Between linear and nonlinear: new tensor perspectives

From 01-10-2022 to 30-09-2026

Description

Computation of the Canonical Polyadic Decomposition (CPD) of a higher-order tensor ―its basic decomposition in a minimal number of rank-1 terms― is known to be NP-hard, and best low-rank approximation of higher-order tensors can be ill-posed. In this project we will develop the opposite point of view, better reflecting engineering practice, namely that CPD is a “tractable” problem unless there is not a close enough match between the observed data and the mathematical model. We will investigate which perturbations can be allowed for the computation to remain “tractable” and we will develop new matrix-like algorithms in the style of numerical linear algebra. We will extend our study to coupled CPDs and to CPDs of tensors that are implicitly given as solutions of sets of linear equations. We will use the new insights to develop new algebraic tools for data analysis and to analyze nonlinear dynamical system behavior. We will develop advanced numerical optimization-based algorithms that cope with “numerical loss of tractability”.

Team

• Lieven De Lathauwer, Promoter

Financing

Funding: KU Leuven - Internal Funding KU Leuven

Program/Grant Type: C1 - KU Leuven Category 1 Funding