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Chen Y, Georgiou TT, Ning L, Tannenbaum A. Matricial Wasserstein-1 Distance. IEEE Control Syst Lett 2017;1(1):14-9.
Last updated on 02/27/2023
We propose an extension of the Wasserstein 1-metric (W1) for density matrices, matrix-valued density measures, and an unbalanced interpretation of mass transport. We use duality theory and, 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.