The Quasi Manhattan Wasserstein Distance (QMWD) is a metric designed to quantify the dissimilarity between two matrices by combining elements of the Wasserstein Distance with specific transformations. It offers improved time and space complexity compared to the Manhattan Wasserstein Distance (MWD) while maintaining accuracy. QMWD is particularly advantageous for large datasets or situations with limited computational resources. This article provides a detailed explanation of QMWD, its computation, complexity analysis, and comparisons with WD and MWD.

翻译：拟曼哈顿沃瑟斯坦距离（QMWD）是一种通过结合沃瑟斯坦距离的元素与特定变换来量化两个矩阵间差异性的度量。与曼哈顿沃瑟斯坦距离（MWD）相比，它在保持精度的同时，具有更优的时间与空间复杂度。QMWD尤其适用于大规模数据集或计算资源有限的情形。本文详细阐述了QMWD的定义、计算方法、复杂度分析，并与WD和MWD进行了比较。