INNC interpolation method

Ising model with nearest-neighbor correlations (INNC) is applied for classification/interpolation of spatial data on a regular grid

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous, real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points using Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm respects locally the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and thus suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, it provides a useful tool for filling gaps in gridded data such as satellite images.