Classification of missing values in spatial data using spin models

Area of Science:

• Geospatial analysis
• Statistical modeling
• Computational physics

Background:

• Estimating spatially distributed processes with missing data is a significant challenge.
• Traditional linear interpolation methods often fail due to unrealistic Gaussian assumptions or limited effectiveness of normalizing transformations.

Purpose of the Study:

• To propose and evaluate spatial classification methods based on spin models for missing value estimation on two-dimensional grids.
• To assess the performance of these novel methods against established classification techniques.

Main Methods:

• Utilizing spin (Ising, Potts, clock) models for interval discretization of process values.
• Applying the 'energy matching' principle to classify unmeasured locations based on spatial correlations.
• Comparing spin-based classifiers with k-nearest neighbor, fuzzy k-nearest neighbor, and support vector machine.

Main Results:

• Spin-based classifiers demonstrated competitive performance in computational speed and accuracy.
• Evaluated using simulated spatial random fields, real rainfall data, and a digital test image.
• Successfully reproduced spatial correlations and class histograms.

Conclusions:

• Spin-based spatial classification offers a viable and competitive alternative for missing value estimation in 2D grids.
• These methods effectively capture spatial correlations and handle deviations from Gaussian distributions.