Faculté des Sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy, France
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 Antipolis-Méditerranée, 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 low-rank tensor approximation problem.
Optimization algorithms on manifolds
Numerical linear algebra
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, Pierre-Alexandre Mattei, Bernard Mourrain. Journal of Symbolic Computation, DOI: j.jsc.2022.04.002.
Newton-Type Methods For Simultaneous Matrix Diagonalization. Rima Khouja, Bernard Mourrain, Jean-Claude Yakoubshon. Calcolo Journal, hal-03390265.
TensorDec: Package for decomposition of tensors and series of moments.
Tensor decomposition for learning Gaussian mixtures from moments at Tensors in statistics, optimization and machine learning workshop, November 21st-25th, 2022, in Warsaw, Poland (invited speaker).
Simultaneous matrix diagonalization algorithm for the tensor rank approximation problem at Algebraic geometry and complexity theory workshop, November 14th-18th, 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 Aromath-Massai seminar.
Riemannian optimization and Veronese manifold for the Waring decomposition, at the Online minisymposuim on Low-rank 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.
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, 28-02-2023.
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).
Vicnesh Venedittan, "Identification of Gaussian Mixtures via Tensor Methods", Master 1 internship in Mathematical Engineering for Data Science at Université de Lorraine (2023).
Participation in the organization of GRETSI'22, XXVIIIème Colloque Francophone de Traitement du Signal et des Images, September 6th–9th, 2022, in Nancy, France.
Python, Julia, Matlab, R, Latex, Beamer, Github, Gitlab.