{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T04:13:47Z","timestamp":1744258427412,"version":"3.40.4"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-21-1-0266"],"award-info":[{"award-number":["FA9550-21-1-0266"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1916439"],"award-info":[{"award-number":["DMS-1916439"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1952339"],"award-info":[{"award-number":["DMS-1952339"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-2006661","DMS-1943758","DMS-2415445"],"award-info":[{"award-number":["CCF-2006661","DMS-1943758","DMS-2415445"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2103261"],"award-info":[{"award-number":["2103261"]}],"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":[[2025,6,30]]},"DOI":"10.1137\/23m1603443","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T08:01:40Z","timestamp":1744185700000},"page":"410-437","source":"Crossref","is-referenced-by-count":0,"title":["\\({O({k})}\\)-Equivariant Dimensionality Reduction on Stiefel Manifolds"],"prefix":"10.1137","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5943-5821","authenticated-orcid":true,"given":"Andrew","family":"Lee","sequence":"first","affiliation":[{"name":"School of STEM, St. Thomas Aquinas College, Sparkill, NY 10976 USA."}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6128-9942","authenticated-orcid":true,"given":"Harlin","family":"Lee","sequence":"additional","affiliation":[{"name":"School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 USA."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6440-5096","authenticated-orcid":true,"given":"Jose A.","family":"Perea","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115 USA."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6177-4865","authenticated-orcid":true,"given":"Nikolas","family":"Schonsheck","sequence":"additional","affiliation":[{"name":"Corresponding author. Center for Studies in Physics and Biology, The Rockefeller University, New York, NY 10065 USA."}]},{"given":"Madeleine","family":"Weinstein","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA 98416 USA."}]}],"member":"351","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"10340","DOI":"10.1038\/ncomms10340","volume":"7","author":"Atasoy S.","year":"2016","journal-title":"Nat. Commun."},{"key":"ref2","doi-asserted-by":"crossref","first-page":"3844","DOI":"10.1073\/pnas.92.9.3844","volume":"92","author":"Ben-Yishai R.","year":"1995","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.1017\/9781009166164","volume-title":"An Introduction to Optimization on Smooth Manifolds","author":"Boumal N.","year":"2023"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1038\/s41593-019-0460-x","volume":"22","author":"Chaudhuri R.","year":"2019","journal-title":"Nat. Neurosci."},{"key":"ref6","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/TMI.2020.3029063","volume":"40","author":"Chen J.","year":"2020","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref7","series-title":"Lecture Notes in Statist.","volume-title":"Statistics on Special Manifolds","author":"Chikuse Y.","year":"2012"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1038\/nature11129","volume":"487","author":"Churchland M. M.","year":"2012","journal-title":"Nature"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/s00454-011-9344-x","volume":"45","author":"de Silva V.","year":"2011","journal-title":"Discrete Comput. Geom."},{"key":"ref10","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1038\/11205","volume":"2","author":"Deneve S.","year":"1999","journal-title":"Nat. Neurosci."},{"key":"ref11","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1214\/19-AOAS1277","volume":"13","author":"Dryden I. L.","year":"2019","journal-title":"Ann. Appl. Stat."},{"key":"ref12","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1090\/S0002-9939-1955-0067841-7","volume":"6","author":"Fan K.","year":"1955","journal-title":"Proc. Amer. Math. Soc."},{"key":"ref14","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1109\/TMI.2004.831793","volume":"23","author":"Fletcher P. T.","year":"2004","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1109\/TPAMI.2007.70711","volume":"29","author":"Gorelick L.","year":"2007","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref16","series-title":"Grad. Texts in Math.","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2189-8","volume-title":"Algebraic Geometry: A First Course","author":"Harris J.","year":"1992"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TAFFC.2014.2330580","volume":"5","author":"Hayat M.","year":"2014","journal-title":"IEEE Trans. Affect. Comput."},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"ref20","volume-title":"Introduction to Statistical Learning with Applications in R","author":"James G.","year":"2013"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1093\/biomet\/ass022","volume":"99","author":"Jung S.","year":"2012","journal-title":"Biometrika"},{"key":"ref22","volume-title":"Directional Statistics","author":"Jupp P.","year":"2000"},{"key":"ref24","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2021.616748","volume":"15","author":"Kang L.","year":"2021","journal-title":"Front. Comput. Neurosci."},{"key":"ref25","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1126\/science.aal4835","volume":"356","author":"Kim S. S.","year":"2017","journal-title":"Science"},{"key":"ref26","series-title":"Grad. Texts in Math.","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9982-5","volume-title":"Introduction to Smooth Manifolds","author":"Lee J.","year":"2012"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1038\/nature12742","volume":"503","author":"Mante V.","year":"2013","journal-title":"Nature"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"490","DOI":"10.3390\/e23040490","volume":"23","author":"Mantoux C.","year":"2021","journal-title":"Entropy"},{"key":"ref29","volume-title":"Advances in Neural Information Processing Systems, Vol. 13","author":"Minka T.","year":"2000"},{"key":"ref30","first-page":"1","volume":"21","author":"Miolane N.","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref31","doi-asserted-by":"crossref","first-page":"e1005076","DOI":"10.1371\/journal.pcbi.1005076","volume":"12","author":"Muldoon S. F.","year":"2016","journal-title":"Plos Comput. Biol."},{"key":"ref32","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00454-017-9927-2","volume":"59","author":"Perea J. A.","year":"2018","journal-title":"Discrete Comput. Geom."},{"key":"ref33","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/978-3-030-43408-3_17","volume-title":"Topological Data Analysis","author":"Perea J. A.","year":"2020"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/978-3-031-13331-2_9","volume-title":"Coherence: In Signal Processing and Machine Learning","author":"Ram\u00edrez D.","year":"2022"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1162\/neco_a_01150","volume":"31","author":"Rybakken E.","year":"2019","journal-title":"Neural Comput."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/140957822"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s41468-023-00141-w","volume":"8","author":"Schonsheck N. C.","year":"2024","journal-title":"J. Appl. Comput. Topol."},{"key":"ref40","doi-asserted-by":"crossref","first-page":"e20","DOI":"10.1017\/fms.2023.16","volume":"11","author":"Scoccola L.","year":"2023","journal-title":"Forum Math. Sigma"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"10749","DOI":"10.1073\/pnas.90.22.10749","volume":"90","author":"Seung H. S.","year":"1993","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1038\/s41597-022-01596-9","volume":"9","author":"\u0160koch A.","year":"2022","journal-title":"Sci. Data"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12859-021-04195-4","volume":"22","author":"Tian J.","year":"2021","journal-title":"BMC Bioinform."},{"key":"ref45","first-page":"1","volume":"17","author":"Townsend J.","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"ref46","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1109\/TPAMI.2011.52","volume":"33","author":"Turaga P.","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref47","doi-asserted-by":"crossref","first-page":"e23496","DOI":"10.7554\/eLife.23496","volume":"6","author":"Turner-Evans D.","year":"2017","journal-title":"eLife"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.59275\/j.melba.2022-234f","volume":"1","author":"Yang C.-H.","year":"2022","journal-title":"Mach. Learn. Biomed. Imag."}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T08:01:50Z","timestamp":1744185710000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1603443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,9]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1137\/23M1603443"],"URL":"https:\/\/doi.org\/10.1137\/23m1603443","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,9]]}}}