PostDoc Project
Title:
Flexible low-rank matrix and polynomial decompositions: uniqueness and algorithms
Dates:
2024/08/01 - 2025/07/31
Description:
Recent solutions to inverse problems in various domains, has led to significant advancements in understanding complex data structures. Although very complex algorithms have been proposed, the interpretability of their results remains a challenge, particularly in scenarios where rigid models are insufficient to capture the complexity of the underlying data, but flexible models are not theoretically understood. Current techniques such as low-rank matrix and tensor decompositions, and independent vector analysis are highly interpretable but also limited by their inflexible nature. Therefore, there is an urgent need to develop versatile models capable of better representing the complexity of the multivariate datasets that are theoretically understood and highly interpretable. The objective of this position is to develop low-rank and polynomial decompositions models suitable for the analysis of large multivariate datasets and to study the generic uniqueness and stability of the decomposition. This is key to ensure the interpretability of the decomposition and support it applicability in practical problems requiring understanding. Numerical algorithms to compute the decompositions efficiently will also be investigated.

References:
[1] T. Adali et al. "Reproducibility in Matrix and Tensor Decompositions: Focus on model match, interpretability, and uniqueness." IEEE Signal Processing Magazine, vol. 39, no. 4, pp. 8-24, 2022.
[2] S. Miron et al. "Tensor methods for multisensor signal processing." IET signal processing, vol. 14, no. 10, pp.693-709, 2020.
[3] T. Adali et al., "Diversity in independent component and vector analyses: Identifiability, algorithms, and applications in medical imaging," IEEE Signal Processing Magazine, vol. 31, no. 3, pp. 18-33, 2014.
Keywords:
Uniqueness, low-rank, décompositions tensorielles, décompositions polynomiales
Conditions:
Between 1 and 3 years post-doctorate or a Ph.D. thesis starting in 2024. The candidate will be jointly supervised by Prof. Sebastian Miron, Dr. Ricardo Borsoi and Prof. David Brie, members of the Multidimensional Signal Processing (SiMul) team (https://cran-simul.github.io/), CRAN Laboratory, University of Lorraine, France. This research will be conducted in collaboration with Prof. Tülay Adali, head of the Machine Learning for Signal Processing (MLSP) Laboratory (https://mlsp.umbc.edu/), University of Maryland Baltimore County (UMBC), USA.

He/She will be based in the CRAN Laboratory, University of Lorraine, in Vandoeuvre-lès-Nancy, France, with the possibility for research visits to the MLSP lab in Baltimore, USA.

Salary and funding: The future researcher will be funded by the NSF-ANR grant AGDAM (ANR-23-CE94-0001). The salary is approximately 2100 euros per month for the doctoral position, and approximately 3000 euros per month (depending on the research experience) for a post-doctoral position.

Candidates should send their application to: sebastian.miron@univ-lorraine.fr, ricardo.borsoi@univ-lorraine.fr, david.brie@univ-lorraine.fr, including an academic CV and a motivation letter (1 page max.) explaining their research interests and their motivation for this position.
Department(s): 
Biology, Signals and Systems in Cancer and Neuroscience
Funds:
The NSF-ANR grant AGDAM (ANR-23-CE94-0001)