Speaker
Description
Many biological datasets can be represented as point clouds, such as cell centres in spatial proteomics or transcriptomics imaging. These can be analysed using diverse specialised spatial metrics \cite{Bull2025MuSpAn}. One important property of a point cloud is the presence of topological features - connected components, loops, or voids. Topological Data Analysis (TDA), and in particular Persistent Homology (PH), provides a framework to quantify these structures.
PH is powerful, but limited by high computational cost: standard algorithms scale at $O(n^6)$ or worse with the number of points, restricting practical usage to thousands of points – far from the millions typical in modern imaging. A second drawback is the difficulty of identifying “representatives” that allow users to interpret PH by identifying boundaries of topological features.
In this talk, we introduce a new computational approach for PH that dramatically reduces complexity, scaling better than $O(n^2)$ and enabling analysis of millions of points without subsampling. It also produces clear geometric representatives, allowing PH-based segmentation of complex biological structures. Finally, we demonstrate powerful applications of our method for huge datasets in both 2D (prostate cancer) and 3D (developing mouse embryo).
Bibliography
@article{Bull2025MuSpAn,
author = {Bull, Joshua A. and Moore, Joshua W. and Corry, Shania M. and Lin, Muyang and Belnoue-Davis, Hayley L. and Mulholland-Illingworth, Eoghan J. and Leedham, Simon J. and Byrne, Helen M.},
title = {MuSpAn: A Toolbox for Multiscale Spatial Analysis},
journal = {bioRxiv},
year = {2025},
doi = {10.1101/2024.12.06.627195},
note = {bioRxiv preprint, version 4}
}
