Chen Yongxin, Georgiou Tryphon T, Ning Lipeng, Tannenbaum Allen
Department of Medical Physics, Memorial Sloan Kettering Cancer Center, NY.
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA.
IEEE Control Syst Lett. 2017 Jul;1(1):14-19. doi: 10.1109/LCSYS.2017.2699319. Epub 2017 Apr 28.
We propose an extension of the Wasserstein 1-metric () 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 . This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.
我们提出了一种针对密度矩阵、矩阵值密度测度的Wasserstein 1-度量（）的扩展，以及质量传输的非平衡解释。我们使用对偶理论，特别是 的一种“对偶的对偶”公式。这种地球移动距离的矩阵类似物具有几个吸引人的特性，包括易于计算。
