Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty
Authors: Du Lei , Liu Kefei , Yao Xiaohui , Yan Jingwen , Risacher Shannon L. , Han Junwei , Guo Lei , Saykin Andrew J. , Shen Li ,   Alzheimer’s Disease Neuroimaging Initiative, Weiner Michael W. , Aisen Paul , Petersen Ronald , Jack Clifford R. , Jagust William , Trojanowki John Q. , Toga Arthur W. , Beckett Laurel , Green Robert C. , Morris John , Shaw Leslie M. , Khachaturian Zaven , Sorensen Greg , Carrillo Maria , Kuller Lew , Raichle Marc , Paul Steven , Davies Peter , Fillit Howard , Hefti Franz , Holtzman David , Mesulam M. Marcel , Potter William , Snyder Peter , Schwartz Adam , Montine Tom , Thomas Ronald G. , Donohue Michael , Walter Sarah , Gessert Devon , Sather Tamie , Jiminez Gus , Balasubramanian Archana B. , Mason Jennifer , Sim Iris , Harvey Danielle , Bernstein Matthew , Fox Nick , Thompson Paul , Schuff Norbert , DeCArli Charles , Borowski Bret , Gunter Jeff , Senjem Matt , Vemuri Prashanthi , Jones David , Kantarci Kejal , Ward Chad , Koeppe Robert A. , Foster Norm , Reiman Eric M. , Chen Kewei , Mathis Chet , Landau Susan , Cairns Nigel J. , Franklin Erin , Taylor-Reinwald Lisa , Lee Virginia , Korecka Magdalena , Figurski Michal , Crawford Karen , Neu Scott , Foroud Tatiana M. , Potkin Steven , Faber Kelley , Kim Sungeun , Nho Kwangsik , Thal Leon , Buckholtz Neil , Albert Marilyn , Frank Richard , Hsiao John , Kaye Jeffrey , Quinn Joseph , Silbert Lisa , Lind Betty , Carter Raina , Dolen Sara , Schneider Lon S. , Pawluczyk Sonia , Beccera Mauricio , Teodoro Liberty , Spann Bryan M. , Brewer James , Vanderswag Helen , Fleisher Adam , Heidebrink Judith L. , Lord Joanne L. , Mason Sara S. , Albers Colleen S. , Knopman David , Johnson Kris , Doody Rachelle S. , Villanueva-Meyer Javier , Pavlik Valory , Shibley Victoria , Chowdhury Munir , Rountree Susan , Dang Mimi , Stern Yaakov , Honig Lawrence S. , Bell Karen L. , Ances Beau , Carroll Maria , Creech Mary L. , Franklin Erin , Mintun Mark A. , Schneider Stacy , Oliver Angela , Marson Daniel , Geldmacher David , Love Marissa Natelson , Griffith Randall , Clark David , Brockington John , Roberson Erik , Grossman Hillel , Mitsis Effie , Shah Raj C. , deToledo-Morrell Leyla , Duara Ranjan , Greig-Custo Maria T. , Barker Warren , Onyike Chiadi , D’Agostino Daniel , Kielb Stephanie , Sadowski Martin , Sheikh Mohammed O. , Ulysse Anaztasia , Gaikwad Mrunalini , Murali Doraiswamy P. , Petrella Jeffrey R. , Borges-Neto Salvador , Wong Terence Z. , Coleman Edward , Arnold Steven E. , Karlawish Jason H. , Wolk David A. , Clark Christopher M. , Smith Charles D. , Jicha Greg , Hardy Peter , Sinha Partha , Oates Elizabeth , Conrad Gary , Lopez Oscar L. , Oakley Mary Ann , Simpson Donna M. , Porsteinsson Anton P. , Goldstein Bonnie S. , Martin Kim , Makino Kelly M. , Ismail M. Saleem , Brand Connie , Preda Adrian , Nguyen Dana , Womack Kyle , Mathews Dana , Quiceno Mary , Levey Allan I. , Lah James J. , Cellar Janet S. , Burns Jeffrey M. , Swerdlow Russell H. , Brooks William M. , Apostolova Liana , Tingus Kathleen , Woo Ellen , Silverman Daniel H. S. , Lu Po H. , Bartzokis George , Graff-Radford Neill R , Parfitt Francine , Poki-Walker Kim , Farlow Martin R. , Marie Hake Ann , Matthews Brandy R. , Brosch Jared R. , Herring Scott , van Dyck Christopher H. , Carson Richard E. , MacAvoy Martha G. , Varma Pradeep , Chertkow Howard , Bergman Howard , Hosein Chris , Black Sandra , Stefanovic Bojana , Caldwell Curtis , Robin Hsiung Ging-Yuek , Mudge Benita , Sossi Vesna , Feldman Howard , Assaly Michele , Finger Elizabeth , Pasternack Stephen , Rachisky Irina , Rogers John , Trost Dick , Kertesz Andrew , Bernick Charles , Munic Donna , Rogalski Emily , Lipowski Kristine , Weintraub Sandra , Bonakdarpour Borna , Kerwin Diana , Wu Chuang-Kuo , Johnson Nancy , Sadowsky Carl , Villena Teresa , Scott Turner Raymond , Johnson Kathleen , Reynolds Brigid , Sperling Reisa A. , Johnson Keith A. , Marshall Gad , Yesavage Jerome , Taylor Joy L. , Lane Barton , Rosen Allyson , Tinklenberg Jared , Sabbagh Marwan N. , Belden Christine M. , Jacobson Sandra A. , Sirrel Sherye A. , Kowall Neil , Killiany Ronald , Budson Andrew E. , Norbash Alexander , Lynn Johnson Patricia , Obisesan Thomas O. , Wolday Saba , Allard Joanne , Lerner Alan , Ogrocki Paula , Tatsuoka Curtis , Fatica Parianne , Fletcher Evan , Maillard Pauline , Olichney John , DeCarli Charles , Carmichael Owen , Kittur Smita , Borrie Michael , Lee T.-Y. , Bartha Rob , Johnson Sterling , Asthana Sanjay , Carlsson Cynthia M. , Tariot Pierre , Burke Anna , Milliken Ann Marie , Trncic Nadira , Fleisher Adam , Reeder Stephanie , Bates Vernice , Capote Horacio , Rainka Michelle , Scharre Douglas W. , Kataki Maria , Kelly Brendan , Zimmerman Earl A. , Celmins Dzintra , Brown Alice D. , Pearlson Godfrey D. , Blank Karen , Anderson Karen , Flashman Laura A. , Seltzer Marc , Hynes Mary L. , Santulli Robert B. , Sink Kaycee M. , Gordineer Leslie , Williamson Jeff D. , Garg Pradeep , Watkins Franklin , Ott Brian R. , Tremont Geoffrey , Daiello Lori A. , Salloway Stephen , Malloy Paul , Correia Stephen , Rosen Howard J. , Miller Bruce L. , Perry David , Mintzer Jacobo , Spicer Kenneth , Bachman David , Pomara Nunzio , Hernando Raymundo , Sarrael Antero , Schultz Susan K. , Ekstam Smith Karen , Koleva Hristina , Nam Ki Won , Shim Hyungsub , Relkin Norman , Chaing Gloria , Lin Michael , Ravdin Lisa , Smith Amanda , Ashok Raj Balebail , Fargher Kristin 
Published: October 2017

Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose $${\ell }_{{\bf{1}}}$$

ℓ

1

-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the $${\ell }_{{\bf{1}}}$$

ℓ

1

-norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer’s disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.