - SIAM Journal on Matrix Analysis and Applications, 2022 - SIAM
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 …

On Uniqueness and Computation of the Decomposition of a Tensor into Multilinear Rank- Terms

I Domanov, LD Lathauwer - SIAM Journal on Matrix Analysis and Applications, 2020 - SIAM
Canonical Polyadic Decomposition (CPD) represents a third-order tensor as the minimal
sum of rank-1 terms. Because of its uniqueness properties the CPD has found many …

Complete decomposition of symmetric tensors in linear time and polylogarithmic precision

P Koiran, S Saha - International Conference on Algorithms and …, 2023 - Springer
We study symmetric tensor decompositions, ie, decompositions of the form where T is a
symmetric tensor of order 3 and. In order to obtain efficient decomposition algorithms, it is …

Derandomization and absolute reconstruction for sums of powers of linear forms

P Koiran, M Skomra - Theoretical Computer Science, 2021 - Elsevier
We study the decomposition of multivariate polynomials as sums of powers of linear forms.
As one of our main results, we give a randomized algorithm for the following problem: given …

Accelerating block coordinate descent for nonnegative tensor factorization

A Man Shun Ang, JE Cohen, N Gillis… - … Linear Algebra with …, 2021 - Wiley Online Library
This paper is concerned with improving the empirical convergence speed of block‐
coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We …