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. 2017 Jul;1(1):14-19.
doi: 10.1109/LCSYS.2017.2699319. Epub 2017 Apr 28.

Matricial Wasserstein-1 Distance

Yongxin Chen  1 , Tryphon T Georgiou  2 , Lipeng Ning  3 , Allen Tannenbaum  4
Affiliations

Matricial Wasserstein-1 Distance

Yongxin Chen et al. IEEE Control Syst Lett. 2017 Jul.

Abstract

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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