{"id":"https://openalex.org/W4398188116","doi":"https://doi.org/10.1109/tnnls.2024.3394598","title":"Deep Geometric Learning With Monotonicity Constraints for Alzheimer\u2019s Disease Progression","display_name":"Deep Geometric Learning With Monotonicity Constraints for Alzheimer\u2019s Disease Progression","publication_year":2024,"publication_date":"2024-05-21","ids":{"openalex":"https://openalex.org/W4398188116","doi":"https://doi.org/10.1109/tnnls.2024.3394598","pmid":"https://pubmed.ncbi.nlm.nih.gov/38771688"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2024.3394598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3394598","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5101478037","display_name":"Seungwoo Jeong","orcid":"https://orcid.org/0009-0000-2141-7399"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Seungwoo Jeong","raw_affiliation_strings":["Department of Artificial Intelligence, Korea University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079491463","display_name":"Wonsik Jung","orcid":"https://orcid.org/0000-0002-0706-4811"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Wonsik Jung","raw_affiliation_strings":["Department of Brain and Cognitive Engineering, Korea University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Brain and Cognitive Engineering, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016820374","display_name":"Junghyo Sohn","orcid":"https://orcid.org/0000-0002-7669-7655"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Junghyo Sohn","raw_affiliation_strings":["Department of Artificial Intelligence, Korea University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033720496","display_name":"Heung\u2010Il Suk","orcid":"https://orcid.org/0000-0001-7019-8962"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Heung-Il Suk","raw_affiliation_strings":["Department of Artificial Intelligence and the Department of Brain and Cognitive Engineering, Korea University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence and the Department of Brain and Cognitive Engineering, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101478037"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":null,"apc_paid":null,"fwci":2.1408,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.84625028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"36","issue":"4","first_page":"7090","last_page":"7102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9628999829292297,"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"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.9628999829292297,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9595000147819519,"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/T12859","display_name":"Cell Image Analysis Techniques","score":0.9370999932289124,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8416123390197754},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6438164710998535},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4890754818916321},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4562074840068817},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.4497329592704773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4347277581691742},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4324013590812683},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.38712361454963684},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3729395568370819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3473803699016571},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3170577883720398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11377358436584473}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8416123390197754},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6438164710998535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4890754818916321},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4562074840068817},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.4497329592704773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4347277581691742},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4324013590812683},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.38712361454963684},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3729395568370819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3473803699016571},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3170577883720398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11377358436584473},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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":[{"descriptor_ui":"D000077321","descriptor_name":"Deep Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000077321","descriptor_name":"Deep Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000077321","descriptor_name":"Deep Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000077321","descriptor_name":"Deep Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000077321","descriptor_name":"Deep Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000544","descriptor_name":"Alzheimer Disease","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":true},{"descriptor_ui":"D000544","descriptor_name":"Alzheimer Disease","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":true},{"descriptor_ui":"D000544","descriptor_name":"Alzheimer Disease","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":true},{"descriptor_ui":"D000544","descriptor_name":"Alzheimer Disease","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":true},{"descriptor_ui":"D000544","descriptor_name":"Alzheimer Disease","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":true},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D005260","descriptor_name":"Female","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005260","descriptor_name":"Female","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005260","descriptor_name":"Female","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005260","descriptor_name":"Female","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005260","descriptor_name":"Female","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D008297","descriptor_name":"Male","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008297","descriptor_name":"Male","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008297","descriptor_name":"Male","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008297","descriptor_name":"Male","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008297","descriptor_name":"Male","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018450","descriptor_name":"Disease Progression","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D018450","descriptor_name":"Disease Progression","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D018450","descriptor_name":"Disease Progression","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D018450","descriptor_name":"Disease Progression","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D018450","descriptor_name":"Disease Progression","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2024.3394598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3394598","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:38771688","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38771688","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1857789879","https://openalex.org/W2000739322","https://openalex.org/W2021505259","https://openalex.org/W2064675550","https://openalex.org/W2100649405","https://openalex.org/W2109409043","https://openalex.org/W2119963163","https://openalex.org/W2157331557","https://openalex.org/W2165289905","https://openalex.org/W2168771200","https://openalex.org/W2517500902","https://openalex.org/W2909627766","https://openalex.org/W2923917921","https://openalex.org/W2947722222","https://openalex.org/W2963351448","https://openalex.org/W2963360736","https://openalex.org/W2969781782","https://openalex.org/W2979455765","https://openalex.org/W2982443576","https://openalex.org/W3009612940","https://openalex.org/W3036550760","https://openalex.org/W3047286661","https://openalex.org/W3144630859","https://openalex.org/W3163616589","https://openalex.org/W3173899333","https://openalex.org/W3215399882","https://openalex.org/W4318827000","https://openalex.org/W4319335604","https://openalex.org/W4385245566","https://openalex.org/W4385757406","https://openalex.org/W4386918813","https://openalex.org/W4387146015","https://openalex.org/W6631190155","https://openalex.org/W6745767635","https://openalex.org/W6749825310","https://openalex.org/W6751354539","https://openalex.org/W6752307458","https://openalex.org/W6755848407","https://openalex.org/W6767145620","https://openalex.org/W6767406340","https://openalex.org/W6767877913","https://openalex.org/W6778353478","https://openalex.org/W6779435032","https://openalex.org/W6803139977","https://openalex.org/W6810523374"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W625783435","https://openalex.org/W2048742619","https://openalex.org/W3095242670","https://openalex.org/W3033597970","https://openalex.org/W3008584592"],"abstract_inverted_index":{"Alzheimer's":[0],"disease":[1],"(AD)":[2],"is":[3,20],"a":[4,109,118,162,190],"devastating":[5],"neurodegenerative":[6],"condition":[7],"that":[8,149,167,193],"precedes":[9],"progressive":[10],"and":[11,25,53,67,92,123,172,183,216,223],"irreversible":[12],"dementia;":[13],"thus,":[14],"predicting":[15,213],"its":[16,130],"progression":[17],"over":[18,219],"time":[19,220],"vital":[21],"for":[22,112],"clinical":[23,156,214],"diagnosis":[24],"treatment.":[26],"For":[27],"this,":[28],"numerous":[29],"studies":[30],"have":[31,69,187],"implemented":[32],"structural":[33],"magnetic":[34],"resonance":[35],"imaging":[36],"(MRI)":[37],"to":[38,71,81,145,201],"model":[39],"AD":[40,95],"progression,":[41],"focusing":[42],"on":[43],"three":[44,177],"integral":[45,80],"aspects:":[46],"1)":[47],"temporal":[48,55],"variability;":[49],"2)":[50],"incomplete":[51,142],"observations;":[52],"3)":[54],"geometric":[56,101,164],"characteristics.":[57],"However,":[58],"many":[59],"pioneer":[60],"deep":[61],"learning-based":[62],"approaches":[63],"addressing":[64],"data":[65,115],"variability":[66],"sparsity":[68],"yet":[70],"consider":[72],"inherent":[73],"geometrical":[74],"properties":[75,78],"sufficiently.":[76],"These":[77],"are":[79,150],"modeling":[82,102,113],"as":[83,108],"they":[84],"correlate":[85],"with":[86,198],"brain":[87],"region":[88],"size,":[89],"thickness,":[90],"volume,":[91],"shape":[93],"in":[94,126,221],"progression.":[96],"The":[97],"ordinary":[98],"differential":[99],"equation-based":[100],"method":[103],"(ODE-RGRU)":[104],"has":[105],"recently":[106],"emerged":[107],"promising":[110],"strategy":[111],"time-series":[114],"by":[116,175,212],"intertwining":[117],"recurrent":[119],"neural":[120],"network":[121],"(RNN)":[122],"an":[124,234],"ODE":[125],"Riemannian":[127],"space.":[128],"Despite":[129],"achievements,":[131],"ODE-RGRU":[132],"encounters":[133],"limitations":[134],"when":[135],"extrapolating":[136],"positive":[137],"definite":[138],"symmetric":[139],"matrices":[140],"from":[141],"samples,":[143],"leading":[144],"feature":[146],"reverse":[147],"occurrences":[148],"particularly":[151],"problematic,":[152],"especially":[153],"within":[154],"the":[155,195],"facet.":[157],"Therefore,":[158],"this":[159],"study":[160],"proposes":[161],"novel":[163],"learning":[165],"approach":[166],"models":[168],"longitudinal":[169],"MRI":[170],"biomarkers":[171],"cognitive":[173,217],"scores":[174,218],"combining":[176],"modules:":[178],"topological":[179],"space":[180],"shift,":[181],"ODE-RGRU,":[182],"trajectory":[184],"estimation.":[185],"We":[186,206],"also":[188],"developed":[189],"training":[191],"algorithm":[192],"integrates":[194],"manifold":[196],"mapping":[197],"monotonicity":[199],"constraints":[200],"reflect":[202],"measurement":[203],"transition":[204],"irreversibility.":[205],"verify":[207],"our":[208,230],"proposed":[209,231],"method's":[210],"efficacy":[211],"labels":[215],"regular":[222],"irregular":[224],"settings.":[225],"Furthermore,":[226],"we":[227],"thoroughly":[228],"analyze":[229],"framework":[232],"through":[233],"ablation":[235],"study.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
