Matrix -valued Monge-Kantorovich optimal mass transport

Lipeng Ning, Tryphon T. Georgiou, Allen Tannenbaum

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3906-3911
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
Country/TerritoryItaly
CityFlorence
Period12/10/1312/13/13

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