{"id":"https://openalex.org/W4392939527","doi":"https://doi.org/10.1109/tsp.2024.3378379","title":"Stability to Deformations of Manifold Filters and Manifold Neural Networks","display_name":"Stability to Deformations of Manifold Filters and Manifold Neural Networks","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4392939527","doi":"https://doi.org/10.1109/tsp.2024.3378379"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2024.3378379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2024.3378379","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100710652","display_name":"Zhiyang Wang","orcid":"https://orcid.org/0000-0001-6124-6571"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiyang Wang","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036583414","display_name":"Luana Ruiz","orcid":"https://orcid.org/0000-0002-9666-1211"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luana Ruiz","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078862959","display_name":"Alejandro Ribeiro","orcid":"https://orcid.org/0000-0003-4230-9906"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alejandro Ribeiro","raw_affiliation_strings":["Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100710652"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":3.036,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91695314,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"72","issue":null,"first_page":"2130","last_page":"2146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9976999759674072,"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":0.9976999759674072,"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/T10812","display_name":"Human Pose and Action Recognition","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9768999814987183,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6676415205001831},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5983415246009827},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.5451028943061829},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5234719514846802},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.48630890250205994},{"id":"https://openalex.org/keywords/manifold-alignment","display_name":"Manifold alignment","score":0.4764852225780487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4242801368236542},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.3851185441017151},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36836308240890503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3492405414581299},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33464086055755615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20580390095710754},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20451951026916504},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19220969080924988},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13400208950042725},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.12899243831634521},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12034779787063599},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.092267245054245}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6676415205001831},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5983415246009827},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.5451028943061829},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5234719514846802},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.48630890250205994},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.4764852225780487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4242801368236542},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.3851185441017151},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36836308240890503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3492405414581299},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33464086055755615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20580390095710754},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20451951026916504},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19220969080924988},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13400208950042725},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.12899243831634521},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12034779787063599},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.092267245054245},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2024.3378379","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2024.3378379","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W313234848","https://openalex.org/W1522301498","https://openalex.org/W1562253575","https://openalex.org/W1920022804","https://openalex.org/W1989368986","https://openalex.org/W1991252559","https://openalex.org/W1994906459","https://openalex.org/W2082102112","https://openalex.org/W2101491865","https://openalex.org/W2116341502","https://openalex.org/W2228388157","https://openalex.org/W2521050763","https://openalex.org/W2558748708","https://openalex.org/W2796026362","https://openalex.org/W2796431263","https://openalex.org/W2798598284","https://openalex.org/W2899457523","https://openalex.org/W2914721378","https://openalex.org/W2943959761","https://openalex.org/W2963272802","https://openalex.org/W2999060662","https://openalex.org/W3049262741","https://openalex.org/W3095521706","https://openalex.org/W3101707147","https://openalex.org/W3104104151","https://openalex.org/W3130869292","https://openalex.org/W3152787073","https://openalex.org/W3152893301","https://openalex.org/W3157286395","https://openalex.org/W3161515948","https://openalex.org/W3162620739","https://openalex.org/W3172109816","https://openalex.org/W3201646649","https://openalex.org/W3206974000","https://openalex.org/W3215025646","https://openalex.org/W4205896075","https://openalex.org/W4212863985","https://openalex.org/W4214879959","https://openalex.org/W4239940917","https://openalex.org/W4323520878","https://openalex.org/W4367016895","https://openalex.org/W4385151982","https://openalex.org/W6631190155","https://openalex.org/W6764047615","https://openalex.org/W6766750229","https://openalex.org/W6779094074","https://openalex.org/W6779367026","https://openalex.org/W6794315554"],"related_works":["https://openalex.org/W117517268","https://openalex.org/W2397338926","https://openalex.org/W2085003924","https://openalex.org/W2573981081","https://openalex.org/W2384392227","https://openalex.org/W2380477800","https://openalex.org/W2387045723","https://openalex.org/W2032133996","https://openalex.org/W1976359930","https://openalex.org/W2888431323"],"abstract_inverted_index":{"The":[0,80,134,186],"paper":[1,86],"defines":[2],"and":[3,9,17,28,37,69,95,112,114,128,151,204],"studies":[4],"manifold":[5,48,93,145],"(M)":[6],"convolutional":[7,75,126],"filters":[8,16,36,52,68,76,94,111,127,150,203],"neural":[10,38,129,184],"networks":[11,39,130],"(NNs).":[12],"<italic":[13,32],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Manifold</i>":[15],"MNNs":[18,96],"are":[19,29,41],"defined":[20],"in":[21,77,131,162,206],"terms":[22],"of":[23,61,66,73,84,92,100,109,120,124,165,178,191,201],"the":[24,47,63,70,85,90,101,163,176,199],"Laplace-Beltrami":[25],"operator":[26],"exponential":[27],"such":[30],"that":[31,138,144,171],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">graph</i>":[34],"(G)":[35],"(NNs)":[40],"recovered":[42],"as":[43,148],"discrete":[44],"approximations":[45],"when":[46],"is":[49,58,87,116,143,168,194],"sampled.":[50],"These":[51],"admit":[53],"a":[54,59,118,169],"spectral":[55,64],"representation":[56,65],"which":[57],"generalization":[60,119],"both":[62],"graph":[67,110,149,202],"frequency":[71,160],"response":[72],"standard":[74,125,152],"continuous":[78,132,153,182],"time.":[79,133],"main":[81],"technical":[82],"contribution":[83],"to":[88,97,195],"analyze":[89],"stability":[91,107,122],"smooth":[98],"deformations":[99],"manifold.":[102],"This":[103,167],"analysis":[104,142,193],"generalizes":[105],"known":[106,121],"properties":[108,123],"GNNs":[113,205],"it":[115],"also":[117],"most":[135,187],"important":[136,188],"observation":[137],"follows":[139],"from":[140],"this":[141,192],"filters,":[146,155],"same":[147],"time":[154,183],"have":[156],"difficulty":[157],"discriminating":[158],"high":[159],"components":[161],"presence":[164],"deformations.":[166],"challenge":[170],"can":[172],"be":[173],"ameliorated":[174],"with":[175],"use":[177],"manifold,":[179],"graph,":[180],"or":[181],"networks.":[185],"practical":[189],"consequence":[190],"shed":[196],"light":[197],"on":[198],"behavior":[200],"large":[207],"scale":[208],"graphs.":[209]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}