
Rima Khouja
Postdoctoral Researcher

Faculté des Sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 VandœuvrelèsNancy, France
email: rima.khouja@univlorraine.fr

Welcome to my web page!
My name is Rima Khouja. Currently, I am a postdoctoral researcher at Le Centre de Recherche en Automatique de Nancy (CRAN) and Institue Élie Cartan de Lorraine (IECL), jointly supervised by Konstantin Usevich and Marianne Clausel. Previously, I was a PhD student in AROMATH team at Inria Sophia AntipolisMéditerranée, under the supervision of Bernard Mourrain. I defended my PhD thesis in mathematics entitled "Optimization algorithms for the tensor rank approximation problem: application to clustering in machine learning" on 9 June 2022.
My research topic is about tensors, optimization algorithms, and their applications in data science, in particular in deep learning and machine learning. My postdoctoral research focuses on developing new deep learning approaches combining tensor methods (such that tensor compression techniques), and optimization methods. I'm also interested in studying fundamental tensor problems such that the conditionning of the lowrank tensor approximation problem.
Research Interests
Tensors
Machine learning
Deep learning
Numerical algorithms
Optimization methods
Optimization algorithms on manifolds
Numerical linear algebra
Numerical analysis
Publications
Riemannian Newton optimization methods for the symmetric tensor approximation problem. Rima Khouja, Houssam Khalil, Bernard Mourrain. Linear Algebra and its Applications Journal, DOI: 10.1016/j.laa.2021.12.008.
Tensor decomposition for learning Gaussian mixtures from moments. Rima Khouja, PierreAlexandre Mattei, Bernard Mourrain. Journal of Symbolic Computation, DOI: j.jsc.2022.04.002.
NewtonType Methods For Simultaneous Matrix Diagonalization. Rima Khouja, Bernard Mourrain, JeanClaude Yakoubshon. Calcolo Journal, hal03390265.
Projects
TensorDec: Package for decomposition of tensors and series of moments.
Presentations
Tensor decomposition for learning Gaussian mixtures from moments at Tensors in statistics, optimization and machine learning workshop, November 21st25th, 2022, in Warsaw, Poland (invited speaker).
Simultaneous matrix diagonalization algorithm for the tensor rank approximation problem at Algebraic geometry and complexity theory workshop, November 14th18th, 2022, in Warsaw, Poland (invited speaker).
Riemannian Newton optimization methods for the symmetric tensor approximation problem, SiMul seminar, at CRAN (invited speaker).
Tensor decomposition for learning Gaussian Mixtures from moments, at AromathMassai seminar.
Riemannian optimization and Veronese manifold for the Waring decomposition, at the Online minisymposuim on Lowrank Geometry and Computation (invited speaker).
Optimizing an homogeneous polynomial on the unit sphere, at Journées nationales de calcul formel (JNCF2020) , in Luminy, in France.
A Riemannian Newton method for the symmetric tensor decomposition problem, at Lebanese International Conference On Mathematics and Applications (LICMA'19) , in Beyrouth, in Lebanon.
Upcoming activities
SIAM Conference on Applied Algebraic Geometry (AG23), July 10  14, 2023, Eindhoven University of Technology  Eindhoven, The Netherlands.
Journée scientifique en IA à Nancy, at Université de Lorraine, 28022023.
Teaching
Statistics and Big Data (matrix/tensor decompositions and machine learning), TD/TP, Master 2 Ingénierie de Systèmes Complexes (ISC) (2022/2023).
Data Analysis and Statistical Learning, TD/TP, Master 1 ISC (2022/2023).
Stochastic Modeling and Machine Learning for Finance, CM/TD, Master 2 IFM (2022/2023).
Supervising
Vicnesh Venedittan, "Identification of Gaussian Mixtures via Tensor Methods", Master 1 internship in Mathematical Engineering for Data Science at Université de Lorraine (2023).
Other activities
Participation in the organization of GRETSI'22, XXVIIIème Colloque Francophone de Traitement du Signal et des Images, September 6th–9th, 2022, in Nancy, France.
Languages
English
French
Arabic
Programming skills
Python, Julia, Matlab, R, Latex, Beamer, Github, Gitlab.