{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:14:10Z","timestamp":1743005650360,"version":"3.40.3"},"publisher-location":"Cham","reference-count":11,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319684444"},{"type":"electronic","value":"9783319684451"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-68445-1_10","type":"book-chapter","created":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T20:40:36Z","timestamp":1508791236000},"page":"83-90","source":"Crossref","is-referenced-by-count":3,"title":["Regularized Barycenters in the Wasserstein Space"],"prefix":"10.1007","author":[{"given":"Elsa","family":"Cazelles","sequence":"first","affiliation":[]},{"given":"J\u00e9r\u00e9mie","family":"Bigot","sequence":"additional","affiliation":[]},{"given":"Nicolas","family":"Papadakis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"issue":"2","key":"10_CR1","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1137\/100805741","volume":"43","author":"M Agueh","year":"2011","unstructured":"Agueh, M., Carlier, G.: Barycenters in the Wasserstein space. SIAM J. Math. Anal. 43(2), 904\u2013924 (2011)","journal-title":"SIAM J. Math. Anal."},{"key":"10_CR2","unstructured":"Bigot, J., Cazelles, E., Papadakis, N.: Penalized barycenters in the Wasserstein space. Submitted. \nhttps:\/\/128.84.21.199\/abs\/1606.01025"},{"key":"10_CR3","unstructured":"Bobkov, S., Ledoux, M.: One-dimensional empirical measures, order statistics and Kantorovich transport distances (2014). Book in preparation. \nhttp:\/\/perso.math.univ-toulouse.fr\/ledoux\/files\/2013\/11\/Order.statistics.10.pdf"},{"issue":"5","key":"10_CR4","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1088\/0266-5611\/20\/5\/005","volume":"20","author":"M Burger","year":"2004","unstructured":"Burger, M., Osher, S.: Convergence rates of convex variational regularization. Inverse Prob. 20(5), 1411 (2004)","journal-title":"Inverse Prob."},{"issue":"1","key":"10_CR5","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1137\/15M1032600","volume":"9","author":"M Cuturi","year":"2016","unstructured":"Cuturi, M., Peyr\u00e9, G.: A smoothed dual approach for variational Wasserstein problems. SIAM J. Imaging Sci. 9(1), 320\u2013343 (2016)","journal-title":"SIAM J. Imaging Sci."},{"key":"10_CR6","first-page":"235","volume":"10","author":"M Fr\u00e9chet","year":"1948","unstructured":"Fr\u00e9chet, M.: Les \u00e9l\u00e9ments al\u00e9atoires de nature quelconque dans un espace distanci\u00e9. Ann. Inst. H. Poincar\u00e9 Sect. B Prob. Stat. 10, 235\u2013310 (1948)","journal-title":"Ann. Inst. H. Poincar\u00e9 Sect. B Prob. Stat."},{"issue":"454","key":"10_CR7","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1198\/016214501753168235","volume":"96","author":"A Kneip","year":"2001","unstructured":"Kneip, A., Utikal, K.J.: Inference for density families using functional principal component analysis. J. Am. Stat. Assoc. 96(454), 519\u2013542 (2001). With comments and a rejoinder by the authors","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10_CR8","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1214\/15-AOS1387","volume":"44","author":"VM Panaretos","year":"2016","unstructured":"Panaretos, V.M., Zemel, Y.: Amplitude and phase variation of point processes. Ann. Stat. 44(2), 771\u2013812 (2016)","journal-title":"Ann. Stat."},{"issue":"1","key":"10_CR9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1214\/15-AOS1363","volume":"44","author":"A Petersen","year":"2016","unstructured":"Petersen, A., M\u00fcller, H.G.: Functional data analysis for density functions by transformation to a Hilbert space. Ann. Stat. 44(1), 183\u2013218 (2016)","journal-title":"Ann. Stat."},{"issue":"3","key":"10_CR10","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/s10827-011-0336-x","volume":"31","author":"W Wu","year":"2011","unstructured":"Wu, W., Srivastava, A.: An information-geometric framework for statistical inferences in the neural spike train space. J. Comput. Neurosci. 31(3), 725\u2013748 (2011)","journal-title":"J. Comput. Neurosci."},{"issue":"7","key":"10_CR11","doi-asserted-by":"crossref","first-page":"2234","DOI":"10.1016\/j.csda.2011.01.007","volume":"55","author":"Z Zhang","year":"2011","unstructured":"Zhang, Z., M\u00fcller, H.-G.: Functional density synchronization. Comput. Stat. Data Anal. 55(7), 2234\u20132249 (2011)","journal-title":"Comput. Stat. Data Anal."}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68445-1_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T19:20:39Z","timestamp":1508872839000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68445-1_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319684444","9783319684451"],"references-count":11,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68445-1_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}