Geographically weighted regression (GWR) introduces the distance weighted kernel function to examine the non-stationarity of geographical phenomena and improve the performance of global regression. However, GWR calibration becomes critical when using a serial computing mode to process large volumes of data. To address this problem, an improved approach based on the compute unified device architecture (CUDA) parallel architecture fast-parallel-GWR (FPGWR) is proposed in this paper to efficiently handle the computational demands of performing GWR over millions of data points. FPGWR is capable of decomposing the serial process into parallel atomic modules and optimizing the memory usage. To verify the computing capability of FPGWR, we designed simulation datasets and performed corresponding testing experiments. We also compared the performance of FPGWR and other GWR software packages using open datasets. The results show that the runtime of FPGWR is negatively correlated with the CUDA core number, and the calculation efficiency of FPGWR achieves a rate of thousands or even tens of thousands times faster than the traditional GWR algorithms. FPGWR provides an effective tool for exploring spatial heterogeneity for large-scale geographic data (geodata).

Geographically weighted regression (GWR) is a classical method for estimating nonstationary relationships. Notwithstanding the great potential of the model for processing geographic data, its large-scale application still faces the challenge of high computational costs. To solve this problem, we proposed a computationally efficient GWR method, called K-Nearest Neighbors Geographically weighted regression (KNN-GWR). First, it utilizes a k-dimensional tree (KD tree) strategy to improve the speed of finding observations around the regression points, and, to optimize the memory complexity, the submatrices of neighbors are extracted from the matrix of the sample dataset. Next, the optimal bandwidth is found by referring to the spatial clustering relationship explained by K-means. Finally, the performance and accuracy of the proposed KNN-GWR method was evaluated using a simulated dataset and a Chinese house price dataset. The results demonstrated that the KNN-GWR method achieved computational efficiency thousands of times faster than existing GWR algorithms, while ensuring accuracy and significantly improving memory optimization. To the best of our knowledge, this method was able to run hundreds of thousands or millions of data on a standard computer, which can inform improvement in the efficiency of local regression models.

A spatial and temporal heterogeneity analysis of residential land prices, in general, is crucial for maintaining high-quality economic development. Previous studies have attempted to explain the geographical evolution rule by studying spatial-temporal heterogeneity, but they have neglected the contextual information, such as school district, industrial zone, population density, and job density, associated with residential land prices. Therefore, in this study, we consider contextual factors and propose a revised local regression algorithm called the contextualized geographically and temporally weighted regression (CGTWR), to effectively address spatiotemporal heterogeneity, and to creatively extend the feasibility of importing the contextualization into the GTWR model. The quantitative impact of contextual information on residential land prices was identified in Shijiazhuang (SJZ) city from 1974 to 2021. Empirical analyses demonstrated that school district and industrial zone factors played important roles in residential land prices. Notably, the distance from a residential area to an industrial zone was significantly positively correlated with residential land prices. In addition, a positive relationship between school districts and residential land prices was also observed. Finally, the R² value of the CGTWR model was 92%, which was superior to those of ordinary least squares (OLS, 76%), geographically weighted regression (GWR, 85%), contextualized geographically weighted regression (CGWR, 86%), and GTWR (90%) models. These evaluation results indicate that the CGTWR algorithm, which incorporates contextual information and spatiotemporal variation, could provide policy makers with evidence for understanding the nature of varying relationships within a land price dataset in China.