Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty


Lei Du, Northwestern Polytechnical University
Kefei Liu, Indiana University-Purdue University Indianapolis
Xiaohui Yao, Indiana University-Purdue University Indianapolis
Jingwen Yan, Indiana University-Purdue University Indianapolis
Shannon L. Risacher, Indiana University-Purdue University Indianapolis
Junwei Han, Northwestern Polytechnical University
Lei Guo, Northwestern Polytechnical University
Andrew J. Saykin, Indiana University-Purdue University Indianapolis
Li Shen, Indiana University-Purdue University Indianapolis
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 Medical School
John Morris, Washington University in St. Louis
Leslie M. Shaw, University of Pennsylvania
Zaven Khachaturian, Prevent Alzheimer’s Disease
Greg Sorensen, Siemens AG
Maria Carrillo, Alzheimer's Association
Lew Kuller, University of Pittsburgh
Marc Raichle, Washington University in St. Louis
Steven Paul, Cornell University
Peter Davies, Albert Einstein College of Medicine of Yeshiva University
Howard Fillit, AD Drug Discovery Foundation
Franz Hefti, Acumen Pharmaceuticals
David Holtzman, Washington University in St. Louis
M. Marcel Mesulam, Northwestern University
William Potter, National Institute of Mental Health (NIMH)

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Scientific Reports





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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 ℓ 1 -norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the ℓ1 -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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