Topological and geometric approaches for machine learning and 3D image analysis

Supervisor: Dr. Rik Sarkar

Enrolled since 2022

Topological methods are not common in machine learning and image analysis. In this project, we aim to develop novel methods based on incorporating topological and geometric features for the analysis of neural networks and 3D scans. In the first part, we introduce novel topological methods for the analysis of 3D scans of human tongues. Further, we propose novel capacity metrics for neural networks, based on a novel topological invariant, called magnitude. In addition, we propose algorithms for speeding up the computation of magnitude and explore more applications in unsupervised representation learning, for which magnitude is suited.


  • Rayna Andreeva, Katharina Limbeck, Bastian Rieck, and Rik Sarkar. "Metric Space Magnitude and Generalisation in Neural Networks." (2023). – accepted for publication at the ICML TAG workshop 2023​. Katharina Limbeck*, Rayna Andreeva*, Rik Sarkar, and Bastian Rieck. "Metric Space Magnitude for Evaluating Unsupervised Representation Learning." (2023) - arXiv preprint​.
  • Andreeva, R., Sarkar, A. and Sarkar, R., 2023. Machine learning and Topological data analysis identify unique features of human papillae in 3D scans. Scientific Reports 13 (1), 21529, 2023​. Beltramo, G., Skraba, P., Andreeva, R., Sarkar, R., Giarratano, Y., & Bernabeu, M. O. (2021). Euler characteristic surfaces. Foundations of Data Science.
  • Saadat-Yazdi, A., Andreeva, R., & Sarkar, R. (2021). Topological Detection of Alzheimer’s Disease Using Betti Curves. In Interpretability of Machine Intelligence in Medical Image Computing, and Topological Data Analysis and Its Applications for Medical Data (pp. 119-128). Springer, Cham.
  • Andreeva, R. *, Fontanella, A. *, Giarratano, Y., & Bernabeu, M. O. (2020, October). DR detection using optical coherence tomography angiography (OCTA): a transfer learning approach with robustness analysis. In International Workshop on Ophthalmic Medical Image Analysis (pp. 11-20). Springer, Cham​.
  • Giarratano, Y., Pavel, A., Lian, J., Andreeva, R., Fontanella, A., Sarkar, R., … & Bernabeu, M. O. (2020, October). A framework for the discovery of retinal biomarkers in Optical Coherence Tomography Angiography (OCTA). In International Workshop on Ophthalmic Medical Image Analysis (pp. 155-164). Springer, Cham.