On the following subject:
"Algorithms for online polyadic canonical decomposition of fluorescence tensors: Application to the detection and monitoring of biological and organic contamination in aquatic environments".
under the direction of
- Stéphane MOUNIER, Senior Lecturer, HDR, Univ. of Toulon (France), Thesis supervisor
Co-supervised by
- Xavier LUCIANI, Senior Lecturer, University of Toulon,
- Roland REDON, Senior Lecturer, University of Toulon,
before a jury made up of
Mr Laurent ALBERA, Professor, University of Rennes, Rapporteur
Ms Marianne CLAUSEL, University Professor, University of Lorraine, Rapporteur
Mr Pierre COMON, CNRS Research Director, Gipsa-lab, Examiner
Ms Nadège THIRION-MOREAU, University Professor, University of Toulon, Examiner
Ms Florence VOUVE, Senior Lecturer, University of Perpignan, Examiner
Xavier LUCIANI, Senior Lecturer, University of Toulon, Co-supervisor
Mr Roland REDON, Senior Lecturer, University of Toulon, Co-supervisor
Mr Stéphane MOUNIER, Senior Lecturer, University of Toulon, Thesis supervisor
Summary:
In this thesis we focus on the problem of canonical polyadic decompositions (CPD/PARAFAC) of third-order tensors under different constraints such as real time.
Canonical polyadic decomposition is used in many fields such as chemistry, biology and medicine. Data from these fields can be dynamic, which leads to the use of real-time or "online" decomposition. Although there are a variety of online tensor decomposition algorithms, the main assumption of all of them is that the rank or number of components of the decomposition is known and/or does not vary over time. However, this should not be the case under experimental conditions. Also, in certain fields of application of online tensor decomposition such as fluorescence spectroscopy and spectral imaging, it is interesting to impose a nonnegativity constraint on the factor matrices because the data from these applications have a physical meaning and are positive. We propose algorithms to compute this non-negative tensor decomposition online based on parsimonious dictionary learning for monitoring chemical components in water using a set of fluorescence emission and excitation matrices. In this context, firstly, the algorithms take into account factors that are not known but also the variation in the rank of the tensor. Secondly, the information extracted previously is used to decompose the new tensors to come. In addition to developing these algorithms, we propose real-time acquisition of fluorescence data in a semi-controlled environment. These algorithms have been applied to these real fluorescence data sets in order to compare our algorithms with state-of-the-art algorithms. The output of the decomposition algorithms can be coupled with data from other sensors for the detection of biological contaminants in aquatic monitoring. These algorithms are presented in the particular case of non-negative CPD of third-order fluorescence tensors, but they are not limited to this field of application and can be easily extended to higher-order tensors.
Key words: Online tensor decomposition, Fluorescence spectroscopy, Optimisation.