{"id":"https://openalex.org/W2790122812","doi":"https://doi.org/10.3390/e20040219","title":"Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold","display_name":"Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold","publication_year":2018,"publication_date":"2018-03-23","ids":{"openalex":"https://openalex.org/W2790122812","doi":"https://doi.org/10.3390/e20040219","mag":"2790122812","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265310"},"language":"en","primary_location":{"id":"doi:10.3390/e20040219","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20040219","pdf_url":"https://www.mdpi.com/1099-4300/20/4/219/pdf?version=1521824431","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/4/219/pdf?version=1521824431","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058024618","display_name":"Xiaoqiang Hua","orcid":"https://orcid.org/0000-0001-7687-7720"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoqiang Hua","raw_affiliation_strings":["School of Electronic Science, National University of Defence Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science, National University of Defence Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009604459","display_name":"Yongqiang Cheng","orcid":"https://orcid.org/0000-0002-0127-384X"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongqiang Cheng","raw_affiliation_strings":["School of Electronic Science, National University of Defence Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science, National University of Defence Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100757637","display_name":"Hongqiang Wang","orcid":"https://orcid.org/0000-0002-2522-9552"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongqiang Wang","raw_affiliation_strings":["School of Electronic Science, National University of Defence Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science, National University of Defence Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064708750","display_name":"Yuliang Qin","orcid":"https://orcid.org/0000-0003-0450-1294"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuliang Qin","raw_affiliation_strings":["School of Electronic Science, National University of Defence Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic Science, National University of Defence Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009604459","https://openalex.org/A5058024618"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.2,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90377513,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"20","issue":"4","first_page":"219","last_page":"219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9817000031471252,"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/estimator","display_name":"Estimator","score":0.8288601040840149},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7276468873023987},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.666726291179657},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6507313251495361},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.6195142269134521},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5784221291542053},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5728898644447327},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5161179304122925},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.4930369555950165},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.466432124376297},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.43162280321121216},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4306972622871399},{"id":"https://openalex.org/keywords/m-estimator","display_name":"M-estimator","score":0.4249427914619446},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3869609236717224},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2857743501663208},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20349827408790588},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12300720810890198},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.06886070966720581}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8288601040840149},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7276468873023987},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.666726291179657},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6507313251495361},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.6195142269134521},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5784221291542053},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5728898644447327},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5161179304122925},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.4930369555950165},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.466432124376297},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.43162280321121216},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4306972622871399},{"id":"https://openalex.org/C143791395","wikidata":"https://www.wikidata.org/wiki/Q475208","display_name":"M-estimator","level":3,"score":0.4249427914619446},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3869609236717224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2857743501663208},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20349827408790588},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12300720810890198},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.06886070966720581},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e20040219","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20040219","pdf_url":"https://www.mdpi.com/1099-4300/20/4/219/pdf?version=1521824431","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33265310","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265310","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:c9c8030879fb4d7da9dcae24b4c837f6","is_oa":true,"landing_page_url":"https://doaj.org/article/c9c8030879fb4d7da9dcae24b4c837f6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 20, Iss 4, p 219 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/4/219/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e20040219","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 20; Issue 4; Pages: 219","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7512735","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512735","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e20040219","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20040219","pdf_url":"https://www.mdpi.com/1099-4300/20/4/219/pdf?version=1521824431","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5096327359","display_name":null,"funder_award_id":"61302149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2790122812.pdf","grobid_xml":"https://content.openalex.org/works/W2790122812.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W4633159","https://openalex.org/W21527348","https://openalex.org/W1580302050","https://openalex.org/W1966320258","https://openalex.org/W1969481231","https://openalex.org/W1994675040","https://openalex.org/W2016538497","https://openalex.org/W2029258199","https://openalex.org/W2031513817","https://openalex.org/W2032236594","https://openalex.org/W2048192550","https://openalex.org/W2055144697","https://openalex.org/W2056716515","https://openalex.org/W2058148606","https://openalex.org/W2075708426","https://openalex.org/W2093064776","https://openalex.org/W2094929092","https://openalex.org/W2108400150","https://openalex.org/W2112162777","https://openalex.org/W2117901044","https://openalex.org/W2130416410","https://openalex.org/W2130573040","https://openalex.org/W2132424427","https://openalex.org/W2143665486","https://openalex.org/W2144833976","https://openalex.org/W2146152062","https://openalex.org/W2149652297","https://openalex.org/W2155969596","https://openalex.org/W2158225132","https://openalex.org/W2163519699","https://openalex.org/W2185737874","https://openalex.org/W2326234545","https://openalex.org/W2486450301","https://openalex.org/W2530061797","https://openalex.org/W2596126413","https://openalex.org/W2731028425","https://openalex.org/W2743611611","https://openalex.org/W2768748907","https://openalex.org/W2963532276","https://openalex.org/W3098748513","https://openalex.org/W3123191024","https://openalex.org/W6665067014","https://openalex.org/W6682936927","https://openalex.org/W6689089946","https://openalex.org/W6785424840"],"related_works":["https://openalex.org/W2546668543","https://openalex.org/W1975282624","https://openalex.org/W2059474323","https://openalex.org/W1532125927","https://openalex.org/W2950501992","https://openalex.org/W4297986345","https://openalex.org/W2391047418","https://openalex.org/W2999284236","https://openalex.org/W2164995684","https://openalex.org/W2152957748"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3],"class":[4],"of":[5,19,28,52,56,62,66,77,93],"covariance":[6,20],"estimators":[7,79,102],"based":[8],"on":[9,24],"information":[10,37],"divergences":[11,38],"in":[12,71],"heterogeneous":[13],"environments.":[14],"In":[15],"particular,":[16],"the":[17,25,44,49,53,57,60,63,75,83,89,105],"problem":[18],"estimation":[21],"is":[22,69,80],"reformulated":[23],"Riemannian":[26,64],"manifold":[27,65],"Hermitian":[29],"positive-definite":[30],"(HPD)":[31],"matrices.":[32],"The":[33],"means":[34],"associated":[35],"with":[36,99,104],"are":[39],"derived":[40],"and":[41,91],"used":[42],"as":[43],"estimators.":[45,73],"Without":[46],"resorting":[47],"to":[48],"complete":[50],"knowledge":[51],"probability":[54],"distribution":[55],"sample":[58],"data,":[59],"geometry":[61],"HPD":[67],"matrices":[68],"considered":[70],"mean":[72,78],"Moreover,":[74],"robustness":[76,90],"analyzed":[81],"using":[82],"influence":[84],"function.":[85],"Simulation":[86],"results":[87],"indicate":[88],"superiority":[92],"an":[94],"adaptive":[95],"normalized":[96],"matched":[97],"filter":[98],"our":[100],"proposed":[101],"compared":[103],"existing":[106],"alternatives.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}