2021-04156 - Topological Data Analysis for Brain Network Exploration

Contract type : Internship

Level of qualifications required : Graduate degree or equivalent

Fonction : Internship Research

Assignment

Network models are currently used in different contexts of application due to the possibility of representing data and their interconnections in an intuitive way. Topological Data Anal-ysis (TDA) provides a set of emerging tools to describe structured data, such as networks. For instance, Betti numbers and persistent homology are gaining attention in a wide variety offields with encouraging results both on the characterization of different graph models and on real-world data [2, 3]. For these reasons, we would like to apply these approaches in the context of brain functional connectivity to extend current state-of-the-art results. In neuroscience, network models can depict the system of connections among regions of the brain [1]. These networks can be leveraged to analyze the brain under diverse conditions, such as in comatose or anesthetized subjects, or to determine discriminant network features. Brain functional connectivity networks usually exhibit small-world properties that will be refined during this internship. In addition, during the network extraction process, edges might be identified incorrectly. The impact of these spurious edges on the topology of the graphs will be evaluated in the second part of the internship.

Main activities

  • Get familiar with topological data analysis theory and algorithm tools.
  • Explore the evolution of Betti numbers with regard to graph sparsity level for different datasets.
  • Extend the work in [3] to small-world networks in order to determine subcategories of graphs in this regime.
  • Explore the relation between the different Betti numbers and the usual graph metrics (clustering coefficients, efficiency, ...) on theoretical graphs (Watts-Strogatz, Erdös–Rényi, ...) and real-world functional connectivity graphs.
  • Explore the impact of spurious edges on the Betti numbers of different theoretical and real-world graphs.

Skills

  • Master 2 or 3rd-year engineering student in a relevant quantitative field
  • Programming language: Python
  • Applied mathematics: graph theory, topology would be a plus

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training