An entropy and dimensional similarity-based geographically Weighted regression (EDSGWR) method

The increasing complexity of spatial data necessitates advanced research into spatial distributions and the interrelationships of geographical phenomena. Classical geographically weighted regression (GWR) methods struggle with abrupt changes in local ranges, such as sudden variations in property prices or pollution levels. This challenge primarily arises because classical GWR models do not account for relationships between the independent variables and their surrounding environmental attributes, limiting their ability to adapt to complex spatial variations. Herein, an entropy-based high-dimensional attribute similarity GWR method—i.e., Entropy and Dimensional Similarity-based Geographically Weighted Regression (EDSGWR)—is proposed to overcome this limitation. This approach dynamically adjusts regression neighborhoods by computing local entropy, refining spatial regression targets for the GWR model. Next, neighborhood contextual data is incorporated into a high-dimensional attribute matrix, where the Hilbert Schmidt independence criterion is used to measure nonlinear dependencies between a target point and its neighbors. These dependencies generate attribute similarity weights, which are then combined with Euclidean spatial weights to form a hybrid model. Finally, Bayesian optimization determines the optimal neighborhood scale and the number of observations in the attribute matrix. Experiments using four open-source spatial datasets demonstrate that EDSGWR outperforms current methods in accuracy, stability, and interpretability, particularly in cases involving abrupt changes and directional data.