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We formulate the above as a generalized optimal transport problem where the cost, the marginals, and the coupling are represented as block matrices and each component block is a SPD matrix. The summation of row blocks and column blocks in the coupling matrix are constrained by the given block-SPD marginals. We endow the set of such block-coupling matrices with a novel Riemannian manifold structure. This allows to exploit the versatile Riemannian optimization framework to solve generic SPD matrix-valued OT problems. We illustrate the usefulness of the proposed approach in several applications.<\/jats:p>","DOI":"10.1007\/s10994-022-06258-w","type":"journal-article","created":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T22:15:42Z","timestamp":1666304142000},"page":"1595-1622","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Riemannian block SPD coupling manifold and its application to optimal transport"],"prefix":"10.1007","volume":"113","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-4655-655X","authenticated-orcid":false,"given":"Andi","family":"Han","sequence":"first","affiliation":[]},{"given":"Bamdev","family":"Mishra","sequence":"additional","affiliation":[]},{"given":"Pratik","family":"Jawanpuria","sequence":"additional","affiliation":[]},{"given":"Junbin","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,20]]},"reference":[{"key":"6258_CR1","doi-asserted-by":"crossref","unstructured":"Absil, P.A., Mahony, R., & Sepulchre, R. 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