Spatial Hierarchical Clustering Using Directional Derivatives

• Activity Number: 87
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 8:30 PM to 10:30 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Candace Berrett and Maria A. Terres and Matthew Heaton*+ and William Christensen
• Companies: Brigham Young University and Duke University and Brigham Young University and Brigham Young University
• Keywords: Geostatistics ; Gaussian process ; Parallel computing ; Spatial partition

Abstract

The Gaussian process forms the statistical basis to perform analysis for spatial data. However, computational requirements for Gaussian process models can be prohibitive for large datasets. We propose to use spatial clustering as a method to distribute the computational burden of Gaussian process model fitting across multiple cores and nodes. Specifically, we consider forming independent spatial clusters using directional derivatives as a measure of cluster dissimilarity. Intuitively, large directional derivatives indicate directions of rapid increase or decrease; therefore, clustering based on directional derivatives will divide spatial observations based on the rate of change in the spatial surface. Spatial contiguity is enforced by only clustering Voronoi neighbors. Spatial kriging is performed by assigning prediction sites to the cluster of its nearest neighbor. We develop hierarchal clustering algorithms that give fixed cluster assignments as well as a model based clustering strategy. The resulting methodology is illustrated using simulated and real spatial data.