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
Events
2/09/2024:
PhD defense - Martijn Oldenhof
Machine Learning for Advanced Chemical Analysis and Structure Recognition in Drug Discovery
3/09/2024:
Meet the Jury Igor Tetko on Advanced Machine Learning in Drug Discovery
12/09/2024:
Multimodal analysis of cell-free DNA for sensitive cancer detection in low-coverage and low-sample settings
Seminar by Antoine Passemiers
News
STADIUS Alumni Herman Verrelst – new CEO of Biocartis
08 June 2017
Herman Verrelst, the founder of KU Leuven spin-off Cartagenia, who has been working in Silicon Valley, US for the last few years will be returning to Belgium to follow the steps of Rudi Pauwels as CEO of the Belgian diagnostic company, Biocartis.
Supporting healthcare policymaking via machine learning – batteries included!
29 May 2017
STADIUS takes the lead in the data analytics efforts in an ambitious European Project MIDAS.
Marc Claesen gives an interview about his PhD for the magazine of the Faculty of Engineering Sciences "Geniaal"
10 February 2017
Did you know that in Belgium approximately one third of type 2 diabetes patients are unaware of their condition?
Joos Vandewalle is nieuwe voorzitter KVAB
09 October 2016
Op 5 oktober 2016 heeft de Algemene Vergadering van de Academie KVAB Joos Vandewalle verkozen tot voorzitter van de KVAB.