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Matrix-valued Monge-Kantorovich Optimal Mass Transport by Ning, Lipeng; Georgiou, Tryphon T.; Tannenbaum, Allen is a scholarly article available to read on EtoBox.

What is Matrix-valued Monge-Kantorovich Optimal Mass Transport about?

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.

Author

Ning, Lipeng; Georgiou, Tryphon T.; Tannenbaum, Allen

Published

2013

Language

EN