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Matricial Wasserstein-1 Distance
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https://doi.org/10.1109/lcsys.2017.2699319Abstract
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.
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