Development And Application Of Fast Algorithm For Geographically And Temporally Weighted Regression Model

With the rapid development of science and technology,a large number of spatiotemporal data sets have been generated and accumulated in finance,meteorology,geography,biology and other fields.How to explore the potential spatiotemporal characteristics of data sets has become a hot research frontier.The spatio-temporal geographically weighted regression(GTWR)model was born.Compared with the traditional regression model,GTWR model can deeply reveal the spatial and temporal distribution law of geographical elements and effectively solve the problem of spatial and temporal non-stationary data.The excellent explanatory properties of GTWR model should enable it to be applied to a wider range of fields.However,the traditional algorithm of searching the optimal window width parameters in twodimensional space and time in network format has a very high time complexity.In the modern society with explosive growth and expansion of data,the shortcoming of low computational efficiency of GTWR model is gradually magnified.The existing computational GTWR model package takes a long time to process big data,which poses a great limitation to the application and promotion of GTWR model.In the aspect of parameter optimization of the model,the traditional network search is improved.Based on the accuracy and rapidity of the golden search segmentation algorithm to search the maximum value of the unimodal function,a two-dimensional golden section algorithm is designed to search the spatio-temporal optimal window width parameters of GTWR model.This algorithm obtains the optimal value by continuously reducing the grid interval where the optimal value is located,which can not only greatly reduce the time complexity of searching for the optimal value,but also ensure the accuracy of the result.At the same time,information transfer interface technology is used to realize parallel computing.The idea of parallel computing is to divide data into several parts for simultaneous computation.Since the way to fit GTWR model is point-by-point fitting,and the calculation process between each point is independent of each other,the results of parallel calculation will not change at all,which can greatly improve the calculation speed and ensure that the results are the same as those of point-by-point fitting.Based on Python software,the GTWR-Python software package was designed and written to solve the calculation and statistical inference problems of non-parametric regression modeling of spatial and temporal data.The new software package was used to explore the spatial and temporal distribution characteristics of housing prices in Shanghai,and the coefficient estimates fitting the GTWR model were obtained and the visual analysis was made.It takes only 3 minutes to use GTWR-Python package to fit the GTWR model of Shanghai housing price data,while it takes nearly 3 hours to use the traditional calculation method under the same conditions.This shows the superiority of GTWR-Python package in calculation.The GTWRPython package designed in this paper introduces the 2-D golden section algorithm of window width optimization,which solves the bottleneck of traditional algorithm with low search efficiency and long time consumption.Meanwhile,the parallel computing technology is used to improve the adaptability of non-stationary analysis of large-scale spatio-temporal data.The results of simulation experiments and empirical analysis both confirm that the computational efficiency of GTWR-Python package is significantly better than that of traditional computing methods.