Huber-Wasserstein barycenters, defined by Huberizing the ground cost of optimal transport, are robust to outlying distributions, have breakdown point near 1/2, and interpolate between Wasserstein means and medians.
Rachev and Ludger Rüschendorf , title =
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Huber-Wasserstein barycenters for robust distribution-valued data
Huber-Wasserstein barycenters, defined by Huberizing the ground cost of optimal transport, are robust to outlying distributions, have breakdown point near 1/2, and interpolate between Wasserstein means and medians.