High-Efficiency Geographically Weighted Regression based on CUDA: an enhanced algorithm with adaptive kernel for investigating spatial non-stationarity in large-scale observations

Abstract

Geographically Weighted Regression (GWR) enables local regression coefficients to vary at each point, thereby providing a more accurate depiction of variable relationships. However, GWR’s need to construct a regression model for each location results in high computational costs, particularly for datasets with tens of millions of records, limiting its applicability in the era of big data. To overcome such limitation, this paper introduces High-Efficiency Geographically Weighted Regression (HE-GWR) for truncated kernels, a scalable open-source implementation leveraging the Compute Unified Device Architecture (CUDA) and the K-nearest neighbor (KNN) technique. In this method, the serial computation process is decomposed into parallel atomic modules and KNN search is utilized to extract neighboring sub-matrices from the sample dataset matrix. This optimization enhances the matrix operations required for computing local regression coefficients, enabling the method to scale effectively to datasets with tens of millions of observations. To assess the performance of HE-GWR, we evaluated it using three large datasets. The results demonstrated that HE-GWR effectively utilizes GPU computational power and significantly outperforms existing open-source GWR packages. Our method provides a valuable solution for enhancing the efficiency of local regression models, enabling the processing of datasets with tens of millions of observations on standard computers.