ABSTRACT As an established spatial analytical tool, Geographically Weighted Regression (GWR) has been applied across a variety of disciplines. However, its usage can be challenging for large datasets, which are increasingly prevalent in today’s digital world. In this study, we propose two high-performance R solutions for GWR via Multi-core Parallel (MP) and Compute Unified Device Architecture (CUDA) techniques, respectively GWR-MP and GWR-CUDA. We compared GWR-MP and GWR-CUDA with three existing solutions available in Geographically Weighted Models (GWmodel), Multi-scale GWR (MGWR) and Fast GWR (FastGWR). Results showed that all five solutions perform differently across varying sample sizes, with no single solution a clear winner in terms of computational efficiency. Specifically, solutions given in GWmodel and MGWR provided acceptable computational costs for GWR studies with a relatively small sample size. For a large sample size, GWR-MP and FastGWR provided coherent solutions on a Personal Computer (PC) with a common multi-core configuration, GWR-MP provided more efficient computing capacity for each core or thread than FastGWR. For cases when the sample size was very large, and for these cases only, GWR-CUDA provided the most efficient solution, but should note its I/O cost with small samples. In summary, GWR-MP and GWR-CUDA provided complementary high-performance R solutions to existing ones, where for certain data-rich GWR studies, they should be preferred.

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High-performance solutions of geographically weighted regression in R

Abstract Incident data, a form of big data frequently used in urban studies, are characterized by point features with high spatial and temporal resolution and categorical values. In contrast to panel data, such spatial data pooled over time reflect multi-directional spatial effects but only unidirectional temporal effects, which are challenging to analyze. This paper presents an innovative approach to address this challenge – a geographically and temporally weighted co-location quotient which includes global and local computation, a method to calculate a spatiotemporal weight matrix and a significance test using Monte Carlo simulation. This new approach is used to identify spatio-temporal crime patterns across Greater Manchester in 2016 from open source recorded crime data. The results show that this approach is suitable for the analysis and visualization of spatio-temporal dependence and heterogeneity in categorical spatial data pooled over time. It is particularly useful for detecting symmetrical spatio-temporal co-location patterns and mapping local clusters. The method also addresses the unbalanced temporal scale problem caused by unidirectional temporal data representation and explores potential impacts. The empirical evidence of the spatiotemporal crime patterns might usefully be deployed to inform the development of criminological theory by helping to disentangle the relationships between crime and the urban environment.

Geographically and temporally weighted co-location quotient: an analysis of spatiotemporal crime patterns in greater Manchester

Vehicle crashes on roads are caused by many factors. However, the influence of these factors is not necessarily homogenous across locations, which is a challenge for non-stationary modeling approaches. To address this problem, this paper adopts two types of methods allowing parameters to fluctuate among observations, that is, the random parameter approach and the geographically weighted regression (GWR) approach. With road curvature, curve length, pavement friction, and traffic volume as independent variables, vehicle crash frequencies are modeled by two non-spatial methods, including the negative binomial (NB) model and random parameter negative binomial (RPNB), as well as three spatial methods (GWR approach). These models are calibrated in microlevel using a dataset of 9415 horizontal curve segments with a total length of 1545 kilometers for a period of three years (2016–2018) over the State of Indiana. The results revealed that the GWR approach can capture spatial heterogeneity and therefore significantly outperforms the conventional non-spatial approach. Based on the Akaike Information Criterion (AICc), geographically weighted negative binomial regression (GWNBR) was proved to be a superior approach for statewide microlevel crash analysis.

https://www.mdpi.com/2220-9964/10/5/286/pdf

Non-Stationary Modeling of Microlevel Road-Curve Crash Frequency with Geographically Weighted Regression

Air pollution has become a global public health risk factor as rapid urbanization advances. To observe the air pollution situation, air monitoring stations have been established in many cities, which record six air pollutants. Previous studies have identified cities exhibiting similar air pollution characteristics by combining principal component analysis (PCA) with cluster analysis (CA). However, spatial and temporal effects were neglected. In this paper, we focus on the combination of GTWPCA and STCA, which fully incorporates spatio-temporal effects. It is then applied to air pollution data from the top 10 urban agglomerations in China during 2016-2021. Key experimental findings include: 1. GTWPCA provides a more detailed interpretation of local variation than PCA. 2. Compared with CA, STCA highlights the coupling effect in the spatial and temporal dimensions. 3. The combination of GTWPCA and STCA captures similar air pollution characteristics from spatio-temporal perspectives, which has the potential to help environmental authorities take further action to control air pollution. 

Exploring air pollution characteristics from spatio-temporal perspective: A case study of the top 10 urban agglomerations in China.

Abstract Data from monitoring programs with high spatial resolution but low temporal resolution are often overlooked when assessing temporal trends, as the data structure does not permit the use of established trend analysis methods. However, the data include uniquely detailed information about geographically differentiated temporal trends driven by large-scale influences, such as climate or airborne deposition. In this study, we used geographically weighted regression models, extended with a temporal component, to evaluate linear and nonlinear trends in environmental monitoring data. To improve the results, we tested approaches for station-wise pre-processing of data and for validation of the resulting models. To illustrate the method, we used data on changes in total organic carbon (TOC) obtained in a monitoring program of around 4800 Swedish lakes observed once every 6 years between 2008 and 2021. On applying the methods developed here, we identified nonlinear changes in TOC from consistent negative trends over most of Sweden around 2010 to positive trends during later years in parts of the country. 

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Temporal trend evaluation in monitoring programs with high spatial resolution and low temporal resolution using geographically weighted regression models

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).

A CUDA-Based Parallel Geographically Weighted Regression for Large-Scale Geographic Data

In spatiotemporal applications, geographically weighted principal component analysis (GWPCA) is commonly adopted to describe spatial heterogeneity. However, time effects are ignored in GWPCA. In this study, the temporal effect was incorporated into GWPCA . Thus, an extended model, geographically and temporally weighted principal component analysis (GTWPCA), was developed to simultaneously explore spatial and temporal non-stationarity. The GTWPCA was implemented using a case study of air pollution in China. The results mainly show that GTWPC1 (the local component one in GTWPCA) corresponds to a ‘winning group’ with constantly varying ‘winning’ variables adapted to the spatiotemporal non-stationary characteristics of air pollution in China. 

/pdf/geographically-and-temporally-weighted-principal-component-1xe58h9u.pdf

Jiakuan Han

Papers

A CUDA-Based Parallel Geographically Weighted Regression for Large-Scale Geographic Data

Geographically and temporally weighted principal component analysis: a new approach for exploring air pollution non-stationarity in China, 2015–2019

Exploring air pollution characteristics from spatio-temporal perspective: A case study of the top 10 urban agglomerations in China.