Why do some teens become addicted while others don't—even with similar life experiences? To answer this, we need to decode highly complex data from the brain, behavior, and environment. But traditional methods fall short: they assume simple patterns, miss subtle shapes, or can't scale to huge (four-dimensional) data from fMRI.
This project explores Topological Data Analysis (TDA), a cutting-edge method to extract the “shape” of high-dimensional data. We focus on Ball Mapper, a tool that reveals hidden structures in brain imaging and behavioral data—especially useful for spotting early signs of addiction risk.
You’ll help build a multilevel Ball Mapper that runs on GPUs, visualize topological “risk clusters,” and compare them with known clinical data.
Objectives of the work (specific tasks will be agreed individually with the student)
• Study fMRI data and TDA, especially Mapper and Ball Mapper.
• Implement Ball Mapper in the TNL library with GPU support.
• Develop multilevel strategy to scale Ball Mapper to large brain datasets.
• Apply TDA to behavioral and neuroimaging data to find risk clusters.
Benefits for the student
• Work with real neuroscience data (e.g., from ABCD study).
• Gain high-performance computing skills (TNL, GPU programming).
• Contribute to a paper on TDA in neuroscience and psychiatry.
• Have a possible chance to take part in an international Czech–Korean research team.
Resources
- Singh, G., Mémoli, F., & Carlsson, G. E. (2007). Topological methods for the analysis of high dimensional data sets and 3d object recognition. PBG@ Eurographics, 2, 091-100.
- Lum, P. Y., Singh, G., Lehman, A., Ishkanov, T., Vejdemo-Johansson, M., Alagappan, M., ... & Carlsson, G. (2013). Extracting insights from the shape of complex data using topology. Scientific reports, 3(1), 1236.
- Carrière, M., Chazal, F., Ike, Y., Lacombe, T., Royer, M., & Umeda, Y. (2020, June). Perslay: A neural network layer for persistence diagrams and new graph topological signatures. In International Conference on Artificial Intelligence and Statistics (pp. 2786-2796). PMLR.
- Dłotko, P., Gurnari, D., & Sazdanovic, R. (2024). Mapper–type algorithms for complex data and relations. Journal of Computational and Graphical Statistics, 33(4), 1383-1396.
