{"id":"https://openalex.org/W4415880582","doi":"https://doi.org/10.1007/s10791-025-09783-z","title":"A unified spectral-persistent homology framework for stable and generalizable topological deep learning","display_name":"A unified spectral-persistent homology framework for stable and generalizable topological deep learning","publication_year":2025,"publication_date":"2025-11-04","ids":{"openalex":"https://openalex.org/W4415880582","doi":"https://doi.org/10.1007/s10791-025-09783-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10791-025-09783-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10791-025-09783-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10791-025-09783-z.pdf","source":{"id":"https://openalex.org/S5407036663","display_name":"Discover Computing","issn_l":"2948-2992","issn":["2948-2992"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discover Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/s10791-025-09783-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119767074","display_name":"Saif Hameed Abbood Al-Waeli","orcid":null},"institutions":[{"id":"https://openalex.org/I39498419","display_name":"University of Wasit","ror":"https://ror.org/02ee2t316","country_code":"IQ","type":"education","lineage":["https://openalex.org/I39498419"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Saif Hameed Abbood Alwaeli","raw_affiliation_strings":["College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq","institution_ids":["https://openalex.org/I39498419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049229342","display_name":"Ali A. Abdulsaeed","orcid":null},"institutions":[{"id":"https://openalex.org/I39498419","display_name":"University of Wasit","ror":"https://ror.org/02ee2t316","country_code":"IQ","type":"education","lineage":["https://openalex.org/I39498419"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Ali A. Abdulsaeed","raw_affiliation_strings":["College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq","institution_ids":["https://openalex.org/I39498419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120250756","display_name":"Shams Jamal Fayyadh","orcid":null},"institutions":[{"id":"https://openalex.org/I39498419","display_name":"University of Wasit","ror":"https://ror.org/02ee2t316","country_code":"IQ","type":"education","lineage":["https://openalex.org/I39498419"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Shams Jamal Fayyadh","raw_affiliation_strings":["College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Information Technology, University of Wasit, Alkut, 52001, Iraq","institution_ids":["https://openalex.org/I39498419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038576392","display_name":"Muhammad Inam Khan","orcid":null},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]},{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB","SA"],"is_corresponding":false,"raw_author_name":"Muhammad I. Khan","raw_affiliation_strings":["Artificial Intelligence & Data Analytics Lab (AIDA), CCIS Prince Sultan University, Riyadh, 11586, Saudi Arabia","School of Engineering, University of Warwick, Warwick Coventry, CV4 7AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Artificial Intelligence & Data Analytics Lab (AIDA), CCIS Prince Sultan University, Riyadh, 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]},{"raw_affiliation_string":"School of Engineering, University of Warwick, Warwick Coventry, CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073901996","display_name":"Abdallah Yousif","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088616","display_name":"University of Science and Technology Omdurman","ror":"https://ror.org/004qjck53","country_code":"SD","type":"education","lineage":["https://openalex.org/I4210088616"]},{"id":"https://openalex.org/I9353105","display_name":"Sudan University of Science and Technology","ror":"https://ror.org/02fwtg066","country_code":"SD","type":"education","lineage":["https://openalex.org/I9353105"]}],"countries":["SD"],"is_corresponding":true,"raw_author_name":"Abdallah Yousif","raw_affiliation_strings":["Department of Computer Science, Sudan Technological University, Omdurman, Khartoum, 11111, Sudan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Sudan Technological University, Omdurman, Khartoum, 11111, Sudan","institution_ids":["https://openalex.org/I4210088616","https://openalex.org/I9353105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5094050788","display_name":"Tanzila Saba","orcid":"https://orcid.org/0000-0003-2579-4209"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tanzila Saba","raw_affiliation_strings":["Artificial Intelligence & Data Analytics Lab (AIDA), CCIS Prince Sultan University, Riyadh, 11586, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Artificial Intelligence & Data Analytics Lab (AIDA), CCIS Prince Sultan University, Riyadh, 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077942586","display_name":"Saeed Ali Bahaj","orcid":"https://orcid.org/0000-0003-4078-0518"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Saeed Ali Bahaj","raw_affiliation_strings":["MIS Department College of Business Administration, Prince Sattam Bin Abdulaziz University, AlKharj, 11942, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIS Department College of Business Administration, Prince Sattam Bin Abdulaziz University, AlKharj, 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5073901996"],"corresponding_institution_ids":["https://openalex.org/I4210088616","https://openalex.org/I9353105"],"apc_list":null,"apc_paid":null,"fwci":2.2606,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.90828463,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"28","issue":"1","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":0.9983000159263611,"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":0.9983000159263611,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.000699999975040555,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00019999999494757503,"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":0.8711000084877014},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.8309999704360962},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6028000116348267},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5800999999046326},{"id":"https://openalex.org/keywords/computational-topology","display_name":"Computational topology","score":0.49790000915527344},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4496999979019165},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4472000002861023},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.3625999987125397},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.35569998621940613}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.8711000084877014},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.8309999704360962},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6028000116348267},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5800999999046326},{"id":"https://openalex.org/C181576044","wikidata":"https://www.wikidata.org/wiki/Q4129926","display_name":"Computational topology","level":3,"score":0.49790000915527344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4553000032901764},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4472000002861023},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40529999136924744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.392300009727478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3781999945640564},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.3427000045776367},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.31049999594688416},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C176032523","wikidata":"https://www.wikidata.org/wiki/Q753127","display_name":"Topological sorting","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C112785775","wikidata":"https://www.wikidata.org/wiki/Q786441","display_name":"Topological skeleton","level":4,"score":0.272599995136261},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2599000036716461},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10791-025-09783-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10791-025-09783-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10791-025-09783-z.pdf","source":{"id":"https://openalex.org/S5407036663","display_name":"Discover Computing","issn_l":"2948-2992","issn":["2948-2992"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discover Computing","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1a3742ec6a584fdb9518f266caae32dd","is_oa":true,"landing_page_url":"https://doaj.org/article/1a3742ec6a584fdb9518f266caae32dd","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discover Computing, Vol 28, Iss 1, Pp 1-22 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10791-025-09783-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10791-025-09783-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10791-025-09783-z.pdf","source":{"id":"https://openalex.org/S5407036663","display_name":"Discover Computing","issn_l":"2948-2992","issn":["2948-2992"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discover Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320327702","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415880582.pdf","grobid_xml":"https://content.openalex.org/works/W4415880582.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W28435248","https://openalex.org/W2481594651","https://openalex.org/W2883165869","https://openalex.org/W2898403988","https://openalex.org/W2943959761","https://openalex.org/W2963518130","https://openalex.org/W3033513666","https://openalex.org/W3112717538","https://openalex.org/W3130702379","https://openalex.org/W3152893301","https://openalex.org/W3172885111","https://openalex.org/W3202868818","https://openalex.org/W3205967997","https://openalex.org/W4212811301","https://openalex.org/W4212890525","https://openalex.org/W4221117548","https://openalex.org/W4285262633","https://openalex.org/W4293565989","https://openalex.org/W4313592093","https://openalex.org/W4319792378","https://openalex.org/W4366733083","https://openalex.org/W4383313469","https://openalex.org/W4386528689","https://openalex.org/W4387623751","https://openalex.org/W4392907809","https://openalex.org/W4403322902","https://openalex.org/W4405119756","https://openalex.org/W4407414774","https://openalex.org/W4414580403"],"related_works":[],"abstract_inverted_index":{"Topological":[0,74],"Deep":[1],"Learning":[2],"(TDL)":[3],"boosts":[4],"the":[5,30,96,99,104,123,174],"capabilities":[6],"of":[7,32,66,98,106,137,146,154,233],"neural":[8],"networks":[9],"by":[10],"integrating":[11],"topological":[12,55,108,200,223,250],"features":[13],"from":[14,122,195,227],"complex":[15],"data":[16,121,247],"structures":[17],"like":[18,239],"graphs":[19],"and":[20,38,44,47,62,89,148,169,188,230,242],"simplicial":[21],"complexes.":[22],"However,":[23],"there":[24],"is":[25],"a":[26,36,59,141],"critical":[27],"gap":[28],"in":[29,86,95,140,143,151,212],"area":[31],"structural":[33,81,243],"perturbations":[34],"within":[35],"model":[37,78,220],"how":[39],"these":[40],"affect":[41],"its":[42],"stability":[43,183],"generalization.":[45],"Overfitting":[46],"brittle":[48],"predictions":[49],"are":[50],"concerns":[51],"when":[52],"dealing":[53],"with":[54,119,160,207,222,248],"noise.":[56],"We":[57,69,110],"propose":[58],"comprehensive":[60],"theoretical":[61,157],"empirical":[63],"evaluation":[64],"framework":[65],"TDL":[67,205],"robustness.":[68,208],"define":[70,103],"two":[71],"complementary":[72],"metrics,":[73],"Drift":[75],"which":[76,92,245],"quantifies":[77],"sensitivity":[79],"to":[80,182,198,218],"noise":[82],"using":[83],"bottleneck":[84],"distance":[85],"persistent":[87,186,196],"homology,":[88],"Spectral":[90],"Variance":[91],"measures":[93],"shifts":[94],"eigenvalues":[97],"Hodge":[100],"Laplacian.":[101],"These":[102,130],"degradation":[105],"learned":[107],"representations.":[109],"conducted":[111],"controlled":[112],"experiments":[113,131],"on":[114,165],"synthetic":[115],"Vietoris-Rips":[116],"complexes,":[117],"together":[118],"real-world":[120],"TDA":[124],"Benchmark\u2019s":[125],"Enzyme":[126],"Function":[127],"Prediction":[128],"dataset.":[129],"support":[132],"our":[133,177],"conclusions.":[134],"High":[135],"levels":[136],"perturbation":[138],"resulted":[139],"drop":[142],"classification":[144],"accuracy":[145],"19.1%,":[147],"an":[149],"increase":[150],"spectral":[152,170,189],"variance":[153],"4.3\u00d7,":[155],"confirming":[156],"expectations.":[158],"Comparison":[159],"neglecting":[161],"frameworks":[162],"after":[163],"2022":[164],"Simplicial":[166],"Neural":[167],"Networks":[168],"graph":[171],"models":[172],"showcases":[173],"need":[175],"for":[176,203,236],"rigorous":[178],"dual-metric":[179],"interpretable":[180],"approach":[181],"analysis.":[184],"Our":[185],"homology":[187,197],"topology":[190],"merger":[191],"lay":[192],"metric":[193],"derived":[194,226],"quantify":[199],"drift":[201],"adaptable":[202],"creating":[204],"architectures":[206],"The":[209],"results":[210],"obtained":[211],"this":[213],"study":[214],"can":[215],"be":[216],"used":[217],"formulate":[219],"equipped":[221],"state":[224],"descriptors":[225],"persistence":[228],"diagrams":[229],"eigen-spectra":[231],"methods":[232],"deep":[234],"learning":[235],"advanced":[237],"fields":[238],"bioinformatics,":[240],"neuroscience,":[241],"biology,":[244],"involve":[246],"inherent":[249],"variations.":[251]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-06-03T09:05:47.796612","created_date":"2025-11-04T00:00:00"}
