Modeling sparse longitudinal data on Riemannian manifolds
Modeling sparse longitudinal data on Riemannian manifolds
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DOI：
10.1111/biom.13385
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发表时间：
2020-10-28
期刊：
影响因子：
1.9
通讯作者：
Muller, Hans-Georg
中科院分区：
文献类型：
--
作者：
Dai, Xiongtao;Lin, Zhenhua;Muller, Hans-Georg
现代数据收集通常需要在黎曼流形上假设值的纵向重复测量。由于观测值的稀疏性和非线性流形约束，分析这种纵向黎曼数据是具有挑战性的。针对这一挑战，我们提出了纵向黎曼数据的内在功能主成分分析。通过局部Frechet回归估计均值曲线，并平滑均值周围切线空间上线性化数据的协方差结构，从而实现跨受试者的信息池化。利用主分量和最佳线性无偏预测实现了流形轨迹的降维和归一。我们表明，提出的均值和协方差函数估计达到了最先进的收敛速度。举例来说，我们通过用仿射不变度量对对称正定矩阵流形上的连通性建模，研究了阿尔茨海默病和正常参与者的纵向队列大脑连通性的发展。在失业工人不规则记录的纵向情感组成数据的第二个例子中，我们表明，所提出的方法可以很好地解释特征函数和主成分得分。准备本文所用的数据来自阿尔茨海默病神经影像学倡议数据库。
Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Frechet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold-valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state-of-the-art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine-invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.