A Spectral Clustering Method for Large-Scale Geostatistical Datasets

Spectral clustering is one of the most popular modern clustering techniques for conventional data. However, the application of the general spectral clustering method in the geostatistical data framework poses a double challenge. Firstly, applied to geostatistical data, the general spectral clustering method produces clusters that are spatially non-contiguous which is undesirable for many geoscience applications. Secondly, it is limited in its applicability to large-scale problems due to its high computational complexity. This paper presents a spectral clustering method dedicated to large-scale geostatistical datasets in which spatial dependence plays an important role. It extends a previous work to large-scale geostatistical datasets by computing the similarity matrix only at a reduced set of locations over the study domain referred to as anchor locations. It has the advantage of using all data during the computation of the similarity matrix at anchor locations; so there is no sacrifice of data. The spectral clustering algorithm can then be efficiently performed on this similarity matrix at anchor locations rather than all data locations. Given the resulting cluster labels of anchor locations, a weighted k-nearest-neighbour classifier is trained using their geographical coordinates as covariates and their cluster labels as the response. The assignment of clustering membership to the entire data locations is obtained by applying the trained classifier. The effectiveness of the proposed method to discover spatially contiguous and meaningful clusters in large-scale geostatistical datasets is illustrated using the US National Geochemical Survey database.