Classification of missing values in spatial data using spin models

TL;DR

This paper introduces a novel spatial classification approach for missing data in two-dimensional grids using spin models like Ising and Potts, which effectively capture spatial correlations without assuming Gaussianity.

Contribution

The study proposes a spin model-based classification method for spatial data missing values, demonstrating competitive performance against standard classifiers and addressing limitations of Gaussian assumptions.

Findings

Spin classifiers are computationally efficient.

Spin methods achieve low misclassification rates.

They effectively reproduce spatial correlations.

Abstract

A problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing. Linear interpolation methods rely on the Gaussian assumption, which is often unrealistic in practice, or normalizing transformations, which are successful only for mild deviations from the Gaussian behavior. We propose to address the problem of missing values estimation on two-dimensional grids by means of spatial classification methods based on spin (Ising, Potts, clock) models. The "spin" variables provide an interval discretization of the process values, and the spatial correlations are captured in terms of interactions between the spins. The spins at the unmeasured locations are classified by means of the "energy matching" principle: the correlation energy of the entire grid (including prediction sites) is estimated from the sample-based correlations. We investigate the performance of the spin classifiers in terms of computational speed, misclassification rate, class histogram and spatial correlations reproduction using simulated realizations of spatial random fields, real rainfall data, and a digital test image. We also compare the spin-based methods with standard classifiers such as the k-nearest neighbor, the fuzzy k-nearest neighbor, and the Support Vector Machine. We find that the spin-based classifiers provide competitive choices.