{"id":"https://openalex.org/W4282945825","doi":"https://doi.org/10.3390/a15060209","title":"Maximum Entropy Approach to Massive Graph Spectrum Learning with Applications","display_name":"Maximum Entropy Approach to Massive Graph Spectrum Learning with Applications","publication_year":2022,"publication_date":"2022-06-15","ids":{"openalex":"https://openalex.org/W4282945825","doi":"https://doi.org/10.3390/a15060209"},"language":"en","primary_location":{"id":"doi:10.3390/a15060209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15060209","pdf_url":"https://www.mdpi.com/1999-4893/15/6/209/pdf?version=1655266577","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/6/209/pdf?version=1655266577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038607215","display_name":"Diego Granziol","orcid":"https://orcid.org/0000-0003-3169-2081"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Diego Granziol","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033650444","display_name":"Binxin Ru","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Binxin Ru","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101579932","display_name":"Xiaowen Dong","orcid":"https://orcid.org/0000-0002-1143-9786"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xiaowen Dong","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090331439","display_name":"Stefan Zohren","orcid":"https://orcid.org/0000-0002-3392-0394"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stefan Zohren","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002007044","display_name":"Michael A. Osborne","orcid":"https://orcid.org/0000-0003-1959-012X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michael Osborne","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058617210","display_name":"Stephen Roberts","orcid":"https://orcid.org/0000-0002-9305-9268"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stephen Roberts","raw_affiliation_strings":["Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK"],"affiliations":[{"raw_affiliation_string":"Machine Learning Research Group, University of Oxford, Eagle House, Walton Well Rd, Oxford OX2 6ED, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5038607215"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1248,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.40846238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"6","first_page":"209","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9976999759674072,"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6451177000999451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.58197420835495},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.5104566812515259},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.4909237027168274},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4719352424144745},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.448871910572052},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44854918122291565},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44415128231048584},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4073679447174072},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37597227096557617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37575769424438477},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36264973878860474},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3070034384727478},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.12373748421669006}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6451177000999451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.58197420835495},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5104566812515259},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.4909237027168274},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4719352424144745},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.448871910572052},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44854918122291565},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44415128231048584},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4073679447174072},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37597227096557617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37575769424438477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36264973878860474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3070034384727478},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.12373748421669006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a15060209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15060209","pdf_url":"https://www.mdpi.com/1999-4893/15/6/209/pdf?version=1655266577","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4a1b55785a39473ba2e3ce9abb0c4fac","is_oa":true,"landing_page_url":"https://doaj.org/article/4a1b55785a39473ba2e3ce9abb0c4fac","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 6, p 209 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/6/209/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15060209","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":"Algorithms; Volume 15; Issue 6; Pages: 209","raw_type":"Text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:80fb33ca-42fe-444c-84c3-e8ba896235d8","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:80fb33ca-42fe-444c-84c3-e8ba896235d8","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"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":"Symplectic Elements","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.3390/a15060209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15060209","pdf_url":"https://www.mdpi.com/1999-4893/15/6/209/pdf?version=1655266577","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4282945825.pdf","grobid_xml":"https://content.openalex.org/works/W4282945825.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1491884104","https://openalex.org/W1984374364","https://openalex.org/W1994473607","https://openalex.org/W2015953751","https://openalex.org/W2075984423","https://openalex.org/W2088164510","https://openalex.org/W2115022330","https://openalex.org/W2132914434","https://openalex.org/W2151936673","https://openalex.org/W2164928285","https://openalex.org/W2607802485","https://openalex.org/W2755088640","https://openalex.org/W2764280570","https://openalex.org/W2947220227","https://openalex.org/W2963225255","https://openalex.org/W2963598015","https://openalex.org/W4229633200","https://openalex.org/W6604594291","https://openalex.org/W6686707004"],"related_works":["https://openalex.org/W2369488729","https://openalex.org/W2355371556","https://openalex.org/W2104827669","https://openalex.org/W3212687977","https://openalex.org/W2375654472","https://openalex.org/W2161690219","https://openalex.org/W3162207007","https://openalex.org/W2920855166","https://openalex.org/W2087391746","https://openalex.org/W2583877436"],"abstract_inverted_index":{"We":[0,114],"propose":[1],"an":[2,72],"alternative":[3],"maximum":[4],"entropy":[5],"approach":[6,28,49,67,75,117],"to":[7,16,76,107],"learning":[8,77,123],"the":[9,35,45,60,63,97,116,129,132],"spectra":[10],"of":[11,37,62,99,112,120],"massive":[12],"graphs.":[13,145],"In":[14],"contrast":[15],"state-of-the-art":[17],"Lanczos":[18],"algorithm":[19],"for":[20],"spectral":[21,64,81,138],"density":[22],"estimation":[23],"and":[24,40,101,124,143],"applications":[25],"thereof,":[26],"our":[27,48],"does":[29],"not":[30],"require":[31],"kernel":[32,38,57],"smoothing.":[33],"As":[34],"choice":[36],"function":[39],"associated":[41],"bandwidth":[42],"heavily":[43],"affect":[44],"resulting":[46],"output,":[47],"mitigates":[50],"these":[51],"issues.":[52],"Furthermore,":[53],"we":[54],"prove":[55],"that":[56],"smoothing":[58],"biases":[59],"moments":[61],"density.":[65],"Our":[66],"can":[68,103],"be":[69,104],"seen":[70],"as":[71],"information-theoretically":[73],"optimal":[74],"a":[78,92],"smooth":[79],"graph":[80,121],"density,":[82],"which":[83],"fully":[84],"respects":[85],"moment":[86],"information.":[87],"The":[88],"proposed":[89,133],"method":[90,134],"has":[91],"computational":[93],"cost":[94],"linear":[95],"in":[96,128],"number":[98,127],"edges,":[100],"hence":[102],"applied":[105],"even":[106],"large":[108],"networks":[109],"with":[110],"millions":[111],"nodes.":[113],"showcase":[115],"on":[118,140],"problems":[119],"similarity":[122],"counting":[125],"cluster":[126],"graph,":[130],"where":[131],"outperforms":[135],"existing":[136],"iterative":[137],"approaches":[139],"both":[141],"synthetic":[142],"real-world":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2022-06-16T00:00:00"}