Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric

NeurIPS 2015 Vivien SeguyMarco Cuturi

Given a family of probability measures in P(X), the space of probability measures on a Hilbert space X, our goal in this paper is to highlight one ore more curves in P(X) that summarize efficiently that family. We propose to study this problem under the optimal transport (Wasserstein) geometry, using curves that are restricted to be geodesic segments under that metric... (read more)

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