An Algorithm for Spatial Data Classification and Automatic Mapping Based on “spin” Correlations

We employ the Ising model from statistical physics in the problem of spatial data classification. We use a multipleclass discretization of the sample values. The proposed algorithm predicts the class identity at unmeasured points based on Monte Carlo simulations that are conditional on the observed data (sample). The algorithm aims to minimize the deviation between the normalized correlation energies of the sample and the entire domain. A hierarchical scheme is used, in which points predicted to belong in lower-level classes retain their identity in the inference of the higher-level classes. The method is non-parametric and thus suitable for application to non-Gaussian data. The method is investigated using real data of surface elevation over a large part of the territory of North America. The effects of the ratio of training to prediction points, the number of classes, and the initial conditions are investigated. Potential extensions of the model are also discussed.