{"id":"https://openalex.org/W2105004029","doi":"https://doi.org/10.5555/2567709.2627676","title":"Joint harmonic functions and their supervised connections","display_name":"Joint harmonic functions and their supervised connections","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2105004029","doi":"https://doi.org/10.5555/2567709.2627676","mag":"2105004029"},"language":"en","primary_location":{"id":"pmh:oai:researchrepository.wvu.edu:faculty_publications-1206","is_oa":true,"landing_page_url":"https://researchrepository.wvu.edu/faculty_publications/207","pdf_url":"https://researchrepository.wvu.edu/faculty_publications/207","source":{"id":"https://openalex.org/S4306402612","display_name":"The Research Repository @ WVU (West Virginia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12097938","host_organization_name":"West Virginia University","host_organization_lineage":["https://openalex.org/I12097938"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty & Staff Scholarship","raw_type":"text"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://researchrepository.wvu.edu/faculty_publications/207","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058272646","display_name":"Mark V. Culp","orcid":null},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark V. Culp","raw_affiliation_strings":["Department of Statistics, West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113769876","display_name":"Kenneth J. Ryan","orcid":null},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth J. Ryan","raw_affiliation_strings":["Department of Statistics, West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I12097938"],"apc_list":null,"apc_paid":null,"fwci":0.3025,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.65628382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"14","issue":"1","first_page":"3721","last_page":"3752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9757999777793884,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.973800003528595,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.7037234306335449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6742396354675293},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6048812866210938},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5002446174621582},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47220832109451294},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.451965868473053},{"id":"https://openalex.org/keywords/semi-supervised-learning","display_name":"Semi-supervised learning","score":0.42110657691955566},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42107611894607544},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4064772427082062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36812305450439453},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3651595115661621},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32347214221954346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29633641242980957},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1710171103477478},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.15579873323440552},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14960816502571106},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10776311159133911}],"concepts":[{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.7037234306335449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6742396354675293},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6048812866210938},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5002446174621582},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47220832109451294},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.451965868473053},{"id":"https://openalex.org/C58973888","wikidata":"https://www.wikidata.org/wiki/Q1041418","display_name":"Semi-supervised learning","level":2,"score":0.42110657691955566},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42107611894607544},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4064772427082062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36812305450439453},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3651595115661621},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32347214221954346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29633641242980957},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1710171103477478},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.15579873323440552},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14960816502571106},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10776311159133911}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:researchrepository.wvu.edu:faculty_publications-1206","is_oa":true,"landing_page_url":"https://researchrepository.wvu.edu/faculty_publications/207","pdf_url":"https://researchrepository.wvu.edu/faculty_publications/207","source":{"id":"https://openalex.org/S4306402612","display_name":"The Research Repository @ WVU (West Virginia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12097938","host_organization_name":"West Virginia University","host_organization_lineage":["https://openalex.org/I12097938"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty & Staff Scholarship","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.404.5312","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.404.5312","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.wvu.edu/~mculp/papers/culp13a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.646.859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.646.859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jmlr.org/papers/volume14/culp13a/culp13a.pdf","raw_type":"text"},{"id":"mag:2105004029","is_oa":false,"landing_page_url":"https://jmlr.csail.mit.edu/papers/volume14/culp13a/culp13a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Machine Learning Research","raw_type":null}],"best_oa_location":{"id":"pmh:oai:researchrepository.wvu.edu:faculty_publications-1206","is_oa":true,"landing_page_url":"https://researchrepository.wvu.edu/faculty_publications/207","pdf_url":"https://researchrepository.wvu.edu/faculty_publications/207","source":{"id":"https://openalex.org/S4306402612","display_name":"The Research Repository @ WVU (West Virginia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12097938","host_organization_name":"West Virginia University","host_organization_lineage":["https://openalex.org/I12097938"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty & Staff Scholarship","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2105004029.pdf","grobid_xml":"https://content.openalex.org/works/W2105004029.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W20856967","https://openalex.org/W1479807131","https://openalex.org/W1554944419","https://openalex.org/W1587427475","https://openalex.org/W1597032530","https://openalex.org/W1821811819","https://openalex.org/W1972222614","https://openalex.org/W1986534176","https://openalex.org/W1990334093","https://openalex.org/W2059177821","https://openalex.org/W2080642200","https://openalex.org/W2103829273","https://openalex.org/W2104290444","https://openalex.org/W2110316582","https://openalex.org/W2114718442","https://openalex.org/W2128817214","https://openalex.org/W2134767644","https://openalex.org/W2136504847","https://openalex.org/W2139823104","https://openalex.org/W2141923507","https://openalex.org/W2147874349","https://openalex.org/W2158522957","https://openalex.org/W2162630660","https://openalex.org/W2163097311","https://openalex.org/W2171710336","https://openalex.org/W2184987264","https://openalex.org/W2273771970","https://openalex.org/W2582743722","https://openalex.org/W3103799282","https://openalex.org/W3104087874","https://openalex.org/W3104527978","https://openalex.org/W3120740533","https://openalex.org/W3149749254","https://openalex.org/W3199143553"],"related_works":["https://openalex.org/W2982589847","https://openalex.org/W2255802415","https://openalex.org/W2554736449","https://openalex.org/W1857939483","https://openalex.org/W2996176234","https://openalex.org/W2012501405","https://openalex.org/W1979075812","https://openalex.org/W2087950056","https://openalex.org/W3133526222","https://openalex.org/W1659440667","https://openalex.org/W1675984130","https://openalex.org/W811226091","https://openalex.org/W2080604425","https://openalex.org/W2125986969","https://openalex.org/W2016408945","https://openalex.org/W1755468095","https://openalex.org/W2126356189","https://openalex.org/W2793894732","https://openalex.org/W2614634292","https://openalex.org/W2274595687"],"abstract_inverted_index":{"The":[0,17],"cluster":[1,117],"assumption":[2,40,83],"had":[3],"a":[4,103,120,145,194],"significant":[5],"impact":[6],"on":[7,123,157],"the":[8,36,54,100,116,124,127,142,153,167,176,181,184,191],"reasoning":[9],"behind":[10],"semi-supervised":[11,73],"classi-fication":[12],"methods":[13],"in":[14,97,113],"graph-based":[15],"learning.":[16],"literature":[18],"includes":[19],"numerous":[20],"applications":[21],"where":[22,152],"harmonic":[23,42,74,104,128,138,171],"functions":[24,43],"provided":[25],"estimates":[26,160],"that":[27,136,166],"conformed":[28],"to":[29,64,108,111],"data":[30,112],"satisfying":[31],"this":[32,39,77],"well-known":[33],"assump-tion,":[34],"but":[35],"relationship":[37],"between":[38],"and":[41,60],"is":[44,84,106,130,134,144,155,173,178,186],"not":[45],"as":[46],"well-understood":[47],"theoretically.":[48],"We":[49,164],"investigate":[50],"these":[51],"matters":[52],"from":[53],"perspective":[55],"of":[56,99,126,149,183],"supervised":[57,95,150,158],"kernel":[58,159],"classification":[59],"provide":[61],"concrete":[62],"answers":[63],"two":[65],"fundamental":[66],"questions.":[67],"(i)":[68],"Under":[69],"what":[70],"conditions":[71],"do":[72],"approaches":[75],"satisfy":[76],"assumption?":[78],"(ii)":[79],"If":[80],"such":[81],"an":[82,90],"satisfied":[85],"then":[86],"why":[87],"precisely":[88],"would":[89],"observation":[91],"sacrifice":[92],"its":[93],"own":[94],"estimate":[96,140],"favor":[98],"cluster?":[101],"First,":[102],"function":[105,129,139],"guaranteed":[107],"assign":[109],"labels":[110],"harmony":[114],"with":[115],"as-sumption":[118],"if":[119],"specific":[121],"condition":[122],"boundary":[125,185],"satisfied.":[131],"Second,":[132],"it":[133],"shown":[135],"any":[137],"within":[141],"interior":[143],"probability":[146],"weighted":[147],"average":[148],"estimates,":[151],"weight":[154],"focused":[156],"near":[161],"labeled":[162],"cases.":[163],"demonstrate":[165],"uniqueness":[168],"criterion":[169],"for":[170,193],"estimators":[172],"sensitive":[174],"when":[175],"graph":[177],"sparse":[179],"or":[180],"size":[182],"relatively":[187],"small.":[188],"This":[189],"sets":[190],"stage":[192],"third":[195],"con-":[196]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}