A New Methodology for Automatic Cluster-Based Kriging Using K-Nearest Neighbor and Genetic Algorithms

Abstract

Kriging is a geostatistical interpolation technique that performs the prediction of observations in unknown locations through previously collected data. The modelling of the variogram is an essential step of the kriging process because it drives the accuracy of the interpolation model. The conventional method of variogram modelling consists of using specialized knowledge and in-depth study to determine which parameters are suitable for the theoretical variogram. However, this situation is not always possible, and, in this case, it becomes interesting to use an automatic process. Thus, this work aims to propose a new methodology to automate the estimation of theoretical variogram parameters of the kriging process. The proposed methodology is based on preprocessing techniques, data clustering, genetic algorithms, and the K-Nearest Neighbor classifier (KNN). The performance of the methodology was evaluated using two databases, and it was compared to other optimization techniques widely used in the literature. The impacts of the clustering step on the stationary hypothesis were also investigated with and without trend removal techniques. The results showed that, in this automated proposal, the clustering process increases the accuracy of the kriging prediction. However, it generates groups that might not be stationary. Genetic algorithms are easily configurable with the proposed heuristic when setting the variable ranges in comparison to other optimization techniques, and the KNN method is satisfactory in solving some problems caused by the clustering task and allocating unknown points into previously determined clusters.

EDISON: An Edge-Native Method and Architecture for Distributed Interpolation

“…Park and Apley [38] present a method for patching together locally fitted spatial GP models by augmenting the data with pseudo-observations at the boundaries of the local models, such that the Kriging model remains formally a GP. Yasojima et al [39] propose a heuristic approach using clustering, genetic algorithms and KNN for automatic estimation of variogram parameters in Kriging. van Stein et al [36] propose a method for reducing the computational complexity of Kriging by partitioning the data set into smaller clusters with multiple Kriging models, and then applying approximative Kriging algorithms.…”

“…However, Yasojima et al [39] do not aim to distribute the heavy computations related to GP regression, Hernández-Peñaloza and Beferull-Lozano [40] and Chowdappa et al [41] only consider spatial interpolation, while Amato et al [37] only consider fixed (i.e., nonmobile) sensors. Further, none of the above studies consider an edge-native architecture to mitigate the distribution of computations and reduce the burden on the core networks.…”

An Adaptive Moving Window Kriging Based on K-Means Clustering for Spatial Interpolation

“…They additionally addressed the issue of boundary misspecification, in which boundary points were located inside unsuitable clusters. Yasojima et al [30] later improved the normalization factor technique by integrating it with genetic algorithms and the K-Nearest Neighbors classifier (KNN) to enhance cluster efficiency. Moreover, instead of using one variogram model for all of the clusters, as presented by Abedini et al, automatic estimation of the variogram parameters for each cluster was also introduced.…”