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 …
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
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 …
become indispensable tools for signal processing, machine learning, and data science …
Nonlinear algebra and applications
We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …
is organized into eight themes: polynomial optimization, partial differential equations …
A recursive eigenspace computation for the canonical polyadic decomposition
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 …
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 …
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 …
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 …
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
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 …
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
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 …
As one of our main results, we give a randomized algorithm for the following problem: given …
Accelerating block coordinate descent for nonnegative tensor factorization
This paper is concerned with improving the empirical convergence speed of block‐
coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We …
coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We …