Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides multiscale descriptors of ``shape" suitable for the analysis of such spatial data. Here we propose a novel visualisation of persistence homology (PH) and fine-tune vectorisations thereof (exploring the effect of different weightings for persistence images, a prominent vectorisation of PH). These approaches offer new biological interpretations and promising avenues for improving the analysis of complex spatial biological data especially in multiple cell type data. To illustrate our methods, we apply them to a lung data set from fatal cases of COVID-19 and a data set from lupus murine spleen.
@article{arxiv.2505.02717,
title = {Topology across Scales on Heterogeneous Cell Data},
author = {Maria Torras-Pérez and Iris H. R. Yoon and Praveen Weeratunga and Ling-Pei Ho and Helen M. Byrne and Ulrike Tillmann and Heather A. Harrington},
journal= {arXiv preprint arXiv:2505.02717},
year = {2025}
}