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.Comment: 8 page
