Adaptive Local Bandwidth Selection for Exact Radial Basis Function Interpolation in Classification and Regression

We present a novel approach to classification and regression using exact radial basis function (RBF) interpolation with adaptive local bandwidth selection. Unliketraditional kernel methods that optimize approximatedecision boundaries, our method solves the kernel interpolation system exactly, guaranteeing perfect reconstruction of training labels. The key innovation is aspatially-adaptive bandwidth scheme where each datapoint is assigned an individual bandwidth parameterderived from its k-nearest neighbor distances. We introduce an automatic selection heuristic k ≈ 1.5√N thatempirically produces well-conditioned kernel matricessuitable for exact solving. Pairwise kernel evaluationsemploy the geometric mean of point-wise bandwidths,enabling smooth interpolation across regions of varying data density. We demonstrate that this approachachieves competitive generalization while providing deterministic, interpretable predictions grounded in exactfunction interpolation theory