{"id":"https://openalex.org/W2973571117","doi":"https://doi.org/10.48550/arxiv.1909.10221","title":"PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds","display_name":"PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds","publication_year":2019,"publication_date":"2019-09-23","ids":{"openalex":"https://openalex.org/W2973571117","doi":"https://doi.org/10.48550/arxiv.1909.10221","mag":"2973571117"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1909.10221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10221","pdf_url":"https://arxiv.org/pdf/1909.10221","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.10221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044004993","display_name":"Oliver M. Crook","orcid":"https://orcid.org/0000-0001-5669-8506","observed_orcids":["https://orcid.org/0000-0001-5669-8506"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210134973","display_name":"MRC Biostatistics Unit","ror":"https://ror.org/046vje122","country_code":"GB","type":"facility","lineage":["https://openalex.org/I241749","https://openalex.org/I4210087105","https://openalex.org/I4210134973","https://openalex.org/I90344618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Crook, Oliver M.","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK","MRC Biostatistics Unit , School of Clinical Medicine , University of Cambridge , Cambridge CB2 0SR , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"MRC Biostatistics Unit , School of Clinical Medicine , University of Cambridge , Cambridge CB2 0SR , UK","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210134973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033879981","display_name":"Tim Hurst","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hurst, Tim","raw_affiliation_strings":["School of Mathematics and the"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and the","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033880300","display_name":"Carola\u2010Bibiane Sch\u00f6nlieb","orcid":"https://orcid.org/0000-0003-0099-6306","observed_orcids":["https://orcid.org/0000-0003-0099-6306"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sch\u00f6nlieb, Carola-Bibiane","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021002385","display_name":"Matthew Thorpe","orcid":"https://orcid.org/0000-0003-2480-5404","observed_orcids":["https://orcid.org/0000-0003-2480-5404"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thorpe, Matthew","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK","Maxwell Institute for Mathematical Sciences , University of Edinburgh , Edinburgh , EH9 3FD , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics , University of Cambridge , Cambridge , CB3 0WA , UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences , University of Edinburgh , Edinburgh , EH9 3FD , UK","institution_ids":["https://openalex.org/I4210117017","https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068361059","display_name":"Konstantinos C. Zygalakis","orcid":"https://orcid.org/0000-0002-3860-9167","observed_orcids":["https://orcid.org/0000-0002-3860-9167"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zygalakis, Konstantinos C.","raw_affiliation_strings":["School of Mathematics and the"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and the","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.8363999724388123,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.8363999724388123,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.037700001150369644,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.020099999383091927,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semi-supervised-learning","display_name":"semi-supervised learning","score":0.9860000014305115},{"id":"https://openalex.org/keywords/point-clouds","display_name":"point clouds","score":0.9959999918937683},{"id":"https://openalex.org/keywords/label-propagation","display_name":"label propagation","score":0.5009999871253967},{"id":"https://openalex.org/keywords/euler-lagrange-equations","display_name":"Euler-Lagrange equations","score":0.8460000157356262},{"id":"https://openalex.org/keywords/pseudospectral-method","display_name":"pseudospectral method","score":0.8849999904632568},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"kernel density estimation","score":0.8730000257492065},{"id":"https://openalex.org/keywords/consistency","display_name":"consistency","score":0.5809999704360962},{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.4169999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.594601571559906},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.5441707968711853},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.540642261505127},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5398160815238953},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.5100863575935364},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.49899935722351074},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4849812984466553},{"id":"https://openalex.org/C84894716","wikidata":"https://www.wikidata.org/wiki/Q6935135","display_name":"Multivariate kernel density estimation","level":5,"score":0.48067507147789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46268120408058167},{"id":"https://openalex.org/C131979681","wikidata":"https://www.wikidata.org/wiki/Q1899648","display_name":"Point cloud","level":2,"score":0.44716960191726685},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4468819797039032},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.42497518658638},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.41456204652786255},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41077935695648193},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38705843687057495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3581833839416504},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3103734254837036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27724725008010864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17116117477416992},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12997299432754517},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.11241170763969421},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09904855489730835},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08156934380531311},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1909.10221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10221","pdf_url":"https://arxiv.org/pdf/1909.10221","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2973571117","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1909.10221v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1909.10221","doi":"https://doi.org/10.48550/arxiv.1909.10221","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.10221","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.10221","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10221","pdf_url":"https://arxiv.org/pdf/1909.10221","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.7400000095367432,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G1309768829","display_name":null,"funder_award_id":"EP/N510129/1.","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G1633672591","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1755984640","display_name":null,"funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2164220759","display_name":null,"funder_award_id":"EP/L016508","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2500306150","display_name":null,"funder_award_id":"EP/L016508/01","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2763947431","display_name":"Nonlocal Methods for Arbitrary Data Sources","funder_award_id":"777826","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3855435662","display_name":null,"funder_award_id":"N510129","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G444630160","display_name":null,"funder_award_id":"EP/N510129/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4500485203","display_name":"The Alan Turing Institute","funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4897358205","display_name":"CHallenges in Preservation of Structure","funder_award_id":"691070","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5639283639","display_name":null,"funder_award_id":"777826","funder_id":"https://openalex.org/F4320313467","funder_display_name":"Alan Turing Institute"},{"id":"https://openalex.org/G5855033780","display_name":"Efficient computational tools for inverse imaging problems","funder_award_id":"EP/M00483X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6579398875","display_name":"EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging","funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7393500401","display_name":null,"funder_award_id":"EP/M00483X/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G8597009950","display_name":null,"funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311518","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93"},{"id":"https://openalex.org/F4320311904","display_name":"Wellcome Trust","ror":"https://ror.org/029chgv08"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320064","display_name":"Scottish Funding Council","ror":"https://ror.org/056bwcz71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332377","display_name":"Goddard Space Flight Center","ror":"https://ror.org/0171mag52"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":75,"referenced_works":["https://openalex.org/W585462275","https://openalex.org/W656727543","https://openalex.org/W1486280163","https://openalex.org/W1490180844","https://openalex.org/W1493594095","https://openalex.org/W1509923322","https://openalex.org/W1511694993","https://openalex.org/W1522301498","https://openalex.org/W1563644419","https://openalex.org/W1644838376","https://openalex.org/W1861295442","https://openalex.org/W1892681330","https://openalex.org/W1964911840","https://openalex.org/W1967320885","https://openalex.org/W1984032850","https://openalex.org/W1985490703","https://openalex.org/W1987371472","https://openalex.org/W1987413591","https://openalex.org/W1990053952","https://openalex.org/W1993099049","https://openalex.org/W2002276939","https://openalex.org/W2002355073","https://openalex.org/W2003767009","https://openalex.org/W2014268383","https://openalex.org/W2032369139","https://openalex.org/W2032433149","https://openalex.org/W2033663831","https://openalex.org/W2036354922","https://openalex.org/W2036986658","https://openalex.org/W2044113963","https://openalex.org/W2049475467","https://openalex.org/W2052309176","https://openalex.org/W2056735347","https://openalex.org/W2059122256","https://openalex.org/W2062721328","https://openalex.org/W2067848592","https://openalex.org/W2081540648","https://openalex.org/W2091178361","https://openalex.org/W2096633276","https://openalex.org/W2103829273","https://openalex.org/W2113240972","https://openalex.org/W2118020555","https://openalex.org/W2119753634","https://openalex.org/W2139823104","https://openalex.org/W2140819685","https://openalex.org/W2146766088","https://openalex.org/W2147874349","https://openalex.org/W2153132823","https://openalex.org/W2160267226","https://openalex.org/W2161690964","https://openalex.org/W2163581538","https://openalex.org/W2265158691","https://openalex.org/W2288664612","https://openalex.org/W2424347292","https://openalex.org/W2504943536","https://openalex.org/W2528062157","https://openalex.org/W2577840663","https://openalex.org/W2604062177","https://openalex.org/W2738326163","https://openalex.org/W2741081039","https://openalex.org/W2766748337","https://openalex.org/W2785523195","https://openalex.org/W2799116291","https://openalex.org/W2811294015","https://openalex.org/W2899203342","https://openalex.org/W2904863873","https://openalex.org/W2910589780","https://openalex.org/W2952521183","https://openalex.org/W2962701197","https://openalex.org/W2962826709","https://openalex.org/W2963629791","https://openalex.org/W2963954124","https://openalex.org/W2976645955","https://openalex.org/W3106413396","https://openalex.org/W3139701703"],"related_works":["https://openalex.org/W1558746853","https://openalex.org/W2096032893","https://openalex.org/W2613940844","https://openalex.org/W1797580194","https://openalex.org/W2494096577","https://openalex.org/W158260078","https://openalex.org/W2183304268","https://openalex.org/W1987772649","https://openalex.org/W3037347970","https://openalex.org/W2883520207","https://openalex.org/W2936582852","https://openalex.org/W2170744156","https://openalex.org/W2231104643","https://openalex.org/W2898080674","https://openalex.org/W2934434822","https://openalex.org/W2884339463","https://openalex.org/W2188295559","https://openalex.org/W2528532538","https://openalex.org/W2964331576","https://openalex.org/W2962737219"],"abstract_inverted_index":{"Given":[0],"a":[1,5,59],"data":[2,25,53,85,111],"set":[3],"and":[4,86,122],"subset":[6],"of":[7,11,58,71,83,116],"labels":[8,21,33],"the":[9,20,23,32,36,44,51,56,65,81,84,97,109],"problem":[10,46],"semi-supervised":[12],"learning":[13],"on":[14],"point":[15],"clouds":[16],"is":[17,106],"to":[18,22,95],"extend":[19,31],"entire":[24],"set.":[26],"In":[27],"this":[28,72],"paper":[29],"we":[30],"by":[34,74],"minimising":[35],"constrained":[37],"discrete":[38,45],"$p$-Dirichlet":[39,62],"energy.":[40],"Under":[41],"suitable":[42],"conditions":[43],"can":[47],"be":[48],"connected,":[49],"in":[50,108],"large":[52,110],"limit,":[54],"with":[55,64],"minimiser":[57],"weighted":[60],"continuum":[61],"energy":[63],"same":[66],"constraints.":[67],"We":[68,101],"take":[69],"advantage":[70],"connection":[73],"designing":[75],"numerical":[76],"schemes":[77],"that":[78,103],"first":[79],"estimate":[80],"density":[82,117,120,125],"then":[87],"apply":[88],"PDE":[89],"methods,":[90,94],"such":[91],"as":[92],"pseudo-spectral":[93],"solve":[96],"corresponding":[98],"Euler-Lagrange":[99],"equation.":[100],"prove":[102],"our":[104],"scheme":[105],"consistent":[107],"limit":[112],"for":[113],"two":[114],"methods":[115],"estimation:":[118],"kernel":[119,124],"estimation":[121],"spline":[123],"estimation.":[126]},"counts_by_year":[],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2025-10-10T00:00:00"}
