Riemannian Metric Learning via Optimal Transport

• URL: http://arxiv.org/abs/2205.09244v1
• Date: Wed, 18 May 2022 23:32:20 GMT
• Title: Riemannian Metric Learning via Optimal Transport
• Authors: Christopher Scarvelis, Justin Solomon
• Abstract summary: We introduce an optimal transport-based model for learning a metric from cross-sectional samples of evolving probability measures. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data.
• Score: 34.557360177483595
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 backpropagation. Using this learned metric, we can nonlinearly 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.

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