title: Manifold learning on brain functional networks in aging.
abstract: We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient and succinct representation of the functional network and facilitates regression analysis, such as ridge regression, on the brain functional network to more accurately predict age when compared to that of the Euclidean space of functional networks with LLE. Interestingly, using the Log-Euclidean analysis framework, we demonstrate the integration and segregation of cortical-subcortical networks as well as among the salience, executive, and emotional networks across lifespan.
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore; Singapore Institute for Clinical Sciences, Agency for Science, Technology and Research, Singapore; Clinical Imaging Research Center, National University of Singapore, Singapore. Electronic address: bieqa@nus.edu.sg.
authors.forename: Anqi
authors.initials: A
authors.lastname: Qiu
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore.
authors.forename: Annie
authors.initials: A
authors.lastname: Lee
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore.
authors.forename: Mingzhen
authors.initials: M
authors.lastname: Tan
authors.affiliation: Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, USA; Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA.
authors.forename: Moo K
authors.initials: MK
authors.lastname: Chung
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000375:Aging / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D005260:Female; D006801:Humans; D008279:Magnetic Resonance Imaging; D008297:Male; D008875:Middle Aged; D009415:Nerve Net / Q000502:physiology*
keywords: Locally linear embedding; Log-Euclidean Riemannian manifold; Resting state fMRI; Ridge regression; Symmetric positive definite matrix