Félicitations à Isaac Wilfried Sanou (MIO & LIS) qui a soutenu sa thèse le vendredi 24 juin

On the following topic:
"Online polyadic canonical decomposition algorithms of fluorescence tensors: Application to the detection and monitoring of biological and organic contamination in aquatic environments"
 
under the supervision of

- Stéphane MOUNIER, Senior Lecturer, HDR, Univ. of Toulon (France), Thesis Director

Co-supervised by

- Xavier LUCIANI, Maitre de Conférences-, University of Toulon,
- Roland REDON, Senior Lecturer, University of Toulon,

before a jury composed of

Mr. Laurent ALBERA, University Professor, University of Rennes, Rapporteur

Mrs Marianne CLAUSEL, Professor of Universities, University of Lorraine, Reporter

Mr. Pierre COMON, CNRS Research Director, Gipsa-lab, Examiner

Mrs. Nadège THIRION-MOREAU, University Professor, University of Toulon, Examiner

Mrs Florence VOUVE, Lecturer, University of Perpignan, Examiner

Mr. Xavier LUCIANI, Lecturer, University of Toulon, Co-supervisor

Mr. Roland REDON, Associate Professor, University of Toulon, Co-supervisor

Mr. Stéphane MOUNIER, Senior Lecturer, University of Toulon, thesis director

Abstract 

In this thesis we focus on the Canonical Polyadic Decomposition problem (CPD/PARAFAC) of third-order tensors under different constraints such as real time. Canonical polyadic decomposition is used in many areas such as chemistry, biology and medicine. The data from these fields can be dynamic, which leads to the use of real-time or "online" decomposition. The main hypothesis of all existing algorithms is that the rank or the number of components of the decomposition is known and/or does not vary over time. However, this should not be the case in experimental conditions. Also, in some application domains of online tensor decomposition, such as fluorescence spectroscopy or spectral imaging, it is interesting to impose a nonnegative constraint on the factors because the data from these applications are known to be positive. We propose algorithms to calculate this nonnegative decomposition of online tensors based on sparse dictionary learning methods for monitoring chemical components in water from a set of excitation and emission matrices of fluorescence (EEMs). In this context, first of all, the algorithms take into account that the factors are a priori unknown and also the rank of the decomposition can vary during the time. Second, the information previously extracted is used to decompose the new tensors. In addition to the development of these algorithms, we propose a real-time acquisition of fluorescence data in a semi-controlled environment. These algorithms were applied to these real fluorescence datasets in order to compare our algorithms to other state-of-the-art algorithms. The output of our algorithms can be coupled with data from other sensors for a best detection of biological contaminants in the context of aquatic monitoring. These algorithms are presented in the particular case of the nonnegative CPD of third-order fluorescence tensors, but they are not limited to this application field and they can be easily extended to tensors of higher order.

Keywords: Online tensor decomposition, Fluorescence spectroscopy, Optimisation.