Matricial Wasserstein-1 Distance


Yongxin Chen, Tryphon T Georgiou, Lipeng Ning, and Allen Tannenbaum. 2017. “Matricial Wasserstein-1 Distance.” IEEE Control Syst Lett, 1, 1, Pp. 14-9.


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.
Last updated on 11/27/2017