TY - GEN
T1 - Matrix -valued Monge-Kantorovich optimal mass transport
AU - Ning, Lipeng
AU - Georgiou, Tryphon T.
AU - Tannenbaum, Allen
PY - 2013
Y1 - 2013
N2 - We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multi variable 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.
AB - We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multi variable 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.
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U2 - 10.1109/CDC.2013.6760486
DO - 10.1109/CDC.2013.6760486
M3 - Conference contribution
AN - SCOPUS:84902337777
SN - 9781467357173
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3906
EP - 3911
BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
Y2 - 10 December 2013 through 13 December 2013
ER -