Karl Arthursson: Using topology and signature methods to study spatiotemporal data with machine learning

This thesis explores a new way to analyze spatiotemporal data. By combining topology, the path signature and machine learning a robust model to analyze swarming behavior over time is created. Using persistent homology a representation of spatial data is obtained and the path signature gives us a representation for how this changes over time. This representation allows us to compare samples even if they have different amounts of time steps and different length of the sequence. It is also resistant to noise in the spatial representation. Using this data is then used to train a gaussian process regressor to extract parameters that govern the movement of swarms. Our analysis shows that the tested method is a good candidate for analyzing spatiotemporal data and that it warrants further studies.