Open Access
December 2016 Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging
Eardi Lila, John A. D. Aston, Laura M. Sangalli
Ann. Appl. Stat. 10(4): 1854-1879 (December 2016). DOI: 10.1214/16-AOAS975


Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For this purpose a regularization approach is adopted, introducing a smoothing penalty coherent with the geodesic distance over the manifold. The model introduced can be applied to any manifold topology, and can naturally handle missing data and functional samples evaluated in different grids of points. We approach the discretization task by means of finite element analysis, and propose an efficient iterative algorithm for its resolution. We compare the performances of the proposed algorithm with other approaches classically adopted in literature. We finally apply the proposed method to resting state functional magnetic resonance imaging data from the Human Connectome Project, where the method shows substantial differential variations between brain regions that were not apparent with other approaches.


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Eardi Lila. John A. D. Aston. Laura M. Sangalli. "Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging." Ann. Appl. Stat. 10 (4) 1854 - 1879, December 2016.


Received: 1 December 2015; Revised: 1 August 2016; Published: December 2016
First available in Project Euclid: 5 January 2017

zbMATH: 06688760
MathSciNet: MR3592040
Digital Object Identifier: 10.1214/16-AOAS975

Keywords: differential regularization , Functional data analysis , functional magnetic resonance imaging , Principal Component Analysis

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 4 • December 2016
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