Nonstationary Gaussian Process Models Using Spatial Hierarchical Clustering from Finite Differences
Nonstationary Gaussian Process Models Using Spatial Hierarchical Clustering from Finite Differences
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DOI：
10.1080/00401706.2015.1102763
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发表时间：
2017-01
期刊：
影响因子：
2.5
通讯作者：
Matthew J. Heaton;W. F. Christensen;Maria A. Terres
中科院分区：
文献类型：
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作者：
Matthew J. Heaton;W. F. Christensen;Maria A. Terres
现代数字数据制作方法，如计算机模拟和遥感，大大增加了在空间领域收集的数据的规模和复杂性。对这些大型空间数据集进行科学调查的分析通常使用高斯过程进行。然而，大型空间数据集的非平稳行为和计算要求可能会阻碍高斯过程模型的有效实现。为了对大型空间数据进行计算上可行的推断，我们考虑使用观测的层次聚类和有限差分作为相异性的度量来将空间区域划分为不相交的集合。直觉上，具有大的有限差分的方向指示快速增加或减少的方向，并且因此适合于划分空间区域。所得到的聚类的空间连续性通过仅聚类Voronoi邻居来实施。在空间聚类之后，我们提出了一个跨集群的非平稳高斯过程模型，该模型允许模型拟合的计算负担分布在多个核心和节点上。该方法的主要动机和说明的应用程序，以验证数字温度数据在休斯顿市以及模拟数据集。本文的补充材料可在网上查阅。
Modern digital data production methods, such as computer simulation and remote sensing, have vastly increased the size and complexity of data collected over spatial domains. Analysis of these large spatial datasets for scientific inquiry is typically carried out using the Gaussian process. However, nonstationary behavior and computational requirements for large spatial datasets can prohibit efficient implementation of Gaussian process models. To perform computationally feasible inference for large spatial data, we consider partitioning a spatial region into disjoint sets using hierarchical clustering of observations and finite differences as a measure of dissimilarity. Intuitively, directions with large finite differences indicate directions of rapid increase or decrease and are, therefore, appropriate for partitioning the spatial region. Spatial contiguity of the resulting clusters is enforced by only clustering Voronoi neighbors. Following spatial clustering, we propose a nonstationary Gaussian process model across the clusters, which allows the computational burden of model fitting to be distributed across multiple cores and nodes. The methodology is primarily motivated and illustrated by an application to the validation of digital temperature data over the city of Houston as well as simulated datasets. Supplementary materials for this article are available online.