{"id":"https://openalex.org/W4392181979","doi":"https://doi.org/10.48550/arxiv.2402.15058","title":"Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds","display_name":"Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds","publication_year":2024,"publication_date":"2024-02-23","ids":{"openalex":"https://openalex.org/W4392181979","doi":"https://doi.org/10.48550/arxiv.2402.15058"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2402.15058","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2402.15058","pdf_url":"https://arxiv.org/pdf/2402.15058","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/2402.15058","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085761158","display_name":"Hubert Wagner","orcid":"https://orcid.org/0009-0009-9111-8429","observed_orcids":["https://orcid.org/0009-0009-9111-8429"]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wagner, Hubert","raw_affiliation_strings":["University of Florida , Gainesville , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida , Gainesville , US","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071835801","display_name":"Nickolas Arustamyan","orcid":"https://orcid.org/0009-0004-2850-5390","observed_orcids":["https://orcid.org/0009-0004-2850-5390"]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arustamyan, Nickolas","raw_affiliation_strings":["University of Florida , Gainesville , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida , Gainesville , US","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Wheeler, Matthew","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wheeler, Matthew","raw_affiliation_strings":["University of Florida , Gainesville , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida , Gainesville , US","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074513715","display_name":"Peter Bubenik","orcid":"https://orcid.org/0000-0001-5262-2133","observed_orcids":["https://orcid.org/0000-0001-5262-2133"]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bubenik, Peter","raw_affiliation_strings":["University of Florida , Gainesville , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida , Gainesville , US","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I33213144"],"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/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/persistent-homology","display_name":"persistent homology","score":0.8650000095367432},{"id":"https://openalex.org/keywords/point-clouds","display_name":"point clouds","score":0.859000027179718},{"id":"https://openalex.org/keywords/shape-characterization","display_name":"shape characterization","score":0.5199999809265137},{"id":"https://openalex.org/keywords/topological-properties","display_name":"topological properties","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C131979681","wikidata":"https://www.wikidata.org/wiki/Q1899648","display_name":"Point cloud","level":2,"score":0.7906834483146667},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.5131993889808655},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5034496188163757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4479823708534241},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3968675434589386},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37261509895324707},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.3388552665710449},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27200525999069214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25219064950942993},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18548700213432312},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17858681082725525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1583927869796753},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09600377082824707}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2402.15058","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2402.15058","pdf_url":"https://arxiv.org/pdf/2402.15058","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":"doi:10.48550/arxiv.2402.15058","doi":"https://doi.org/10.48550/arxiv.2402.15058","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.15058","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:2402.15058","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2402.15058","pdf_url":"https://arxiv.org/pdf/2402.15058","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392181979.pdf","grobid_xml":"https://content.openalex.org/works/W4392181979.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3036427183","https://openalex.org/W3016928466","https://openalex.org/W4389574804","https://openalex.org/W2886923060","https://openalex.org/W3119689987","https://openalex.org/W2936725271","https://openalex.org/W3150655618","https://openalex.org/W2295788148","https://openalex.org/W3210518039","https://openalex.org/W2567662842"],"abstract_inverted_index":{"We":[0],"combine":[1],"standard":[2],"persistent":[3,7,122],"homology":[4,8],"with":[5,68],"image":[6],"to":[9,80,117,129],"define":[10],"a":[11,26,59,63,72,81,105],"novel":[12],"way":[13],"of":[14,55,74,95,121,133],"characterizing":[15,109],"shapes":[16],"and":[17,47,113],"interactions":[18,32,57,110],"between":[19,34],"them.":[20],"In":[21,87],"particular,":[22,88],"we":[23,76,89],"introduce:":[24],"(1)":[25],"mixup":[27,46,103],"barcode,":[28],"which":[29,51,137],"captures":[30],"geometric-topological":[31],"(mixup)":[33],"two":[35],"point":[36],"sets":[37],"in":[38,93],"arbitrary":[39],"dimension;":[40],"(2)":[41],"simple":[42],"summary":[43],"statistics,":[44],"total":[45,48],"percentage":[49],"mixup,":[50],"quantify":[52],"the":[53,56,69,91,118,124,130,134],"complexity":[54],"as":[58],"single":[60],"number;":[61],"(3)":[62],"software":[64],"tool":[65,79,126],"for":[66,108,111],"playing":[67],"above.":[70],"As":[71],"proof":[73],"concept,":[75],"apply":[77],"this":[78],"problem":[82],"arising":[83],"from":[84],"machine":[85],"learning.":[86],"study":[90],"disentanglement":[92],"embeddings":[94],"different":[96],"classes.":[97],"The":[98],"results":[99],"suggest":[100],"that":[101],"topological":[102,135],"is":[104,127,138],"useful":[106],"method":[107],"low":[112],"high-dimensional":[114],"data.":[115],"Compared":[116],"typical":[119],"usage":[120],"homology,":[123],"new":[125],"sensitive":[128],"geometric":[131],"locations":[132],"features,":[136],"often":[139],"desirable.":[140]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2024-02-27T00:00:00"}