Lei Du, Northwestern Polytechnical University, China
Kefei Liu, Indiana University
Xiaohui Yao, Indiana University
Jingwen Yan, Indiana University
Shannon L. Risacher, Indiana University
Junwei Han, Northwestern Polytechnical University, China
Lei Guo, Northwestern Polytechnical University, China
Andrew J. Saykin, Indiana University
Li Shen, Indiana University
Michael W. Weiner, University of California - San Francisco
Paul Aisen, University of Southern California
Ronald Petersen, Mayo Clinic
Clifford R. Jack, Mayo Clinic
William Jagust, University of California - Berkeley
John Q. Trojanowki, University of Pennsylvania
Arthur W. Toga, University of Southern California
Laurel Beckett, University of California - Davis
Robert C. Green, Harvard University
John Morris, Washington University in St. Louis
Leslie M. Shaw, University of Pennsylvania
Zaven Khachaturian, Prevent Alzheimer’s Disease, 2020, Inc.
Greg Sorensen, Siemens, Germany
Maria Carrillo, Alzheimer’s Association
Lew Kuller, University of Pittsburgh
Marc Raichle, Washington University in St. Louis
Steven Paul, Cornell University
Peter Davies, Yeshiva University
Howard Fillit, AD Drug Discovery Foundation
Franz Hefti, Acumen Pharmaceuticals
David Holtzman, Washington University in St. Louis
Charles D. Smith, University of KentuckyFollow
Gregory Jicha, University of KentuckyFollow
Peter A. Hardy, University of KentuckyFollow
Partha Sinha, University of Kentucky
Elizabeth Oates, University of KentuckyFollow
Gary Conrad, University of KentuckyFollow


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 1-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the 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.

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Notes/Citation Information

Published in Scientific Reports, v. 7, article no. 14052, p. 1-14.

© The Author(s) 2017

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit

Due to the large number of authors, only the first 30 and the authors affiliated with the University of Kentucky are listed in the author section above. For the complete list of authors, please download this article or visit:

This group of authors is collectively known as the Alzheimer’s Disease Neuroimaging Initiative.

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Funding Information

Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics.

Due to the large number of funding sources, only the first few are listed in this section. For the complete list of funding sources, please download this article.

Related Content

The synthetic data sets generated in this work are available from the corresponding authors’ web sites, and The real data set is publicly available in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database repository,