Similarity-weighted and geographically weighted regression using a dual-branch neural network architecture

Similarity and geographically weighted regression (SGWR), proposed by Lessani and Li, innovatively combines attribute similarity with geographical proximity. However, SGWR employs a simple kernel function to map attribute weights and uses a globally consistent fusion parameter to combine them, rendering it incapable of adapting to local variations in dominant factors. Furthermore, SGWR employs an equal-weight summation method to compute attribute distances, thereby disregarding variations in the importance of individual attributes. This study introduces a similarity-weighted and geographically weighted regression using neural networks (SGNNWR) to address these issues. It offers two key advantages. First, SGNNWR employs a dual-branch neural network architecture to construct kernel functions, thereby precisely adapting to the nonlinear distance-decay processes in both the geospatial and attribute spaces. Second, it introduces a dual-attention mechanism to improve interpretability and adaptability. Channel attention identifies dominant attributes and calculates attribute distances. Branch attention adjusts local fusion parameters between geographic and attribute branches. Evaluations across three empirical datasets demonstrate that SGNNWR outperforms baseline models in both goodness-of-fit and prediction accuracy. Ablation experiments further validate the effectiveness of the attention mechanisms.