Matricial Wasserstein-1 Distance
Abstract
In this note, we propose an extension of the Wasserstein 1-metric (W1) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular, a "dual of the dual" formulation of W1. This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.
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