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Matricial Wasserstein-1 Distance (1702.07921v2)
Published 25 Feb 2017 in math.FA, math-ph, and math.MP
Abstract: In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) 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 $W_1$. This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.
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