SMOOTH PRINCIPAL COMPONENT ANALYSIS OVER TWO-DIMENSIONAL MANIFOLDS WITH AN APPLICATION TO NEUROIMAGING
SMOOTH PRINCIPAL COMPONENT ANALYSIS OVER TWO-DIMENSIONAL MANIFOLDS WITH AN APPLICATION TO NEUROIMAGING
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DOI：
10.1214/16-aoas975
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发表时间：
2016-12-01
影响因子：
1.8
通讯作者：
Sangalli, Laura M.
中科院分区：
文献类型：
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作者：
Lila, Eardi;Aston, John A. D.;Sangalli, Laura M.
在分析位于皮质表面的高维神经影像信号的推动下，我们引入了一种新颖的主成分分析技术，该技术可以处理位于二维流形上的功能数据。为此，采用正则化方法，引入与流形上的测地距离一致的平滑惩罚。引入的模型可以应用于任何流形拓扑，并且可以自然地处理缺失数据和在不同点网格中评估的功能样本。我们通过有限元分析来处理离散化任务，并提出了一种有效的迭代算法来解决它。我们将所提出的算法的性能与文献中经典采用的其他方法进行了比较。我们最终将所提出的方法应用于来自人类连接组项目的静息态功能磁共振成像数据，其中该方法显示了大脑区域之间的显着差异变化，而其他方法并不明显。
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.