Kriging Riemannian Data via Random Domain Decompositions
Kriging Riemannian Data via Random Domain Decompositions
复制标题
通过随机域分解克里格黎曼数据
DOI：
10.1080/10618600.2020.1853548
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
P. Secchi
中科院分区：
文献类型：
--
作者：
A. Menafoglio;D. Pigoli;P. Secchi
摘要黎曼流形上的数据在复杂的空间域上的观测在环境科学和地球科学等领域的应用越来越频繁。对这些数据的分析需要依赖于局部模型来考虑生成随机过程的非平稳性、流形的非线性以及域的复杂拓扑结构。在这篇文章中，我们建议使用一个随机区域分解方法来估计一个整体的本地模型，然后通过Fréchet平均聚合本地模型的预测。该算法介绍了完整的一般性，是有效的数据属于任何光滑黎曼流形，但它随后详细描述的情况下，流形的正定矩阵，超球和Cholesky流形。通过对协方差矩阵和相关矩阵的仿真研究来探索该方法的预测性能，其中使用了Cholesky流形几何。最后，该方法被说明在切萨皮克湾（美国）的环境数据集上观察。本文的补充材料可在网上查阅。
Abstract Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more frequent in applications, for example, in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to account for the nonstationarity of the generating random process, the nonlinearity of the manifold, and the complex topology of the domain. In this article, we propose to use a random domain decomposition approach to estimate an ensemble of local models and then to aggregate the predictions of the local models through Fréchet averaging. The algorithm is introduced in complete generality and is valid for data belonging to any smooth Riemannian manifold but it is then described in details for the case of the manifold of positive definite matrices, the hypersphere and the Cholesky manifold. The predictive performances of the method are explored via simulation studies for covariance matrices and correlation matrices, where the Cholesky manifold geometry is used. Finally, the method is illustrated on an environmental dataset observed over the Chesapeake Bay (USA). Supplementary materials for this article are available online.
DOI：
10.1111/rssb.12320
发表时间：
2018-01
期刊：
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
影响因子：
--
作者：
Mu Niu;P. Cheung;Lizhen Lin;Zhenwen Dai;Neil D. Lawrence;D. Dunson
通讯作者：
Mu Niu;P. Cheung;Lizhen Lin;Zhenwen Dai;Neil D. Lawrence;D. Dunson