distances between point clouds

I spent the last two days working at Apple Paris, which was fun! I worked with the open-source ott-jax package, which can do some amazing things. I worked with Soledad Villar (Apple & JHU) to generalize the k-means algorithm to point clouds! It can cluster point clouds morphologically, even if the different point clouds have different numbers of points, and even if the different point clouds live in spaces of different dimensions! Everything obeys permutation and rotation symmetries.