The Annals of Applied Statistics
- Ann. Appl. Stat.
- Volume 10, Number 4 (2016), 1854-1879.
Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging
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.
Ann. Appl. Stat., Volume 10, Number 4 (2016), 1854-1879.
Received: December 2015
Revised: August 2016
First available in Project Euclid: 5 January 2017
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Lila, Eardi; Aston, John A. D.; Sangalli, Laura M. Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging. Ann. Appl. Stat. 10 (2016), no. 4, 1854--1879. doi:10.1214/16-AOAS975. https://projecteuclid.org/euclid.aoas/1483606843
- Supplement to “Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging”. The online supplementary material contains the theoretic details of the Finite Element discretization approach. Moreover, it includes further simulations on the sphere investigating both the methodology and its robustness to alignment issues.