Topological learning for spatial and dynamic biomedical data

Topological data analysis (TDA) offers powerful tools for studying biological phenomena. In this talk, I will present recent applications to spatial and dynamic biomedical data. First, I will discuss topological model selection in tumour-induced angiogenesis, where TDA combined with approximate Bayesian computation enables parameter inference and objective comparison of spatial models. Second, I will present two relational TDA techniques based on Dowker and Witness complexes that encode spatial relation in multispecies data, i.e. datasets with multiple subtypes of data points. Our relational TDA features can extract biological insight and integrate naturally with popular machine learning approaches for spatial data, such as graph neural networks. Finally, I will show how we can apply path signatures to capture underlying structural relations in time series of multivariate dynamical processes, such as neural recordings.