Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

Inria, the French national research institute for the digital sciences, promotes scientific excellence and technology transfer to maximise its impact.
It employs 2,400 people. Its 200 agile project teams, generally with academic partners, involve more than 3,000 scientists in meeting the challenges of computer science and mathematics, often at the interface of other disciplines.
Inria works with many companies and has assisted in the creation of over 160 startups.
It strives to meet the challenges of the digital transformation of science, society and the economy.


Mapping the connectivity of brain circuits is crucial for investigating the neuronal underpinnings of the healthy as well as pathological brain. Over the last decade, some research projects such as the Human Connectome Project (HCP) have proposed to map the connections between neural pathways that underlie brain function and behavior, in order to improve our understanding of the brain functioning. Mathematical modeling from graph theory provides an extremely powerful approach in the study of brain networks. Indeed, the connectivity map can be represented by a graph in which the nodes represent the different cortical zones and the edges symbolize the connections between these nodes.  

Electroencephalography (EEG), functional magnetic resonance imaging (fMRI) or near infrared spectroscopy (NIRS) are procedures used to obtain direct and indirect measurements of brain neural activity, at different spatial and temporal scales: EEG has a high temporal and low spatial resolutions, while fMRI has high spatial and low temporal resolutions, NIRS being intermediate. Integrating simultaneously these modalities, to establish an enhanced high-resolution spatiotemporal imaging technique could yield a powerful tool, to expand the knowledge of our brain and to exhibit robust biomarkers, more sensitive to pathophysiological changes. However, the integration challenge of these three modalities, as well as the resulting graph estimation remains a real challenge that needs to overcome various spatial and temporal resolutions as well as temporal properties of the data. This methodological challenge increases if at the same time we want to integrate information describing how axons connect structurally these different regions. This is what can provide diffusion MRI through the microstructural modeling of the diffusion of water molecule along the axons in the brain.



This thesis will address this challenge of modeling at the group or the individual level how brain territories connect together. We propose to tackle this challenge by exploring how graph theory can handle the joint modelling of the brain structural and functional connectivity. As such, two major challenges will be addressed: 1) How to combine neuroimaging data as a multidimensional graph? 2) Methodological developments will combine machine learning techniques (including deep learning) with from signal processing one.

Main activities

The first challenge of this PhD is to estimate a robust multimodal graph-based connectome, considering the temporal and statistic properties of the data.  Solutions from the emerging field of graph signal processing (GSP) and graph theory are tailored for this purpose, such as graph Fourier transform, graph signal filtering or Wavelet, or even Convolutional Graphs implementing machine learning solutions. Moreover, novel integration strategy will be proposed to enrich our estimation of the connectome.

The second aim is to develop a predictive model to identify patterns that can act as biomarkers for different diseases. Machine learning techniques have become increasingly popular in the field of network-based classification. However, the application of convolutional networks has been proposed only very recently and has remained largely unexplored, especially in the context of multimodal graphs. In this PhD, we intend to develop new method considering the multimodality nature of our graphs, i.e. through Graph Convolutional Network (GCN).


Fox, M. D., & Raichle, M. E. (2007). Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nature reviews neuroscience, 8(9), 700.

Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J., & Sporns, O. (2008). Mapping the structural core of human cerebral cortex. PLoS biology, 6(7), e159.

Huang, W., Bolton, T. A., Medaglia, J. D., Bassett, D. S., Ribeiro, A., & Van De Ville, D. (2018). A Graph Signal Processing Perspective on Functional Brain Imaging. Proceedings of the IEEE.

Richiardi, J., Achard, S., Bunke, H., & Van De Ville, D. (2013). Machine learning with brain graphs: predictive modeling approaches for functional imaging in systems neuroscience. IEEE Signal Processing Magazine, 30(3), 58-70.

Kipf, T. N., & Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907.

Puy, G., & Pérez, P. (2017). Structured sampling and fast reconstruction of smooth graph signals. Information and Inference: A Journal of the IMA.

Preti, M. G., & Van De Ville, D. (2017). Graph slepians to probe into large-scale network organization of resting-state functional connectivity. In Signals, Systems, and Computers, 2017 51st Asilomar Conference on (pp. 1539-1543). IEEE.

Huang, W., Bolton, T. A., Medaglia, J. D., Bassett, D. S., Ribeiro, A., & Van De Ville, D. (2018). A Graph Signal Processing Perspective on Functional Brain Imaging. Proceedings of the IEEE.



We are seeking a highly motivated student who has completed a MSc or equivalent degree with a strong background in Signal processing, Applied mathematics, Machine learning; experience with high Python, matlab and C/C++ proficiency is also required. Besides, we are expecting good written and spoken communication skills in English.



Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


Monthly gross salary amounting to 1982 euros for the first and second years and 2085 euros for the third year