{"id":"https://openalex.org/W2805139353","doi":"https://doi.org/10.1109/tpami.2018.2885516","title":"Persistence Paths and Signature Features in Topological Data Analysis","display_name":"Persistence Paths and Signature Features in Topological Data Analysis","publication_year":2018,"publication_date":"2018-12-07","ids":{"openalex":"https://openalex.org/W2805139353","doi":"https://doi.org/10.1109/tpami.2018.2885516","mag":"2805139353","pmid":"https://pubmed.ncbi.nlm.nih.gov/30530312"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2018.2885516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2885516","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.00381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018284042","display_name":"Ilya Chevyrev","orcid":"https://orcid.org/0000-0002-5630-9694"},"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":"Ilya Chevyrev","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0002-5630-9694","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069873248","display_name":"Vidit Nanda","orcid":"https://orcid.org/0000-0001-9243-6749"},"institutions":[{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]},{"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","US"],"is_corresponding":false,"raw_author_name":"Vidit Nanda","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom","School of Mathematics, Institute for Advanced Study, Princeton, USA"],"raw_orcid":"https://orcid.org/0000-0001-9243-6749","affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"School of Mathematics, Institute for Advanced Study, Princeton, USA","institution_ids":["https://openalex.org/I40036882"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024452289","display_name":"Harald Oberhauser","orcid":"https://orcid.org/0000-0003-2644-8906"},"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":"Harald Oberhauser","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5006,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.96598608,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"42","issue":"1","first_page":"192","last_page":"202"},"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9222000241279602,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9125999808311462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.6448862552642822},{"id":"https://openalex.org/keywords/barcode","display_name":"Barcode","score":0.6318529844284058},{"id":"https://openalex.org/keywords/feature-vector","display_name":"Feature vector","score":0.6199468374252319},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5533391237258911},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.541977047920227},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.5082380175590515},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.44931501150131226},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4484460949897766},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.44731906056404114},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.42175114154815674},{"id":"https://openalex.org/keywords/universality","display_name":"Universality (dynamical systems)","score":0.4205303490161896},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3804657757282257},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37696152925491333},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.371561199426651},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3200361132621765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31626760959625244},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11953061819076538},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09894213080406189},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07939419150352478}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.6448862552642822},{"id":"https://openalex.org/C2776841711","wikidata":"https://www.wikidata.org/wiki/Q856","display_name":"Barcode","level":2,"score":0.6318529844284058},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.6199468374252319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5533391237258911},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.541977047920227},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.5082380175590515},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.44931501150131226},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4484460949897766},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.44731906056404114},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.42175114154815674},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.4205303490161896},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3804657757282257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37696152925491333},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.371561199426651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3200361132621765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31626760959625244},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11953061819076538},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09894213080406189},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07939419150352478},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1109/tpami.2018.2885516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2018.2885516","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:30530312","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30530312","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:arXiv.org:1806.00381","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.00381","pdf_url":"https://arxiv.org/pdf/1806.00381","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,"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:ora.ox.ac.uk:uuid:3086b7fc-4ce4-486a-9623-2f57b4a232b2","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:3086b7fc-4ce4-486a-9623-2f57b4a232b2","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:82605093-e5f6-4c1b-b0ce-4dbd07181f2e","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:82605093-e5f6-4c1b-b0ce-4dbd07181f2e","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:b5f8c42c-0354-4284-b19c-24af2b74b1a6","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:b5f8c42c-0354-4284-b19c-24af2b74b1a6","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/0d9a3cbd-9612-4e36-a44a-981ff1912d50","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/0d9a3cbd-9612-4e36-a44a-981ff1912d50","pdf_url":null,"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,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Chevyrev, I, Nanda, V & Oberhauser, H 2020, 'Persistence paths and signature features in topological data analysis', IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 42, no. 1, pp. 192-202. https://doi.org/10.1109/TPAMI.2018.2885516","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/0d9a3cbd-9612-4e36-a44a-981ff1912d50","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/0d9a3cbd-9612-4e36-a44a-981ff1912d50","pdf_url":null,"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,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Chevyrev, I, Nanda, V & Oberhauser, H 2020, 'Persistence paths and signature features in topological data analysis', IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 42, no. 1, pp. 192-202. https://doi.org/10.1109/TPAMI.2018.2885516","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.00381","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.00381","pdf_url":"https://arxiv.org/pdf/1806.00381","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,"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":[],"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/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/G5005012656","display_name":null,"funder_award_id":"EP/S026347/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8593039737","display_name":"Unparameterised multi-modal data, high order signatures, and the mathematics of data science","funder_award_id":"EP/S026347/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"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/F4320308316","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"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":52,"referenced_works":["https://openalex.org/W38176413","https://openalex.org/W337289788","https://openalex.org/W616109306","https://openalex.org/W617501864","https://openalex.org/W1588476105","https://openalex.org/W1596721197","https://openalex.org/W1928559544","https://openalex.org/W1957046493","https://openalex.org/W1968445443","https://openalex.org/W1999528235","https://openalex.org/W2002165972","https://openalex.org/W2027130342","https://openalex.org/W2032868343","https://openalex.org/W2037613900","https://openalex.org/W2071391326","https://openalex.org/W2101234009","https://openalex.org/W2102368730","https://openalex.org/W2135610119","https://openalex.org/W2144044408","https://openalex.org/W2149185044","https://openalex.org/W2150372924","https://openalex.org/W2153986241","https://openalex.org/W2159988601","https://openalex.org/W2261585608","https://openalex.org/W2263883519","https://openalex.org/W2338075189","https://openalex.org/W2411877106","https://openalex.org/W2415461781","https://openalex.org/W2609252852","https://openalex.org/W2626898927","https://openalex.org/W2898407550","https://openalex.org/W2962706934","https://openalex.org/W2962818398","https://openalex.org/W2963611658","https://openalex.org/W2964143464","https://openalex.org/W2964209273","https://openalex.org/W2964237352","https://openalex.org/W3015234645","https://openalex.org/W3040586665","https://openalex.org/W3081627906","https://openalex.org/W3104291232","https://openalex.org/W3123536599","https://openalex.org/W3123940972","https://openalex.org/W4289606391","https://openalex.org/W4293182332","https://openalex.org/W4298062438","https://openalex.org/W6619091367","https://openalex.org/W6675354045","https://openalex.org/W6681677808","https://openalex.org/W6694154208","https://openalex.org/W6748167941","https://openalex.org/W6756019395"],"related_works":["https://openalex.org/W2886923060","https://openalex.org/W2887690685","https://openalex.org/W2129730857","https://openalex.org/W4287394697","https://openalex.org/W3119689987","https://openalex.org/W3120766012","https://openalex.org/W4287826795","https://openalex.org/W3128725485","https://openalex.org/W3204835693","https://openalex.org/W4224300916"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,25,28,63],"new":[3],"feature":[4,64],"map":[5,65],"for":[6,71],"barcodes":[7],"as":[8,24,75],"they":[9],"arise":[10],"in":[11,27,42,62],"persistent":[12],"homology":[13],"computation.":[14],"The":[15,50],"main":[16],"idea":[17],"is":[18],"to":[19,33,56,59],"first":[20],"realize":[21],"each":[22],"barcode":[23],"path":[26,37,58],"convenient":[29],"vector":[30,48],"space,":[31],"and":[32,77,79],"then":[34],"compute":[35],"its":[36],"signature":[38],"which":[39],"takes":[40],"values":[41],"the":[43],"tensor":[44,60],"algebra":[45],"of":[46,52],"that":[47,66],"space.":[49],"composition":[51],"these":[53],"two":[54],"operations-barcode":[55],"path,":[57],"series-results":[61],"has":[67],"several":[68],"desirable":[69],"properties":[70],"statistical":[72],"learning,":[73],"such":[74],"universality":[76],"characteristicness,":[78],"achieves":[80],"state-of-the-art":[81],"results":[82],"on":[83],"common":[84],"classification":[85],"benchmarks.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2}],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-10T00:00:00"}
