M-SGWR: Multiscale Similarity and Geographically Weighted Regression

2026-01-27

AI Summary

This study addresses the limitation of traditional Geographically Weighted Regression (GWR), which relies solely on geographic proximity to model spatial relationships and thus fails to capture associations between non-adjacent yet attribute-similar regions—a critical shortcoming in an era of globalization and digital connectivity. To overcome this, we propose a Multiscale Similarity-enhanced GWR (M-SGWR) framework that, for the first time, integrates attribute similarity as an additional dimension into local regression. M-SGWR constructs a dual-weight matrix combining both geographic proximity and attribute similarity, with a tunable parameter α adaptively balancing their respective contributions for each predictor variable. Extensive experiments across two simulations and one real-world case study demonstrate that M-SGWR consistently outperforms conventional GWR, Similarity-based GWR (SGWR), and Multiscale GWR (MGWR) across all goodness-of-fit metrics, effectively transcending the constraints of spatial adjacency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The first law of geography is a cornerstone of spatial analysis, emphasizing that nearby and related locations tend to be more similar, however, defining what constitutes"near"and"related"remains challenging, as different phenomena exhibit distinct spatial patterns. Traditional local regression models, such as Geographically Weighted Regression (GWR) and Multiscale GWR (MGWR), quantify spatial relationships solely through geographic proximity. In an era of globalization and digital connectivity, however, geographic proximity alone may be insufficient to capture how locations are interconnected. To address this limitation, we propose a new multiscale local regression framework, termed M-SGWR, which characterizes spatial interaction across two dimensions: geographic proximity and attribute (variable) similarity. For each predictor, geographic and attribute-based weight matrices are constructed separately and then combined using an optimized parameter, alpha, which governs their relative contribution to local model fitting. Analogous to variable-specific bandwidths in MGWR, the optimal alpha varies by predictor, allowing the model to flexibly account for geographic, mixed, or non-spatial (remote similarity) effects. Results from two simulation experiments and one empirical application demonstrate that M-SGWR consistently outperforms GWR, SGWR, and MGWR across all goodness-of-fit metrics.

Problem

• spatial analysis
• geographic proximity
• attribute similarity
• local regression
• spatial interaction

Innovation

• Multiscale GWR
• Attribute Similarity
• Spatial Interaction
• Geographically Weighted Regression
• Local Regression