Vaccination doesn’t just protect against infections—it also reshapes the gut microbiome. Analyzing these changes is tricky: microbiome data are high-dimensional, sparse, and full of subtle patterns missed by standard tools like dimension reduction (PCA, UMAP, tSNE) or clustering.
Topological Data Analysis (TDA) offers a completely new lens. It focuses on the “shape” of data—continuity, loops, and structure—without needing huge sample sizes or training. In this project, we’ll explore Ball Mapper, a TDA tool that visualizes hidden microbial patterns and differences between vaccinated and control groups.
You’ll help build a statistically enhanced Ball Mapper and apply it to real microbiome data from animal vaccine studies. Can we find invisible transitions in microbial communities—and make them visible through computational topology?
Objectives of the work (specific tasks will be agreed individually with the student)
• Get familiar with TDA and microbiome data, especially Ball Mapper.
• Implement Ball Mapper and enhancements in Python or C++.
• Analyze real or synthetic microbiome data and visualize metadata (e.g. vaccine, age).
• Compare results with classical methods (PCA, clustering, diversity indices).
Benefits for the student
• Learn modern tools in mathematical data science and computational topology.
• Work with real microbiome data and meaningful biological metadata.
• Gain experience with high-dimensional data and visualization.
• Have a possible chance to Take part in an international Czech–Korean research collaboration.
Resources
- Liao, T., Wei, Y., Luo, M., Zhao, G. P., & Zhou, H. (2019). tmap: an integrative framework based on topological data analysis for population-scale microbiome stratification and association studies. Genome Biology, 20, 1-19.
- 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.
