Work

Optimal estimation of the canonical polyadic decomposition from low-rank tensor trains

Year: 2025

Type: article

Abstract: Tensor factorization has been steadily used to represent high-dimensional data.In particular, the canonical polyadic decomposition (CPD) is very appreciated for its remarkable uniqueness properties.However, computing the high-order CPD is challenging: numerical issues and high needs for storage and processing can lead algorithms to diverge.Furthermore, the recovery of the CP factors is an ill-posed problem.One way to circumvent this limitation is to exploit the equivalence between the CPD and the Tensor Train Decomposition.This paper formulates the dimensionality reduction problem as a global marginally convex optimization problem. This global optimization scheme estimates the CP factors with minimal error.The resulting approach, Dimensionality Reduction, joint Estimation of the Ambiguity Matrices and the CP FACtors (DREAMFAC), reaches the global optimum when estimating the CP factors.DREAMFAC is shown to be an optimal estimator that reaches the corresponding constrained Cramér-Rao bounds.It therefore appears as a state-of-the-art solution for estimation of the best rank-K CPD of a tensor (when it exists).Its performance is illustrated on the problem of parameter estimation in a dual-polarized MIMO system.Numerical experiments show the excellent practical performance of DREAMFAC, even with very low SNR.

Source: Signal Processing

DOI: 10.1016/j.sigpro.2025.110001

Authors: Clémence Prévost, Pierre Chainais

Institutions: Centre National de la Recherche Scientifique, Université de Lille, Centre de Recherche en Informatique, Signal et Automatique de Lille, Centrale Lille Institut

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Agence Nationale de la Recherche