{"id":"https://openalex.org/W7213446735","doi":"https://doi.org/10.3390/ijt3040025","title":"Beyond the Lower-Star Filtration: Alternative Filtration Methods for Persistent Homology","display_name":"Beyond the Lower-Star Filtration: Alternative Filtration Methods for Persistent Homology","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7213446735","doi":"https://doi.org/10.3390/ijt3040025"},"language":"en","primary_location":{"id":"doi:10.3390/ijt3040025","doi":"https://doi.org/10.3390/ijt3040025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijt3040025","pdf_url":null,"source":{"id":"https://openalex.org/S5407034202","display_name":"International Journal of Topology","issn_l":"2813-9542","issn":["2813-9542"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Topology","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/ijt3040025","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119987147","display_name":"Innocent Abaa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Innocent Abaa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5141886131","display_name":"Umar Islambekov","orcid":"https://orcid.org/0000-0002-5103-3238","observed_orcids":["https://orcid.org/0000-0002-5103-3238"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Umar Islambekov","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5103-3238","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5119987147"],"corresponding_institution_ids":[],"apc_list":{"value":1000,"currency":"CHF","value_usd":1207},"apc_paid":{"value":1000,"currency":"CHF","value_usd":1207},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.69725404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":"4","first_page":"25","last_page":"25"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"persistent homology","score":0.8849999904632568},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.746999979019165},{"id":"https://openalex.org/keywords/filtration","display_name":"filtration","score":0.578000009059906},{"id":"https://openalex.org/keywords/aggregation-operators","display_name":"aggregation operators","score":0.8069999814033508},{"id":"https://openalex.org/keywords/persistence-diagrams","display_name":"persistence diagrams","score":0.7590000033378601},{"id":"https://openalex.org/keywords/topological-properties","display_name":"topological properties","score":0.7149999737739563}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.8162999749183655},{"id":"https://openalex.org/C128489963","wikidata":"https://www.wikidata.org/wiki/Q1187724","display_name":"Filtration (mathematics)","level":2,"score":0.7620000243186951},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6248000264167786},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.5540000200271606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5447999835014343},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4341000020503998},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3528999984264374},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.33719998598098755},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3116999864578247},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C55919133","wikidata":"https://www.wikidata.org/wiki/Q7644297","display_name":"Supertree","level":4,"score":0.26600000262260437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2572999894618988},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/ijt3040025","doi":"https://doi.org/10.3390/ijt3040025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijt3040025","pdf_url":null,"source":{"id":"https://openalex.org/S5407034202","display_name":"International Journal of Topology","issn_l":"2813-9542","issn":["2813-9542"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Topology","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202609.1332.v1","doi":"https://doi.org/10.20944/preprints202609.1332.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202609.1332.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.3390/ijt3040025","doi":"https://doi.org/10.3390/ijt3040025","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijt3040025","pdf_url":null,"source":{"id":"https://openalex.org/S5407034202","display_name":"International Journal of Topology","issn_l":"2813-9542","issn":["2813-9542"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Topology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W38176413","https://openalex.org/W1848620603","https://openalex.org/W1869425271","https://openalex.org/W1976863970","https://openalex.org/W1987349051","https://openalex.org/W1991566301","https://openalex.org/W2009746817","https://openalex.org/W2037613900","https://openalex.org/W2066459332","https://openalex.org/W2071391326","https://openalex.org/W2083252561","https://openalex.org/W2144044408","https://openalex.org/W2294510945","https://openalex.org/W2500763358","https://openalex.org/W2618265628","https://openalex.org/W2763959081","https://openalex.org/W2795696711","https://openalex.org/W2938995766","https://openalex.org/W2945456722","https://openalex.org/W2963407101","https://openalex.org/W3034922525","https://openalex.org/W4391619735","https://openalex.org/W4415151394"],"related_works":["https://openalex.org/W2998916836","https://openalex.org/W3035006751","https://openalex.org/W4289417973","https://openalex.org/W2888620915","https://openalex.org/W4402702079","https://openalex.org/W2096736341","https://openalex.org/W4391991719","https://openalex.org/W3107878091","https://openalex.org/W7101111865","https://openalex.org/W3198173525"],"abstract_inverted_index":{"In":[0],"the":[1,12,19,57,70,74,79,112,140,172,188],"lower-star":[2],"filtration":[3,8,20,68,72,76,81,90,113,132,174],"(LSF),":[4],"simplices":[5,34,109],"are":[6,153,176],"assigned":[7],"values":[9,91,100,133],"according":[10],"to":[11,46,56,110,184],"maximum-vertex":[13],"rule,":[14],"with":[15,38],"each":[16],"simplex":[17,89],"entering":[18],"when":[21],"its":[22],"highest-valued":[23],"vertex":[24,99],"appears.":[25],"A":[26],"limitation":[27],"of":[28,131],"this":[29,62],"construction":[30],"is":[31],"that":[32,95,117,152,171],"higher-dimensional":[33],"may":[35,125,144],"enter":[36,111],"simultaneously":[37],"their":[39,105],"boundary":[40],"faces,":[41],"causing":[42],"some":[43],"topological":[44,118,150],"features":[45,119,151],"be":[47],"filled":[48,137],"immediately":[49],"upon":[50],"formation":[51],"and":[52,78,123,147,167,179],"therefore":[53],"not":[54,154],"contributing":[55],"persistence":[58,142],"diagram.":[59],"To":[60],"address":[61],"limitation,":[63],"we":[64],"propose":[65],"three":[66],"alternative":[67],"methods:":[69],"\u03b5-lower-star":[71],"(ELSF),":[73],"Lp":[75],"(LpF),":[77],"softmax":[80],"(SMF).":[82],"These":[83],"methods":[84,175],"generalize":[85],"LSF":[86],"by":[87],"assigning":[88],"using":[92],"aggregation":[93],"functions":[94],"depend":[96],"on":[97,104,165],"all":[98],"rather":[101,134],"than":[102,135,190],"solely":[103],"maximum.":[106],"This":[107],"allows":[108],"more":[114,148],"progressively,":[115],"so":[116],"such":[120],"as":[121],"loops":[122],"voids":[124],"persist":[126],"across":[127],"a":[128],"wider":[129],"range":[130],"being":[136],"immediately.":[138],"Consequently,":[139],"resulting":[141],"diagrams":[143],"contain":[145],"additional":[146],"persistent":[149],"observed":[155],"under":[156],"LSF,":[157],"potentially":[158],"providing":[159],"greater":[160,182],"discriminative":[161],"power.":[162],"Experimental":[163],"results":[164],"simulated":[166],"real-world":[168],"datasets":[169],"demonstrate":[170],"proposed":[173],"computationally":[177],"efficient":[178],"can":[180],"provide":[181],"sensitivity":[183],"structural":[185],"differences":[186],"in":[187],"data":[189],"LSF.":[191]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-17T00:00:00"}
