We propose a metric learning paradigm, Regression-based Elastic Metric
Learning (REML), which optimizes the elastic metric for geodesic regression on
the manifold of discrete curves. Geodesic regression is most accurate when the
chosen metric models the data trajectory close to a geodesic on the discrete
curve manifold. When tested on cell shape trajectories, regression with REML's
learned metric has better predictive power than with the conventionally used
square-root-velocity (SRV) metric.Comment: 4 pages, 2 figures, derivations in appendi