In-Person Poster presentation / poster accept
Riemannian Metric Learning via Optimal Transport
Christopher Basil Scarvelis · Justin Solomon
MH1-2-3-4 #107
Keywords: [ Probabilistic Methods ] [ riemannian geometry ] [ manifold learning ] [ optimal transport ] [ time series ]
We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using a simple alternating scheme. Using this learned metric, we can non-linearly interpolate between probability measures and compute geodesics on the manifold. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sectional data.