Geographically Weighted Principal Component Analysis (GWPCA)

The standard approach is to minimize a cross-validation (CV) score or the corrected Akaike Information Criterion (AICc) over a grid of candidate bandwidths. For adaptive kernels the bandwidth is expressed as a number of nearest neighbors rather than a fixed distance, which helps in datasets with uneven spatial sampling density. The GWmodel package in R automates both fixed and adaptive bandwidth selection.

Local eigenvectors are only defined up to a sign change, so a raw map of loadings may show spurious sign reversals. The recommended practice is to apply a sign-alignment convention — for example, constrain the largest-magnitude loading of each local eigenvector to be positive — before mapping. Some implementations in GWmodel include this alignment by default, but it should always be verified.

Yes, in principle. The spatial kernel requires only a symmetric distance matrix, so road-network distance or great-circle distance on a sphere can replace Euclidean distance. However, standard bandwidth-selection routines assume Euclidean space, so custom implementations may be needed when using non-Euclidean metrics. Computational cost also increases substantially with precomputed distance matrices for large datasets.