Featurization of sinlge cell trajectories through kernel mean embedding of optimal transport maps

Longitudinal single-cell data has spurred the development of computationaltrajectory models with the power to make time-resolved, testable predictionsabout cell fates. As ”real-time” trajectory inference methods proliferate, there isa growing need for tools that integrate their inherently high-dimensional outputs.In this work, we propose a novel strategy to facilitate downstream analysis ofsingle-cell optimal-transport trajectory models, by constructing feature vectorsthat contain information about a cell’s state across the entirety of its trajectory.This approach leverages kernel mean embedding of distributions to createtrajectory features with applications in several domains, including cell clusteringand comparison of perturbation response trajectories. We demonstrate howk-means clustering on trajectory features produces interpretable clusters thatrespect the underlying cell trajectories. Furthermore, we develop a divergencemetric between single-cell trajectories based on the maximum mean discrepancy(MMD). We use this trajectory divergence to show that modeling perturbationtrajectories may help uncover experimentally interesting perturbations at highersignificance levels than by comparing perturbation responses at only a single timepoint.