{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T08:49:34Z","timestamp":1743151774447,"version":"3.40.3"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030269791"},{"type":"electronic","value":"9783030269807"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-26980-7_49","type":"book-chapter","created":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T23:03:04Z","timestamp":1566169384000},"page":"475-483","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Unified Formulation for the Bures-Wasserstein and Log-Euclidean\/Log-Hilbert-Schmidt Distances between Positive Definite Operators"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3926-8875","authenticated-orcid":false,"given":"H\u00e0 Quang","family":"Minh","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,2]]},"reference":[{"issue":"1","key":"49_CR1","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1137\/050637996","volume":"29","author":"V Arsigny","year":"2007","unstructured":"Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 29(1), 328\u2013347 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"49_CR2","doi-asserted-by":"crossref","unstructured":"Bhatia, R., Jain, T., Lim, Y.: On the Bures-Wasserstein distance between positive definite matrices. Expositiones Mathematicae (2018)","DOI":"10.1016\/j.exmath.2018.01.002"},{"issue":"3","key":"49_CR3","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1016\/0047-259X(82)90077-X","volume":"12","author":"D Dowson","year":"1982","unstructured":"Dowson, D., Landau, B.: The Fr\u00e9chet distance between multivariate normal distributions. J. Multivar. Anal. 12(3), 450\u2013455 (1982)","journal-title":"J. Multivar. Anal."},{"key":"49_CR4","doi-asserted-by":"publisher","first-page":"1102","DOI":"10.1214\/09-AOAS249","volume":"3","author":"I Dryden","year":"2009","unstructured":"Dryden, I., Koloydenko, A., Zhou, D.: Non-euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Ann. Appl. Stat. 3, 1102\u20131123 (2009)","journal-title":"Ann. Appl. Stat."},{"issue":"1","key":"49_CR5","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1002\/mana.19901470121","volume":"147","author":"M Gelbrich","year":"1990","unstructured":"Gelbrich, M.: On a formula for the L2 Wasserstein metric between measures on Euclidean and Hilbert spaces. Mathematische Nachrichten 147(1), 185\u2013203 (1990)","journal-title":"Mathematische Nachrichten"},{"issue":"2","key":"49_CR6","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1307\/mmj\/1029003026","volume":"31","author":"CR Givens","year":"1984","unstructured":"Givens, C.R., Shortt, R.M.: A class of Wasserstein metrics for probability distributions. Michigan Math. J. 31(2), 231\u2013240 (1984)","journal-title":"Michigan Math. J."},{"key":"49_CR7","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/j.difgeo.2007.06.016","volume":"25","author":"G Larotonda","year":"2007","unstructured":"Larotonda, G.: Nonpositive curvature: a geometrical approach to Hilbert-Schmidt operators. Differ. Geom. Appl. 25, 679\u2013700 (2007)","journal-title":"Differ. Geom. Appl."},{"issue":"2","key":"49_CR8","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s41884-018-0014-4","volume":"1","author":"L Malag\u00f2","year":"2018","unstructured":"Malag\u00f2, L., Montrucchio, L., Pistone, G.: Wasserstein Riemannian geometry of Gaussian densities. Inf. Geom. 1(2), 137\u2013179 (2018)","journal-title":"Inf. Geom."},{"key":"49_CR9","first-page":"1","volume":"80","author":"V Masarotto","year":"2018","unstructured":"Masarotto, V., Panaretos, V., Zemel, Y.: Procrustes metrics on covariance operators and optimal transportation of Gaussian processes. Sankhya A 80, 1\u201342 (2018)","journal-title":"Sankhya A"},{"key":"49_CR10","first-page":"388","volume":"27","author":"HQ Minh","year":"2014","unstructured":"Minh, H.Q., Biagio, M.S., Murino, V.: Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces. Adv. Neural Inf. Process. Syst. 27, 388\u2013396 (2014). (NIPS 2014)","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"49_CR11","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/j.laa.2016.09.018","volume":"528","author":"H Minh","year":"2017","unstructured":"Minh, H.: Infinite-dimensional log-determinant divergences between positive definite trace class operators. Linear Algebra Appl. 528, 331\u2013383 (2017)","journal-title":"Linear Algebra Appl."},{"key":"49_CR12","series-title":"Springer Proceedings in Mathematics & Statistics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-97798-0_8","volume-title":"Inf. Geom. Appl.","author":"H Minh","year":"2016","unstructured":"Minh, H.: Infinite-dimensional Log-Determinant divergences III: Log-Euclidean and Log-Hilbert\u2013Schmidt divergences. In: Ay, N., Gibilisco, P., Matus, F. (eds.) Inf. Geom. Appl. Springer Proceedings in Mathematics & Statistics, vol. 252. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-97798-0_8"},{"key":"49_CR13","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0024-3795(82)90112-4","volume":"48","author":"I Olkin","year":"1982","unstructured":"Olkin, I., Pukelsheim, F.: The distance between two random vectors with given dispersion matrices. Linear Algebra Appl. 48, 257\u2013263 (1982)","journal-title":"Linear Algebra Appl."},{"key":"49_CR14","volume-title":"Support Vector Machines","author":"I Steinwart","year":"2008","unstructured":"Steinwart, I., Christmann, A.: Support Vector Machines. Springer Science & Business Media, Berlin (2008)"},{"key":"49_CR15","volume-title":"Optimal Transport: Old and New","author":"C Villani","year":"2008","unstructured":"Villani, C.: Optimal Transport: Old and New, vol. 338. Springer Science & Business Media, Berlin (2008)"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-26980-7_49","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T18:05:31Z","timestamp":1710266731000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-26980-7_49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030269791","9783030269807"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-26980-7_49","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"2 August 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GSI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Geometric Science of Information","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Toulouse","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.see.asso.fr\/GSI2019","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}