Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer’s disease
Authors: Lila Eardi , Zhang Wenbo , Rane Levendovszky Swati ,   Alzheimer’s Disease Neuroimaging Initiative, Weiner Michael W , Aisen Paul , Weiner Michael W , Aisen Paul , Petersen Ronald , Jack Clifford R , Jagust William , Trojanowki John Q , Toga Arthur W , Beckett Laurel , Green Robert C , Saykin Andrew J , Morris John C , Perrin Richard J , Shaw Leslie M , Khachaturian Zaven , Carrillo Maria , Potter William , Barnes Lisa , Bernard Marie , Ho Carole , Hsiao John K , Jackson Jonathan , Masliah Eliezer , Masterman Donna , Okonkwo Ozioma , Perrin Richard , Ryan Laurie , Silverberg Nina , Fleisher Adam , Weiner Michael W , Fockler Juliet , Conti Cat , Veitch Dallas , Neuhaus John , Jin Chengshi , Nosheny Rachel , Ashford Miriam , Flenniken Derek , Kormos Adrienne , Green Robert C , Montine Tom , Conti Cat , Petersen Ronald , Aisen Paul , Rafii Michael , Raman Rema , Jimenez Gustavo , Donohue Michael , Gessert Devon , Salazar Jennifer , Zimmerman Caileigh , Cabrera Yuliana , Walter Sarah , Miller Garrett , Coker Godfrey , Clanton Taylor , Hergesheimer Lindsey , Smith Stephanie , Adegoke Olusegun , Mahboubi Payam , Moore Shelley , Pizzola Jeremy , Shaffer Elizabeth , Sloan Brittany , Beckett Laurel , Harvey Danielle , Donohue Michael , Jack Clifford R , Forghanian-Arani Arvin , Borowski Bret , Ward Chad , Schwarz Christopher , Jones David , Gunter Jeff , Kantarci Kejal , Senjem Matthew , Vemuri Prashanthi , Reid Robert , Fox Nick C , Malone Ian , Thompson Paul , Thomopoulos Sophia I , Nir Talia M , Jahanshad Neda , DeCarli Charles , Knaack Alexander , Fletcher Evan , Harvey Danielle , Tosun-Turgut Duygu , Chen Stephanie Rossi , Choe Mark , Crawford Karen , Yushkevich Paul A , Das Sandhitsu , Jagust William , Koeppe Robert A , Reiman Eric M , Chen Kewei , Mathis Chet , Landau Susan , Morris John C , Perrin Richard , Cairns Nigel J , Householder Erin , Franklin Erin , Bernhardt Haley , Taylor-Reinwald Lisa , Shaw Leslie M , Trojanowki John Q , Korecka Magdalena , Figurski Michal , Toga Arthur W , Crawford Karen , Neu Scott , Saykin Andrew J , Nho Kwangsik , Risacher Shannon L , Apostolova Liana G , Shen Li , Foroud Tatiana M , Nudelman Kelly , Faber Kelley , Wilmes Kristi , Weiner Michael W , Thal Leon , Khachaturian Zaven , Hsiao John K , Silbert Lisa C , Lind Betty , Crissey Rachel , Kaye Jeffrey A , Carter Raina , Dolen Sara , Quinn Joseph , Schneider Lon S , Pawluczyk Sonia , Becerra Mauricio , Teodoro Liberty , Dagerman Karen , Spann Bryan M , Brewer James , Vanderswag Helen , Fleisher Adam , Ziolkowski Jaimie , Heidebrink Judith L , Zbizek-Nulph Lisa , Lord Joanne L , Zbizek-Nulph Lisa , Petersen Ronald , Mason Sara S , Albers Colleen S , Knopman David , Johnson Kris , Villanueva-Meyer Javier , Pavlik Valory , Pacini Nathaniel , Lamb Ashley , Kass Joseph S , Doody Rachelle S , Shibley Victoria , Chowdhury Munir , Rountree Susan , Dang Mimi , Stern Yaakov , Honig Lawrence S , Mintz Akiva , Ances Beau , Morris John C , Winkfield David , Carroll Maria , Stobbs-Cucchi Georgia , Oliver Angela , Creech Mary L , Mintun Mark A , Schneider Stacy , Geldmacher David , Love Marissa Natelson , Griffith Randall , Clark David , Brockington John , Marson Daniel , Grossman Hillel , Goldstein Martin A , Greenberg Jonathan , Mitsis Effie , Shah Raj C , Lamar Melissa , Samuels Patricia , Duara Ranjan , Greig-Custo Maria T , Rodriguez Rosemarie , Albert Marilyn , Onyike Chiadi , Farrington Leonie , Rudow Scott , Brichko Rottislav , Kielb Stephanie , Smith Amanda , Raj Balebail Ashok , Fargher Kristin , Sadowski Martin , Wisniewski Thomas , Shulman Melanie , Faustin Arline , Rao Julia , Castro Karen M , Ulysse Anaztasia , Chen Shannon , Sheikh Mohammed O , Singleton-Garvin Jamika , Doraiswamy P Murali , Petrella Jeffrey R , James Olga , Wong Terence Z , Borges-Neto Salvador , Karlawish Jason H , Wolk David A , Vaishnavi Sanjeev , Clark Christopher M , Arnold Steven E , Smith Charles D , Jicha Gregory A , El Khouli Riham , Raslau Flavius D , Lopez Oscar L , Oakley MaryAnn , Simpson Donna M , Porsteinsson Anton P , Martin Kim , Kowalski Nancy , Keltz Melanie , Goldstein Bonnie S , Makino Kelly M , Ismail M Saleem , Brand Connie , Thai Gaby , Pierce Aimee , Yanez Beatriz , Sosa Elizabeth , Witbracht Megan , Kelley Brendan , Nguyen Trung , Womack Kyle , Mathews Dana , Quiceno Mary , Levey Allan I , Lah James J , Hajjar Ihab , Cellar Janet S , Burns Jeffrey M , Swerdlow Russell H , Brooks William M , Silverman Daniel H S , Kremen Sarah , Apostolova Liana , Tingus Kathleen , Lu Po H , Bartzokis George , Woo Ellen , Teng Edmond , Graff-Radford Neill R , Parfitt Francine , Poki-Walker Kim , Farlow Martin R , Hake Ann Marie , Matthews Brandy R , Brosch Jared R , Herring Scott , van Dyck Christopher H , Mecca Adam P , Mecca Adam P , Good Susan P , MacAvoy Martha G , Carson Richard E , Varma Pradeep , Chertkow Howard , Vaitekunis Susan , Hosein Chris , Black Sandra , Stefanovic Bojana , Heyn Chris (Chinthaka) , Hsiung Ging-Yuek Robin , Kim Ellen , Mudge Benita , Sossi Vesna , Feldman Howard , Assaly Michele , Finger Elizabeth , Pasternak Stephen , Rachinsky Irina , Kertesz Andrew , Drost Dick , Rogers John , Grant Ian , Muse Brittanie , Rogalski Emily , Robson Jordan , Mesulam M -Marsel , Kerwin Diana , Wu Chuang-Kuo , Johnson Nancy , Lipowski Kristine , Weintraub Sandra , Bonakdarpour Borna , Pomara Nunzio , Hernando Raymundo , Sarrael Antero , Rosen Howard J , Miller Bruce L , Perry David , Turner Raymond Scott , Johnson Kathleen , Reynolds Brigid , MCCann Kelly , Poe Jessica , Sperling Reisa A , Johnson Keith A , Marshall Gad A , Yesavage Jerome , Taylor Joy L , Chao Steven , Coleman Jaila , White Jessica D , Lane Barton , Rosen Allyson , Tinklenberg Jared , Belden Christine M , Atri Alireza , Spann Bryan M , Clark Kelly A , Zamrini Edward , Sabbagh Marwan , Killiany Ronald , Stern Robert , Mez Jesse , Kowall Neil , Budson Andrew E , Obisesan Thomas O , Ntekim Oyonumo E , Wolday Saba , Khan Javed I , Nwulia Evaristus , Nadarajah Sheeba , Lerner Alan , Ogrocki Paula , Tatsuoka Curtis , Fatica Parianne , Fletcher Evan , Maillard Pauline , Olichney John , DeCarli Charles , Carmichael Owen , Bates Vernice , Capote Horacio , Rainka Michelle , Borrie Michael , Lee T-Y , Bartha Rob , Johnson Sterling , Asthana Sanjay , Carlsson Cynthia M , Perrin Allison , Burke Anna , Scharre Douglas W , Kataki Maria , Tarawneh Rawan , Kelley Brendan , Hart David , Zimmerman Earl A , Celmins Dzintra , Miller Delwyn D , Ponto Laura L Boles , Smith Karen Ekstam , Koleva Hristina , Shim Hyungsub , Nam Ki Won , Schultz Susan K , Williamson Jeff D , Craft Suzanne , Cleveland Jo , Yang Mia , Sink Kaycee M , Ott Brian R , Drake Jonathan , Tremont Geoffrey , Daiello Lori A , Drake Jonathan D , Sabbagh Marwan , Ritter Aaron , Bernick Charles , Munic Donna , Mintz Akiva , O’Connelll Abigail , Mintzer Jacobo , Wiliams Arthur , Masdeu Joseph , Shi Jiong , Garcia Angelica , Sabbagh Marwan , Newhouse Paul , Potkin Steven , Salloway Stephen , Malloy Paul , Correia Stephen , Kittur Smita , Pearlson Godfrey D , Blank Karen , Anderson Karen , Flashman Laura A , Seltzer Marc , Hynes Mary L , Santulli Robert B , Relkin Norman , Chiang Gloria , Lin Michael , Ravdin Lisa , Lee Athena , Weiner Michael W , Aisen Paul , Weiner Michael W , Aisen Paul , Petersen Ronald , Green Robert C , Harvey Danielle , Jack Clifford R , Jagust William , Morris John C , Saykin Andrew J , Shaw Leslie M , Toga Arthur W , Trojanowki John Q , Neylan Thomas , Grafman Jordan , Green Robert C , Montine Tom , Weiner Michael W , Petersen Ronald , Aisen Paul , Jimenez Gustavo , Donohue Michael , Gessert Devon , Salazar Jennifer , Zimmerman Caileigh , Walter Sarah , Adegoke Olusegun , Mahboubi Payam , Hergesheimer Lindsey , Danowski Sarah , Coker Godfrey , Clanton Taylor , Pizzola Jeremy , Shaffer Elizabeth , Nguyen-Barrera Catherine , Neylan Thomas , Hayes Jacqueline , Finley Shannon , Harvey Danielle , Donohue Michael , Jack Clifford R , Bernstein Matthew , Borowski Bret , Gunter Jeff , Senjem Matt , Kantarci Kejal , Ward Chad , Tosun-Turgut Duygu , Chen Stephanie Rossi , Landau Susan , Koeppe Robert A , Foster Norm , Reiman Eric M , Chen Kewei , Morris John C , Perrin Richard J , Franklin Erin , Shaw Leslie M , Trojanowki John Q , Korecka Magdalena , Figurski Michal , Toga Arthur W , Neu Scott , Saykin Andrew J , Foroud Tatiana M , Potkin Steven , Shen Li , Faber Kelley , Kim Sungeun , Nho Kwangsik , Wilmes Kristi , Schneider Lon S , Pawluczyk Sonia , Becerra Mauricio , Teodoro Liberty , Dagerman Karen , Spann Bryan M , Brewer James , Vanderswag Helen , Fleisher Adam , Stern Yaakov , Honig Lawrence S , Mintz Akiva , Shah Raj C , Sood Ajay , Blanchard Kimberly S , Fleischman Debra , Arfanakis Konstantinos , Duara Ranjan , Varon Daniel , Greig Maria T , Doraiswamy P Murali , Petrella Jeffrey R , James Olga , Borges-Neto Salvador , Wong Terence Z , Porsteinsson Anton P , Goldstein Bonnie , Martin Kimberly S , Thai Gaby , Pierce Aimee , Reist Christopher , Yanez Beatriz , Sosa Elizabeth , Witbracht Megan , Sadowsky Carl , Martinez Walter , Villena Teresa , Rosen Howard , Perry David , Turner Raymond Scott , Johnson Kathleen , Reynolds Brigid , MCCann Kelly , Poe Jessica , Sperling Reisa A , Johnson Keith A , Marshall Gad , Belden Christine M , Atri Alireza , Spann Bryan M , Clark Kelly A , Zamrini Edward , Sabbagh Marwan , Obisesan Thomas O , Ntekim Oyonumo E , Wolday Saba , Nwulia Evaristus , Nadarajah Sheeba , Johnson Sterling , Asthana Sanjay , Carlsson Cynthia M , Peskind Elaine R , Petrie Eric C , Li Gail , Yesavage Jerome , Taylor Joy L , Chao Steven , Coleman Jaila , White Jessica D , Lane Barton , Rosen Allyson , Tinklenberg Jared , Lin Michael , Chiang Gloria , Ravdin Lisa , Relkin Norman , O’Connelll Abigail , Mintzer Jacobo , Wiliams Arthur , Mackin Scott , Aisen Paul , Raman Rema , Jimenez-Maggiora Gustavo , Donohue Michael , Gessert Devon , Salazar Jennifer , Zimmerman Caileigh , Walter Sarah , Adegoke Olusegun , Mahboubi Payam , Mackin Scott , Weiner Michael W , Aisen Paul , Raman Rema , Jack Clifford R , Landau Susan , Saykin Andrew J , Toga Arthur W , DeCarli Charles , Koeppe Robert A , Green Robert C , Drake Erin , Weiner Michael W , Aisen Paul , Raman Rema , Donohue Mike , Mackin Scott , Nelson Craig , Bickford David , Butters Meryl , Zmuda Michelle , Jack Clifford R , Bernstein Matthew , Borowski Bret , Gunter Jeff , Senjem Matt , Kantarci Kejal , Ward Chad , Reyes Denise , Koeppe Robert A , Landau Susan , Toga Arthur W , Crawford Karen , Neu Scott , Saykin Andrew J , Foroud Tatiana M , Faber Kelley M , Nho Kwangsik , Nudelman Kelly N , Mackin Scott , Rosen Howard , Nelson Craig , Bickford David , Au Yiu Ho , Scherer Kelly , Catalinotto Daniel , Stark Samuel , Ong Elise , Fernandez Dariella , Butters Meryl , Zmuda Michelle , Lopez Oscar L , Oakley MaryAnn , Simpson Donna M 
Published: March 2024

Abstract
We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer’s disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem as a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally prohibitive in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from Alzheimer’s Disease Neuroimaging Initiative and Parkinson’s Progression Markers Initiative. Through this application, we identify discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer’s disease that are consistent with the existing neuroscience literature.