{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T21:16:11Z","timestamp":1779311771443,"version":"3.51.4"},"reference-count":86,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1109\/tit.2022.3231645","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T18:39:47Z","timestamp":1671734387000},"page":"3150-3171","source":"Crossref","is-referenced-by-count":10,"title":["On <i>f<\/i>-Divergences Between Cauchy Distributions"],"prefix":"10.1109","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5728-0726","authenticated-orcid":false,"given":"Frank","family":"Nielsen","sequence":"first","affiliation":[{"name":"Sony Computer Science Laboratories, Inc., Tokyo, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4467-4165","authenticated-orcid":false,"given":"Kazuki","family":"Okamura","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Shizuoka University, Shizuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT50566.2022.9834769"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1007\/BF02517812"},{"key":"ref12","first-page":"1","article-title":"Visualizing data using t-SNE","volume":"9","author":"van der maaten","year":"2008","journal-title":"J Mach Learn Res"},{"key":"ref56","first-page":"415","article-title":"On powers of f-divergences defining a distance","volume":"26","author":"kafka","year":"1991","journal-title":"Studia Sci Math Hungar"},{"key":"ref15","first-page":"1","volume":"1","author":"tsallis","year":"2009","journal-title":"Introduction to Nonextensive Statistical Mechanics Approaching a Complex World"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2004.1365067"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.3390\/e22070713"},{"key":"ref58","first-page":"885","article-title":"On metric divergences of probability measures","volume":"45","author":"vajda","year":"2009","journal-title":"Kybernetika"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1063\/1.4822863"},{"key":"ref52","article-title":"On power Chi expansions of f-divergences","author":"nielsen","year":"2019","journal-title":"arXiv 1903 05818"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1984.1056920"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.11650\/twjm\/1500405733"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2771209"},{"key":"ref54","first-page":"85","article-title":"On symmetric information divergence measures of Csiszar&#x2019;s f-divergence class","volume":"3","author":"jain","year":"2007","journal-title":"Journal of Applied Mathematics Statistics and Informatics"},{"key":"ref17","first-page":"229","article-title":"Information-type measures of difference of probability distributions and indirect observation","volume":"2","author":"csisz\u00e1r","year":"1967","journal-title":"Studia Scientiarum Mathematicarum Hungarica"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1966.tb00626.x"},{"key":"ref19","author":"cover","year":"2012","journal-title":"Elements of Information Theory"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1561\/9781933019543"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-13-6678-9"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(72)90038-3"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.3390\/e22101100"},{"key":"ref45","author":"needham","year":"1998","journal-title":"Visual Complex Analysis"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-021-00818-y"},{"key":"ref47","article-title":"On information projections between multivariate elliptical and location-scale families","author":"nielsen","year":"2021","journal-title":"arXiv 2101 03839"},{"key":"ref42","volume":"494","author":"mardia","year":"2009","journal-title":"Directional Statistics"},{"key":"ref86","doi-asserted-by":"publisher","DOI":"10.3390\/e22030346"},{"key":"ref41","author":"marshall","year":"2007","journal-title":"Life distributions Structure of nonparametric semiparametric and parametric families"},{"key":"ref85","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-012-0467-9"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1007\/BF01832962"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2010.2047340"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-04972-4"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2132590"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/18.165447"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2014.6875400"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1515\/9783110293586.97"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-355-8"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1972.1054787"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/978-3-319-31611-6_3","article-title":"Special continuous probability distributions","author":"\u0161irca","year":"2016","journal-title":"Probability for Physicists"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1137\/0523025"},{"key":"ref81","volume":"58","author":"barndorff-nielsen","year":"2012","journal-title":"Decomposition and Invariance of Measures and Statistical Transformation Models"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1080\/02664768800000029"},{"key":"ref84","first-page":"185","article-title":"A truncated bivariate Cauchy distribution","volume":"30","author":"nadarajah","year":"2007","journal-title":"Bull Malaysian Math Sci Society 2nd Ser"},{"key":"ref83","first-page":"122","article-title":"A truncated t distribution","volume":"29","author":"nadarajah","year":"2004","journal-title":"Math Scientist"},{"key":"ref80","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-010-9256-1"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0038202"},{"key":"ref79","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1032894465"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.3018661"},{"key":"ref78","volume":"171","author":"petersen","year":"2006","journal-title":"Riemannian Geometry"},{"key":"ref37","first-page":"99","article-title":"On a measure of divergence between two statistical populations defined by their probability distributions","volume":"35","author":"bhattacharyya","year":"1943","journal-title":"Bull Calcutta Math Soc"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2013.2243726"},{"key":"ref31","first-page":"475","article-title":"On the distribution of the Cauchy maximum-likelihood estimator","volume":"440","author":"mccullagh","year":"1993","journal-title":"Proc Roy Soc London A Math Phys Sci"},{"key":"ref75","first-page":"1396a","article-title":"Fonctions sph&#x00E9;riques de type positif sur les espaces hyperboliques","volume":"274","author":"faraut","year":"1972","journal-title":"C R Acad Sci"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3071489"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1598"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1214\/cbms\/1462061029"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1128-0"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1976-0394803-6"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(70)90037-X"},{"key":"ref2","volume":"908","author":"kass","year":"2011","journal-title":"Geometrical Foundations of Asymptotic Inference"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/79.2.247"},{"key":"ref39","author":"pewsey","year":"2013","journal-title":"Circular Statistics in R"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.3150\/11-BEJ397"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.2307\/1989894"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.32917\/hmj\/1206128508"},{"key":"ref73","author":"gradshteyn","year":"2015","journal-title":"Table of Integrals Series and Products"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.5802\/aif.525"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2013.2288355"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1137\/0516080"},{"key":"ref23","article-title":"A closed-form formula for the Kullback&#x2013;Leibler divergence between Cauchy distributions","author":"chyzak","year":"2019","journal-title":"arXiv 1905 10965"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2159046"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2603151"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.3390\/e21050485"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346246"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55978-8"},{"key":"ref64","first-page":"147","article-title":"Using the triangle inequality to accelerate k-means","author":"elkan","year":"2003","journal-title":"Proc 20th Int Conf Mach Learn (ICML)"},{"key":"ref63","first-page":"311","article-title":"Data structures and algorithms for nearest neighbor","volume":"66","author":"yianilos","year":"1993","journal-title":"Proc 9th Annual ACM-SIAM Symp on Discrete Algorithms"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-80209-7_86"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1436"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.881731"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.924656"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0237477-8"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2904508"},{"key":"ref29","volume":"1","author":"bronstein","year":"2005","journal-title":"Symbolic Integration I Transcendental Functions"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972832.53"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1982.1056489"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03427-9"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/10106509\/09997561.pdf?arnumber=9997561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,8]],"date-time":"2023-05-08T18:42:06Z","timestamp":1683571326000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9997561\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":86,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tit.2022.3231645","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5]]}}}