Ph. D. Project
Tensor methods for data fusion with shared and distinct features : Application to subgroup identification in multi-subject fMRI data
2023/10/01 - 2026/09/30
Other supervisor(s):
Tulay Adali (
Discovering common and distinct features (DCDF) across multiple datasets is a fundamental problem in various disciplines, including the analysis of multi-task functional magnetic resonance imaging (fMRI) data [1] or multimodal image fusion [2]. The distinct features in each dataset may originate from, e.g., uncontrolled acquisition conditions [3], or from features unique to each subject in medical data [4]. This constitutes a challenging scenario that goes beyond the capabilities of classical models and require more flexible methods to be developed. DCDF in multisubject fMRI data can have significant societal impact through personalized medicine by finding features shared by subgroups of individuals that are predictive of mental disorders [1]. Of particular interest are longitudinal studies such as the ABCD [5], which collect fMRI and non-neuroimaging data (e.g., cognitive scores, substance use) of the same subjects over time. This requires methods to identify homogeneous subgroups of subjects in longitudinal fMRI and non-neuroimaging data, revealing the evolution of cognitive processes and characterizing subtypes of diseases and risk groups for addictive behavior early in the study. Identifying which subgroup an individual belongs to can be an important step towards personalized medicine.

Neuroimaging raises fundamental methodological questions. It requires algorithms that are data-driven, highly interpretable (e.g., with identifiability guarantees) and reproducible, what made approaches based on matrix and tensor decomposition, and independent component analysis the gold standard in the field. However, the study of uniqueness of more flexible factorizations is still in its infancy. The uniqueness of coupled tensor decompositions was only investigated recently [6]. Algorithms considering shared and distinct components were proposed in [7] without identifiability guarantees. The identifiability of coupled tensor decomposition with shared individual components for image fusion was recently established in [2].

Research program: The Ph.D. candidate will focus on developing new flexible matrix/tensor decomposition methods with shared and distinct components with application to neuroimaging. The objectives include: 1) develop coupled low-rank tensor decomposition methods with shared and distinct components applicable to neuroimaging and investigate their identifiability; 2) develop physically interpretable decompositions that account for longitudinal data and multiple (e.g., non-neuroimaging) modalities; 3) validate the methods for homogeneous subgroup identification in longitudinal
multisubject fMRI data for personalized medicine.


[1] M. Akhonda et al., "Disjoint subspaces for common and distinct component analysis: Application to the fusion of multi-task FMRI data," Journal of Neuroscience Methods, vol. 358, p. 109214, 2021.
[2] R. A. Borsoi et al., "Coupled tensor decomposition for hyperspectral and multispectral image fusion with inter-image variability," IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 3, pp. 702-717, 2021.
[3] A. K. Smilde et al., "Common and distinct components in data fusion," Journal of Chemometrics, vol. 31, no. 7, p. e2900, 2017.
[4] E. S. Finn et al., "Functional connectome fingerprinting: identifying individuals using pat- terns of brain connectivity," Nature Neuroscience, vol. 18, no. 11, pp. 1664-1671, 2015.
[5] B. J. Casey et al., "The adolescent brain cognitive development (ABCD) study: imaging acquisition across 21 sites," Developmental Cognitive Neuroscience, vol. 32, pp. 43-54, 2018.
[6] M. Sørensen and L. D. De Lathauwer, "Coupled canonical polyadic decompositions and (cou- pled) decompositions in multilinear rank-(lr,n,lr,n,1) terms-part I: Uniqueness," SIAM Journal on Matrix Analysis and Applications, vol. 36, no. 2, pp. 496-522, 2015.
[7] E. Acar et al., "Structure-revealing data fusion," BMC Bioinformatics, vol. 15, no. 1, pp. 1-17, 2014.
Machine learning, Data fusion, Tensor methods, Neuroimaging.
Thesis in 36 months, the candidate will be based on the Faculty of Sciences & Technologies, (UL), in Vandoeuvre-lès-Nancy (54). The thesis will be in close collaboration with the Machine Learning for Signal Processing Lab (MLSP Lab), University of Maryland Baltimore County (UMBC), USA.
Expected profile: Master's degree or equivalent, experience in one or more of the following topics: data analysis, signal processing, machine learning, and/or applied mathematics. Good communication skills, knowledge of English.
Biology, Signals and Systems in Cancer and Neuroscience
International thesis or university doctoral contract