{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T00:59:26Z","timestamp":1778979566810,"version":"3.51.4"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-14-1-0245"],"award-info":[{"award-number":["N00014-14-1-0245"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-16-1-2147"],"award-info":[{"award-number":["N00014-16-1-2147"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2107934"],"award-info":[{"award-number":["DMS-2107934"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2022,12,31]]},"DOI":"10.1137\/21m1461551","type":"journal-article","created":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T00:45:43Z","timestamp":1671497143000},"page":"1347-1368","source":"Crossref","is-referenced-by-count":6,"title":["Exponential-Wrapped Distributions on Symmetric Spaces"],"prefix":"10.1137","volume":"4","author":[{"given":"Emmanuel","family":"Chevallier","sequence":"first","affiliation":[{"name":"Aix Marseille Univ., CNRS, Centrale Marseille, Institut Fresnel, Marseille, France."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Didong","family":"Li","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ., CNRS, Centrale Marseille, Institut Fresnel, Marseille, France."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yulong","family":"Lu","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ., CNRS, Centrale Marseille, Institut Fresnel, Marseille, France."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Dunson","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ., CNRS, Centrale Marseille, Institut Fresnel, Marseille, France."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2022,12,20]]},"reference":[{"key":"ref2","doi-asserted-by":"crossref","first-page":"396","DOI":"10.3390\/e18110396","volume":"18","author":"Chevallier E.","year":"2016","journal-title":"Entropy"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/15M1053566"},{"key":"ref4","first-page":"1","volume":"12","author":"Ding J.","year":"2020","journal-title":"Nature Commun."},{"key":"ref5","first-page":"3244","volume":"89","author":"Falorsi L.","year":"2019","journal-title":"Proc. Mach. Learn. Res. (PMLR)"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1098\/rspa.1953.0064","volume":"217","author":"Fisher R. A.","year":"1953","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Sci. Eng."},{"key":"ref8","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s11202-007-0006-4","volume":"48","author":"Gavrilov A. V.","year":"2007","journal-title":"Sib. Math. J."},{"key":"ref9","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1093\/biomet\/74.4.751","volume":"74","author":"Hall P.","year":"1987","journal-title":"Biometrika"},{"key":"ref11","volume-title":"Differential Geometry, Lie Groups, and Symmetric Spaces","author":"Helgason S.","year":"1979"},{"key":"ref12","first-page":"832","author":"Hendriks H.","year":"1990","journal-title":"Ann. Statist."},{"key":"ref13","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1214\/09-AOS783","volume":"38","author":"Huckemann S. F.","year":"2010","journal-title":"Ann. Stat."},{"key":"ref14","first-page":"1478","volume":"6","author":"Jona-Lasino G.","year":"2012","journal-title":"Ann. Appl. Stat."},{"key":"ref15","doi-asserted-by":"crossref","first-page":"3224","DOI":"10.3150\/20-BEJ1222","volume":"26","author":"Kato S.","year":"2020","journal-title":"Bernoulli"},{"key":"ref16","first-page":"1083","volume":"26","author":"Kim P. T.","year":"1998","journal-title":"Ann. Statist."},{"key":"ref17","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1080\/01621459.2012.699770","volume":"107","author":"Kurtek S.","year":"2012","journal-title":"J. Amer. Statist. Assoc."},{"key":"ref18","unstructured":"M. T. Law  and \nJ. Stam  (2020), Ultrahyperbolic Representation Learning, in Adv. Neural Inf. Process. Syst. 34, Curran Associates, Red Hook, NY, pp. 1668\u20131678."},{"key":"ref19","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10208-020-09459-8","volume":"21","author":"Lim L.-H.","year":"2021","journal-title":"Found. Comput. Math."},{"key":"ref22","volume-title":"Statistics of Directional Data","author":"Mardia K. V.","year":"1972"},{"key":"ref23","first-page":"12544","volume-title":"Advances in Neural Information Processing Systems","author":"Mathieu E.","year":"2019"},{"key":"ref24","first-page":"1","volume":"21","author":"Miolane N.","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref25","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10851-020-00945-w","volume":"62","author":"Nava-Yazdani E.","year":"2020","journal-title":"J. Math. Imaging Vision"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/2372398","volume":"76","author":"Nomizu K.","year":"1954","journal-title":"Amer. J. Math."},{"key":"ref27","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.spl.2005.04.004","volume":"73","author":"Pelletier B.","year":"2005","journal-title":"Statist. Probab. Lett."},{"key":"ref28","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10851-006-6228-4","volume":"25","author":"Pennec X.","year":"2006","journal-title":"J. Math. Imaging Vision"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/B978-0-12-814725-2.00012-1","volume-title":"Riemannian Geometric Statistics in Medical Image Analysis","author":"Pennec X.","year":"2020"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1109\/TIT.2017.2653803","volume":"63","author":"Said S.","year":"2017","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1109\/TIT.2017.2713829","volume":"64","author":"Said S.","year":"2017","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.patcog.2014.08.011","volume":"48","author":"Slama R.","year":"2015","journal-title":"Pattern Recognit."},{"key":"ref35","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1109\/TPAMI.2005.86","volume":"27","author":"Srivastava A.","year":"2005","journal-title":"Trans. Pattern Anal. Mach. Intell."},{"key":"ref36","first-page":"177","volume":"7","author":"Taniguchi H.","year":"1984","journal-title":"Tokyo J. Math."},{"key":"ref37","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3820-1","volume-title":"Harmonic Analysis on Symmetric Spaces and Applications II","author":"Terras A.","year":"1988"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1109\/TPAMI.2011.52","volume":"33","author":"Turaga P.","year":"2011","journal-title":"Trans. Pattern Anal. Mach. Intell."}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T16:17:50Z","timestamp":1671725870000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1461551"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,20]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,12,31]]}},"alternative-id":["10.1137\/21M1461551"],"URL":"https:\/\/doi.org\/10.1137\/21m1461551","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,20]]}}}