{"id":"https://openalex.org/W4400611191","doi":"https://doi.org/10.48550/arxiv.2407.07524","title":"Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More","display_name":"Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More","publication_year":2024,"publication_date":"2024-07-10","ids":{"openalex":"https://openalex.org/W4400611191","doi":"https://doi.org/10.48550/arxiv.2407.07524"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2407.07524","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.07524","pdf_url":"https://arxiv.org/pdf/2407.07524","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/2407.07524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113131195","display_name":"Om Roy","orcid":"https://orcid.org/0009-0004-8020-996X","observed_orcids":["https://orcid.org/0009-0004-8020-996X","https://orcid.org/0009-0008-3011-8233"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roy, Om","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020404611","display_name":"Avalon Campbell-Cousins","orcid":"https://orcid.org/0009-0005-2263-0593","observed_orcids":["https://orcid.org/0009-0005-2263-0593"]},"institutions":[{"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":"Campbell-Cousins, Avalon","raw_affiliation_strings":["School of Engineering , Institute for Imaging, Data and Communications , University of Edinburgh , Edinburgh , Scotland , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering , Institute for Imaging, Data and Communications , University of Edinburgh , Edinburgh , Scotland , United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029062751","display_name":"John Stewart Fabila Carrasco","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carrasco, John Stewart Fabila","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088247542","display_name":"Mario A. Parra","orcid":"https://orcid.org/0000-0002-2412-648X","observed_orcids":["https://orcid.org/0000-0002-2412-648X"]},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]},{"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":"Parra, Mario A","raw_affiliation_strings":["Psychological Sciences and Health , University of Strathclyde , Glasgow , Scotland , United Kingdom","School of informatics , University of Edinburgh , Edinburgh , Scotland , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Psychological Sciences and Health , University of Strathclyde , Glasgow , Scotland , United Kingdom","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"School of informatics , University of Edinburgh , Edinburgh , Scotland , United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060254662","display_name":"Javier Escudero","orcid":"https://orcid.org/0000-0002-2105-8725","observed_orcids":["https://orcid.org/0000-0002-2105-8725"]},"institutions":[{"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":"Escudero, Javier","raw_affiliation_strings":["School of Engineering , Institute for Imaging, Data and Communications , University of Edinburgh , Edinburgh , Scotland , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering , Institute for Imaging, Data and Communications , University of Edinburgh , Edinburgh , Scotland , United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.12729999423027039,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.12729999423027039,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.08749999850988388,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.08399999886751175,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation-entropy","display_name":"permutation entropy","score":0.9070000052452087},{"id":"https://openalex.org/keywords/graph-signals","display_name":"graph signals","score":0.8100000023841858},{"id":"https://openalex.org/keywords/graph-signal-processing","display_name":"graph signal processing","score":0.47699999809265137},{"id":"https://openalex.org/keywords/nonlinear-signal-analysis","display_name":"nonlinear signal analysis","score":0.6179999709129333},{"id":"https://openalex.org/keywords/image-representation","display_name":"image representation","score":0.6830000281333923},{"id":"https://openalex.org/keywords/mri-data","display_name":"MRI data","score":0.45899999141693115},{"id":"https://openalex.org/keywords/fractal-patterns","display_name":"fractal patterns","score":0.8949999809265137},{"id":"https://openalex.org/keywords/nonlinear-maps","display_name":"nonlinear maps","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5248059034347534},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.503419816493988},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4652147591114044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4581831991672516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40877753496170044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33298322558403015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06471416354179382},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2407.07524","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.07524","pdf_url":"https://arxiv.org/pdf/2407.07524","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":"pmh:oai:pure.ed.ac.uk:publications/451bf9a4-38be-45c4-9eaf-45ee3ccd69d3","doi":null,"is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/files/457600418/RoyEtalArXiv2024GraphPermutationEntropy.pdf","pdf_url":"https://www.research.ed.ac.uk/files/457600418/RoyEtalArXiv2024GraphPermutationEntropy.pdf","source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Roy, O, Campbell-Cousins, A, Carrasco, J S F, Parra, M A & Escudero, J 2024 'Graph permutation entropy : Extensions to the continuous case, a step towards ordinal deep learning, and more'. https://doi.org/10.48550/arXiv.2407.07524","raw_type":"workingPaper"},{"id":"doi:10.48550/arxiv.2407.07524","doi":"https://doi.org/10.48550/arxiv.2407.07524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2407.07524","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:2407.07524","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2407.07524","pdf_url":"https://arxiv.org/pdf/2407.07524","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8211788080","display_name":null,"funder_award_id":"RPG-2020-158","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400611191.pdf","grobid_xml":"https://content.openalex.org/works/W4400611191.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Nonlinear":[0],"dynamics":[1],"play":[2],"an":[3],"important":[4],"role":[5],"in":[6,114,145,224],"the":[7,26,56,67,95,122,133,150,169,179,182,194,201],"analysis":[8,27,37,123,211],"of":[9,28,38,50,69,100,103,124,139,171,181,203,212,216],"signals.":[10],"A":[11],"popular,":[12],"readily":[13],"interpretable":[14],"nonlinear":[15,210],"measure":[16],"is":[17,73,112],"Permutation":[18,51],"Entropy.":[19],"It":[20],"has":[21],"recently":[22,85],"been":[23],"extended":[24],"for":[25,35,121],"graph":[29,57,96,134,143,195],"signals,":[30,144],"thus":[31],"providing":[32],"a":[33,47,61,74,80,137,146,213],"framework":[34],"non-linear":[36,162],"data":[39,167,217,225],"sampled":[40],"on":[41],"irregular":[42],"domains.":[43],"Here,":[44],"we":[45,197],"introduce":[46],"continuous":[48],"version":[49],"Entropy,":[52],"extend":[53,91],"it":[54,129],"to":[55,66,94,132,149,154,190,193,199,208],"domain,":[58,196],"and":[59,83,109,126,160,164,175,218],"develop":[60],"ordinal":[62,92,101],"activation":[63],"function":[64],"akin":[65],"one":[68],"neural":[70],"networks.":[71],"This":[72],"step":[75],"towards":[76],"Ordinal":[77],"Deep":[78],"Learning,":[79],"potentially":[81],"effective":[82],"very":[84,186],"posited":[86],"concept.":[87],"We":[88,116],"also":[89,107,117],"formally":[90],"contrasts":[93,102,120],"domain.":[97],"Continuous":[98],"versions":[99],"length":[104],"3":[105],"are":[106],"introduced":[108],"their":[110],"advantage":[111],"shown":[113],"experiments.":[115],"integrate":[118],"specific":[119],"images":[125],"show":[127,168],"that":[128],"generalizes":[130],"well":[131],"domain":[135],"allowing":[136],"representation":[138],"images,":[140],"represented":[141],"as":[142],"plane":[147],"similar":[148],"entropy-complexity":[151],"one.":[152],"Applications":[153],"synthetic":[155],"data,":[156],"including":[157],"fractal":[158],"patterns":[159],"popular":[161],"maps,":[163],"real-life":[165],"MRI":[166],"validity":[170],"these":[172],"novel":[173],"extensions":[174],"potential":[176],"benefits":[177],"over":[178],"state":[180],"art.":[183],"By":[184],"extending":[185],"recent":[187],"concepts":[188],"related":[189],"permutation":[191],"entropy":[192,206],"expect":[198],"accelerate":[200],"development":[202],"more":[204],"graph-based":[205],"methods":[207],"enable":[209],"broader":[214],"kind":[215],"establishing":[219],"relationships":[220],"with":[221],"emerging":[222],"ideas":[223],"science.":[226]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2025-10-10T00:00:00"}