Matrix-valued Monge-Kantorovich optimal mass transport
Matrix-valued Monge-Kantorovich optimal mass transport
复制标题
矩阵值 Monge-Kantorovich 最优质量传递
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Tannenbaum
中科院分区：
文献类型：
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作者：
L. Ning;T. Georgiou;A. Tannenbaum
我们制定了矩阵值密度函数的最优运输问题。这在多变量时间序列的谱分析中是相关的。“质量”代表各种频率的能量，而除了通常的跨频率传输成本之外，还考虑了旋转成本。我们表明，这是自然的，以寻求运输计划的张量积空间的两个矩阵值的边缘。与经典的Monge-Kantorovich设置相反，运输计划不再支持薄零测度集。
We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multivariable time-series. The “mass” represents energy at various frequencies whereas, in addition to a usual transportation cost across frequencies, a cost of rotation is also taken into account. We show that it is natural to seek the transportation plan in the tensor product of the spaces for the two matrix-valued marginals. In contrast to the classical Monge-Kantorovich setting, the transportation plan is no longer supported on a thin zero-measure set.