{"id":"https://openalex.org/W2126250321","doi":"https://doi.org/10.1109/tsp.2011.2178601","title":"Geometric Methods for Spectral Analysis","display_name":"Geometric Methods for Spectral Analysis","publication_year":2011,"publication_date":"2011-12-09","ids":{"openalex":"https://openalex.org/W2126250321","doi":"https://doi.org/10.1109/tsp.2011.2178601","mag":"2126250321"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2178601","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2178601","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/84bae72a-67db-4129-bd0e-7732fdb48220/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110724473","display_name":"Xianhua Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xianhua Jiang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101766226","display_name":"Zhi\u2010Quan Luo","orcid":"https://orcid.org/0000-0003-3995-914X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhi-Quan Luo","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035194316","display_name":"Tryphon T. Georgiou","orcid":"https://orcid.org/0000-0003-0012-5447"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tryphon T. Georgiou","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.388,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.9265117,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"3","first_page":"1064","last_page":"1074"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9675999879837036,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9675999879837036,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11309","display_name":"Music and Audio Processing","score":0.9646000266075134,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9574000239372253,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.7525029182434082},{"id":"https://openalex.org/keywords/spectral-density","display_name":"Spectral density","score":0.6521103382110596},{"id":"https://openalex.org/keywords/morphing","display_name":"Morphing","score":0.6030102968215942},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5355315804481506},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5082990527153015},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"Spectral analysis","score":0.46216344833374023},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.45626354217529297},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.4436371326446533},{"id":"https://openalex.org/keywords/spectral-shape-analysis","display_name":"Spectral shape analysis","score":0.437019944190979},{"id":"https://openalex.org/keywords/spectral-density-estimation","display_name":"Spectral density estimation","score":0.43442851305007935},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.43039751052856445},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.4297037124633789},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.42462190985679626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42116397619247437},{"id":"https://openalex.org/keywords/spectral-envelope","display_name":"Spectral envelope","score":0.4102972447872162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36848825216293335},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35728389024734497},{"id":"https://openalex.org/keywords/spectral-line","display_name":"Spectral line","score":0.3372398018836975},{"id":"https://openalex.org/keywords/speech-recognition","display_name":"Speech recognition","score":0.2702704668045044},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2442607283592224},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.16129574179649353},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13815537095069885},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12891313433647156},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1285456418991089},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12065565586090088},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10559657216072083},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.08788749575614929}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7525029182434082},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.6521103382110596},{"id":"https://openalex.org/C50637493","wikidata":"https://www.wikidata.org/wiki/Q1136781","display_name":"Morphing","level":2,"score":0.6030102968215942},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5355315804481506},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5082990527153015},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.46216344833374023},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.45626354217529297},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.4436371326446533},{"id":"https://openalex.org/C152822103","wikidata":"https://www.wikidata.org/wiki/Q7575207","display_name":"Spectral shape analysis","level":3,"score":0.437019944190979},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.43442851305007935},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.43039751052856445},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.4297037124633789},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.42462190985679626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42116397619247437},{"id":"https://openalex.org/C54926389","wikidata":"https://www.wikidata.org/wiki/Q7575188","display_name":"Spectral envelope","level":2,"score":0.4102972447872162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36848825216293335},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35728389024734497},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.3372398018836975},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.2702704668045044},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2442607283592224},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.16129574179649353},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13815537095069885},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12891313433647156},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1285456418991089},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12065565586090088},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10559657216072083},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.08788749575614929},{"id":"https://openalex.org/C32891209","wikidata":"https://www.wikidata.org/wiki/Q483666","display_name":"Spectroscopy","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2011.2178601","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2178601","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/119341","is_oa":true,"landing_page_url":"http://purl.umn.edu/119341","pdf_url":"https://conservancy.umn.edu/bitstreams/84bae72a-67db-4129-bd0e-7732fdb48220/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis or Dissertation"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.261.4141","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.261.4141","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.umn.edu/%7Egeorgiou/papers/jiang_luo_georgiou.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.380.1922","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.380.1922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.umn.edu/~georgiou/papers/jiang_thesis.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/119341","is_oa":true,"landing_page_url":"http://purl.umn.edu/119341","pdf_url":"https://conservancy.umn.edu/bitstreams/84bae72a-67db-4129-bd0e-7732fdb48220/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis or Dissertation"},"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2126250321.pdf","grobid_xml":"https://content.openalex.org/works/W2126250321.grobid-xml"},"referenced_works_count":125,"referenced_works":["https://openalex.org/W85439921","https://openalex.org/W91382447","https://openalex.org/W107085514","https://openalex.org/W129305155","https://openalex.org/W158030646","https://openalex.org/W193385438","https://openalex.org/W210359992","https://openalex.org/W583356579","https://openalex.org/W585133165","https://openalex.org/W599494534","https://openalex.org/W641242542","https://openalex.org/W1483072194","https://openalex.org/W1485598997","https://openalex.org/W1488435683","https://openalex.org/W1489110551","https://openalex.org/W1494145268","https://openalex.org/W1495164570","https://openalex.org/W1496554474","https://openalex.org/W1506440477","https://openalex.org/W1515878031","https://openalex.org/W1520168181","https://openalex.org/W1560642549","https://openalex.org/W1561929708","https://openalex.org/W1574861711","https://openalex.org/W1583154192","https://openalex.org/W1585160083","https://openalex.org/W1590447358","https://openalex.org/W1598517949","https://openalex.org/W1652518220","https://openalex.org/W1685862830","https://openalex.org/W1740425075","https://openalex.org/W1947917047","https://openalex.org/W1963871118","https://openalex.org/W1964348979","https://openalex.org/W1968087916","https://openalex.org/W1968333723","https://openalex.org/W1974200742","https://openalex.org/W1978210787","https://openalex.org/W1979610031","https://openalex.org/W1979949628","https://openalex.org/W1986964250","https://openalex.org/W1990139510","https://openalex.org/W1992392421","https://openalex.org/W1996021349","https://openalex.org/W1996404462","https://openalex.org/W1997441999","https://openalex.org/W2001050163","https://openalex.org/W2004433847","https://openalex.org/W2005581725","https://openalex.org/W2007737215","https://openalex.org/W2020872171","https://openalex.org/W2020934227","https://openalex.org/W2021704127","https://openalex.org/W2024974438","https://openalex.org/W2031903553","https://openalex.org/W2031922654","https://openalex.org/W2032236594","https://openalex.org/W2043397919","https://openalex.org/W2045463928","https://openalex.org/W2048435560","https://openalex.org/W2048901266","https://openalex.org/W2052424080","https://openalex.org/W2052608203","https://openalex.org/W2062626385","https://openalex.org/W2070316439","https://openalex.org/W2070336476","https://openalex.org/W2087844534","https://openalex.org/W2088071204","https://openalex.org/W2089465567","https://openalex.org/W2091891040","https://openalex.org/W2098301339","https://openalex.org/W2099111195","https://openalex.org/W2099448014","https://openalex.org/W2099515730","https://openalex.org/W2101997269","https://openalex.org/W2102762459","https://openalex.org/W2106746318","https://openalex.org/W2106822551","https://openalex.org/W2109258005","https://openalex.org/W2113587986","https://openalex.org/W2115834725","https://openalex.org/W2121647670","https://openalex.org/W2123838014","https://openalex.org/W2125524200","https://openalex.org/W2126163471","https://openalex.org/W2129343891","https://openalex.org/W2130327601","https://openalex.org/W2132105090","https://openalex.org/W2133186968","https://openalex.org/W2137089646","https://openalex.org/W2138358404","https://openalex.org/W2140971281","https://openalex.org/W2144638120","https://openalex.org/W2145200953","https://openalex.org/W2151699927","https://openalex.org/W2151773880","https://openalex.org/W2155098255","https://openalex.org/W2159496808","https://openalex.org/W2159628417","https://openalex.org/W2160573809","https://openalex.org/W2164240509","https://openalex.org/W2166334548","https://openalex.org/W2166897825","https://openalex.org/W2168088676","https://openalex.org/W2169127870","https://openalex.org/W2172144506","https://openalex.org/W2188563164","https://openalex.org/W2296319761","https://openalex.org/W2498896499","https://openalex.org/W2610857016","https://openalex.org/W2773620921","https://openalex.org/W2794413559","https://openalex.org/W2799061466","https://openalex.org/W3043585151","https://openalex.org/W3104827932","https://openalex.org/W3127686677","https://openalex.org/W3129186208","https://openalex.org/W3150304496","https://openalex.org/W3151807103","https://openalex.org/W4241166324","https://openalex.org/W4249637202","https://openalex.org/W4250589301","https://openalex.org/W4256217162","https://openalex.org/W4285719527","https://openalex.org/W6683602070"],"related_works":["https://openalex.org/W4230751513","https://openalex.org/W4243908963","https://openalex.org/W2140014531","https://openalex.org/W2008537336","https://openalex.org/W2896210013","https://openalex.org/W2017942857","https://openalex.org/W2158216108","https://openalex.org/W2007390852","https://openalex.org/W2048672698","https://openalex.org/W1970766714"],"abstract_inverted_index":{"This":[0],"paper":[1],"explores":[2],"a":[3,35],"geometric":[4],"framework":[5,39,71],"for":[6],"modeling":[7],"nonstationary":[8],"but":[9],"slowly":[10],"varying":[11],"time":[12],"series,":[13],"based":[14],"on":[15,41],"the":[16,31,57,67],"assumption":[17],"that":[18,27],"short-windowed":[19],"power":[20,58],"spectra":[21],"capture":[22],"their":[23,48],"spectral":[24,59,75,77],"character,":[25],"and":[26,47,79],"energy":[28],"transference":[29],"in":[30,56,74],"frequency":[32],"domain":[33],"has":[34],"physical":[36],"significance.":[37],"The":[38],"relies":[40],"certain":[42],"notions":[43],"of":[44,69],"transportation":[45],"distance":[46],"respective":[49],"geodesics":[50],"to":[51,63,72],"model":[52],"possible":[53],"nonparametric":[54],"changes":[55],"density":[60],"with":[61],"respect":[62],"time.":[64],"We":[65],"discuss":[66],"relevance":[68],"this":[70],"applications":[73],"tracking,":[76],"averaging,":[78],"speech":[80],"morphing.":[81]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}