A spatiotemporal geographically weighted regression method and device for count data, equipment and storage medium

Abstract

The application provides a spatiotemporal geographical weighted regression method for count data, device, equipment and storage medium, relates to the technical field of spatiotemporal information data analysis. The method comprises the following steps: acquiring multi-source spatiotemporal observation data of a target area; constructing a geographical weighted Poisson regression model or a geographical weighted logistic regression model based on a generalized linear model framework to fit the local spatiotemporal variation relationship between a count type or binary type response variable and an independent variable; solving the regression coefficient of spatiotemporal variation through an iterative algorithm; and finally converting the model output into early warning information, a diversion scheme or a planning decision. The application unifies the description of data discrete characteristics and process spatiotemporal heterogeneity, solves the modeling bias and insufficient precision problem caused by ignoring the spatiotemporal coupling effect and distribution mismatch when the traditional model deals with spatiotemporal data with discrete distribution characteristics, and significantly improves the accuracy and decision support capability of dynamic risk early warning and refined resource allocation in the fields of environmental monitoring, traffic safety and land planning.

Description

Technical Field

[0001] This application relates to the field of spatiotemporal information data analysis technology, and in particular to a spatiotemporal geographic weighted regression method, apparatus, device and storage medium for counting data. Background Technology

[0002] In multiple technological fields such as environmental monitoring, public safety, and land planning, decision-making and analysis heavily rely on the accurate modeling and analysis of count data with spatiotemporal attributes. This type of data, such as the number of times pollutant concentrations exceed standards in a given area (count data), whether traffic accidents occur on a certain road segment (binary data), or the frequency of land use type conversions for a plot of land (count data), generally exhibits complex characteristics of intertwined spatial heterogeneity and temporal dynamics. However, existing mainstream analytical methods have significant limitations in addressing the dual spatiotemporal non-stationarity of this type of data, leading to a series of specific technical problems such as delayed early warnings, inaccurate risk identification, and inappropriate resource allocation.

[0003] Specifically, the existing technical solutions have the following main shortcomings: In terms of precise early warning of environmental pollution, traditional environmental risk analysis models, such as global Poisson regression or logistic regression models, assume that the relationship between influencing factors (such as meteorological conditions and emission source intensity) and the incidence of pollution events is consistent across the entire region and does not change over time. This is clearly inconsistent with the physical reality that pollutant diffusion is affected by local wind fields and temperature stratification, and changes over time. Although models such as geographically weighted Poisson regression (GWPR) introduce spatial heterogeneity analysis capabilities and can characterize the risk differences between different regions, they fail to incorporate the time dimension and cannot effectively predict the dynamic evolution of pollution risk during periods of adverse meteorological conditions, different seasons, or day and night. This results in insufficient time accuracy in early warning information, making it difficult to support real-time and precise emergency response.

[0004] In the dynamic management of traffic safety, traffic accident risk analysis widely employs statistical models fitted with historical data. Global models cannot identify the spatial specificity of accident hotspots, while Geographically Weighted Logical Models (GWLR), which only consider spatial heterogeneity, ignore the time-varying characteristics of the impact of factors such as traffic flow and weather conditions on risk during peak hours, weekends, or severe weather. This results in static or periodically averaged risk hotspot maps that fail to reflect real-time dynamic risk changes caused by temporary construction, large-scale events, or sudden weather events. Consequently, police deployment and early warning issuance lack foresight and dynamic adaptability, hindering the improvement of proactive prevention and control capabilities.

[0005] In optimizing land resource allocation, analyzing the driving forces of land use change is fundamental to scientific planning. Existing research often employs global regression models to explore the average impact of various factors (such as population, economy, and topography) or spatial regression models to capture spatial differentiation. However, land conversion processes are driven by both spatial location (e.g., distance from the city center) and temporal stages, and the importance of these driving forces varies with time and space. Current methods lack the ability to simultaneously characterize the spatiotemporal non-stationarity of these driving forces, making it difficult to reveal when, where, and which factors play a dominant role. This weakens the spatiotemporal relevance and scientific rigor of planning decisions, potentially leading to inefficient land resource allocation.

[0006] In summary, current analytical methods for count-based data in specific technological fields such as environment, transportation, and land use lack the ability to simultaneously model spatial heterogeneity and temporal dynamics. Global models are too general, and purely spatial models ignore the evolutionary process, neither of which can meet the needs of accurate perception, dynamic early warning, and refined management at high spatiotemporal resolution. Therefore, there is an urgent need to develop a novel modeling and analysis method that can unify and integrate spatiotemporal dimensions and is specifically applicable to the characteristics of count and binary data, in order to address the specific technical bottlenecks in these fields. Summary of the Invention

[0007] This application provides a spatiotemporal geographic weighted regression method, apparatus, device, and storage medium for count data. It addresses the shortcomings of existing methods in simultaneously capturing the spatiotemporal nonstationarity of count data, solving problems such as poor real-time warnings, static risk identification, and one-sided decision-making basis caused by the inability of analytical models to simultaneously account for spatiotemporal heterogeneity in specific technical fields such as environmental pollution early warning, traffic safety management, and land resource optimization. Specifically, this application is the first to systematically integrate Poisson regression and logistic regression models into a spatiotemporal geographic weighted regression framework, successfully constructing a spatiotemporal geographic weighted Poisson regression model for count data and a spatiotemporal geographic weighted logistic regression model for binary discrete data. This technical solution achieves methodological innovation in uniformly representing the discrete distribution characteristics of data and the spatiotemporal heterogeneity of processes. Furthermore, this application constructs a complete link from spatiotemporal data modeling to technical decision execution, enabling the direct conversion of high-dimensional analysis results output by the model into control commands that can drive the operation of monitoring and early warning systems, traffic control terminals, and planning auxiliary platforms.

[0008] In a first aspect, this application provides a spatiotemporal geographic weighted regression method for count data, including: Acquire observation data collected at multiple spatiotemporal observation points within a target geographic area, the observation data including the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable The response variable Count data that is a non-negative integer or binary data that takes the value 0 or 1; Based on the spatiotemporal location information of the observation points, a spatiotemporal geographic weighted regression model is constructed through fitting to describe the response variable. With the independent variable The local relationships between them vary with their spatiotemporal locations; the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. ; Based on the spatiotemporal geographic weighted regression model, an analysis result is generated to describe the spatiotemporal distribution pattern of the response variable within the target geographic region, and at least one of the following operations is performed based on the analysis result: outputting prediction and early warning information or optimizing resource allocation strategies.

[0009] In one possible design, the response variable When the count data are non-negative integers, the spatiotemporal geographic weighted regression model is a spatiotemporal geographic weighted Poisson regression model, and its expression is: ; In the formula, express Follows the principle that the mean and variance are both equal. The Poisson distribution, For the regression point number, The number of observation points. No. One variable, For the total number of variables, Indicates the first The spatiotemporal local intercept term of each regression point; Local regression coefficients The estimation is performed using the following iterative formula: ; In the formula, Regression point In the The estimated local regression coefficients for the next iteration; Represents the matrix of independent variables. It is an independent variable matrix transpose; Represents the spatiotemporal weight matrix; It is the first At the regression point in the next iteration The model applies to all observation locations. Predicted value The diagonal weight matrix formed It is a vector composed of the adjusted dependent variable.

[0010] In one possible design, the elements of the spatiotemporal weight matrix are calculated using the following formula: ; In the formula, Indicates the observation point For the regression point Influence weight; Indicates the observation point Regression point The spatiotemporal distance between them; For bandwidth parameters; Represented by natural constant An exponential function with base 0; In the In the next iteration, with the regression point Related weighting matrix With the adjusted dependent variable vector The weighted matrix is ​​defined as follows. This is a diagonal matrix, where the diagonal elements are the predicted estimates of the number of events occurring at each location: ; Adjusted dependent variable vector Defined as a column vector of its components: ; Among them, the Each component Calculated by the following formula: ; In the formula, For the first During the next iteration The corresponding number Linear prediction values ​​for each observation. For the first Regression point at the next iteration The estimated values ​​of the intercept term coefficients, For the first Regression point at the next iteration The Estimates of the coefficients of the independent variables; Indicates the first At the observation location, the first Observed values ​​of the independent variables; For the first The actual observed number of events occurring at each observation location; Indicated based on regression coefficients For the The predicted estimate of the number of times an event will occur at a given location.

[0011] In one possible design, when the response variable When the data is binary data with values ​​of 0 or 1, the spatiotemporal geographic weighted regression model is a spatiotemporal geographic weighted logistic regression model, and its expression is: ; In the formula, right conduct Transformation, express The probability, For the regression point number, The number of sample points. as independent variable The first in One variable, For the total number of variables, Indicates the first The spatiotemporal local intercept term of each regression point; Local regression coefficients The estimation is performed using the following iterative formula: ; ; In the formula, Regression point Position The estimated local regression coefficients for the next iteration; Represents the matrix of independent variables. It is an independent variable matrix transpose; Represents the spatiotemporal weight matrix; It is a vector composed of the adjusted dependent variables. Indicates the first l iteration The probability of.

[0012] In one possible design, the spatiotemporal local regression coefficients at each observation point are solved using an iterative algorithm. At that time, the first The convergence criterion formula for the next iteration is as follows: ; ; ; In the formula, Indicates the first The numerator of the convergence criterion for the next iteration. Indicates the first The denominator of the convergence criterion for the next iteration. Indicates the first Regression point at the next iteration The Estimates of the regression coefficients of the independent variables. Indicates the first The estimated value corresponding to the next iteration. Indicates the first The convergence criterion value of the next iteration. When the value is less than a preset threshold, the iteration is considered to have converged.

[0013] In one possible design, the optimal spatiotemporal bandwidth parameter of the spatiotemporal geographic weighted regression model is adaptively determined by minimizing the Akaike Information Criterion (AICc); wherein the formula for calculating AICc is: ; In the formula, Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. The trace of the hat matrix is ​​a function of the bandwidth.

[0014] In one possible design, the observation data includes environmental pollution monitoring data, traffic accident record data, or regional land use change data; When the observed data is environmental pollution monitoring data, the response variable The independent variable represents the number of events where pollutant concentrations exceed the standard. The analysis includes one or more meteorological parameters such as wind speed, wind direction, temperature, humidity, and air pressure, as well as industrial emission source information; the analysis result is a spatiotemporal distribution map of pollution risk, and the operation performed includes sending early warning information to environmental monitoring terminals in designated areas.

[0015] When the observed data is specifically traffic accident record data, the response variable The independent variable serves as an indicator of the number of accidents or whether an accident has occurred within a specified spatiotemporal unit. The analysis includes one or more traffic and environmental factors such as traffic flow, average vehicle speed, road type, weather conditions, and lighting conditions; the analysis results are a dynamic traffic safety heat map; and the operations performed include generating traffic diversion plans for high-risk road sections or pushing early warning prompts to in-vehicle navigation devices. When the observed data is specifically regional land use change data, the response variable The independent variable is used to define the number of land use type conversions or whether a conversion has occurred for a plot of land within a unit of time. The analysis includes one or more natural and socioeconomic factors such as the administrative division where the land parcel is located, population density, slope, aspect, distance from major transportation routes, and distance from the city center; the analysis results are a spatiotemporal heterogeneity map of the driving forces of land use change, and the operation performed is to optimize the allocation of regional land resources and planning decisions based on the map.

[0016] Secondly, this application provides a spatiotemporal geographic weighted regression apparatus for counting data, the apparatus comprising: The data acquisition module is configured to acquire observation data collected at multiple spatiotemporal observation points within a target geographic area, the observation data including the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable The response variable Count data that is a non-negative integer or binary data that takes the value 0 or 1; The model building module is configured to construct a spatiotemporally weighted regression model based on the spatiotemporal location information of the observation points to describe the response variable. With the independent variable The local relationships between them that change with their spatiotemporal positions; wherein, the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. ; The model application module is configured to generate analysis results based on the spatiotemporal geographic weighted regression model to describe the spatiotemporal distribution pattern of the response variables within the target geographic region, and to perform at least one of the following operations based on the analysis results: outputting prediction and early warning information or optimizing resource allocation strategies.

[0017] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, causing the at least one processor to perform the spatiotemporal geographic weighted regression method for counting data as described in the first aspect and various possible designs of the first aspect.

[0018] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the spatiotemporal geographic weighted regression method for counting data as described in the first aspect and various possible designs of the first aspect.

[0019] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the spatiotemporal geographic weighted regression method for counting data as described in the first aspect and various possible designs of the first aspect.

[0020] The spatiotemporal geographic weighted regression method, apparatus, device, and storage medium for count data provided in this application have at least the following beneficial effects: This application combines the Poisson / logistic regression join function with a spatiotemporal geographic weighting framework, and for the first time constructs GTWPR and GTWLR models. It overcomes the dual limitations of traditional global models neglecting spatial differences and pure spatial geographic weighting models neglecting temporal evolution. It provides a unified and powerful tool for analyzing complex spatiotemporal processes of various count and binary data, expanding the applicability of geographic weighted regression technology from simple spatial analysis to dynamic spatiotemporal modeling, and possesses fundamental theoretical innovation value. Specifically: In terms of environmental pollution monitoring and early warning, this application enables the model to analyze the dynamic evolution mechanism of pollution risk with meteorological processes, seasonal cycles, and diurnal rhythms by coupling the time dimension. The generated spatiotemporal distribution map of pollution risk is transformed from a static spatial snapshot into a dynamic spatiotemporal projection picture, supporting environmental protection departments to implement advanced early warning and precise deployment of emergency resources, and significantly enhancing the ability of proactive intervention and process-based management of environmental risks.

[0021] In terms of traffic safety management, this application can collaboratively identify high-risk road sections in the spatial dimension and high-incidence periods in the temporal dimension. Based on the dynamic risk map output by the model, it can guide traffic management departments to achieve flexible deployment and adaptive scheduling of police resources, and issue risk warnings with spatiotemporal context awareness to connected vehicles, thereby improving the real-time response capability and proactive safety protection level of the traffic system.

[0022] In the field of land resource planning and management, this application can quantitatively reveal the spatiotemporal differentiation patterns of the impact of different natural and socioeconomic driving factors on land use change. The resulting spatiotemporal heterogeneity map of driving forces can provide precise decision-making basis with spatiotemporal differentiation characteristics for territorial spatial planning, assist in the formulation of land use schemes deeply coupled with regional development stages, and optimize the efficiency and sustainability of territorial spatial resource allocation from a technical perspective. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0024] Figure 1 This is a schematic diagram illustrating an application scenario of a spatiotemporal geographic weighted regression method for count data provided in an embodiment of this application. Figure 2 A flowchart illustrating a spatiotemporal geographic weighted regression method for count data provided in this application embodiment; Figure 3 A technical roadmap for a spatiotemporal geographic weighted regression method for count data provided in this application embodiment; Figure 4 Regression coefficients of the first set of simulation experiments provided for embodiments of this application exist Spatial distribution map of time; Figure 5 Regression coefficients of the second set of simulation experiments provided in the embodiments of this application exist Spatial distribution map of time; Figure 6 Regression coefficients of the third set of simulation experiments provided in the embodiments of this application exist Spatial distribution map of time; Figure 7 This is a structural diagram of a spatiotemporal geographic weighted regression device for counting data provided in an embodiment of this application.

[0025] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0026] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0027] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0028] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, they do not mean that the applicant has used or necessarily used the solution.

[0029] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0030] This application provides a spatiotemporal geographic weighted regression method for counting data. For example... Figure 1 The diagram illustrates an application scenario of the spatiotemporal geographic weighted regression method for count data provided in this application embodiment. This application scenario includes a data acquisition component 101, a first terminal 102, and a second terminal 103. The data acquisition component 101 collects observation data from multiple spatiotemporal observation points within a target geographic area and feeds it to the first terminal 102. The first terminal 102, based on the spatiotemporal location information of the observation points in the received observation data, constructs a spatiotemporal geographic weighted regression model through fitting to describe the response variable. With independent variable The local relationships between them change with time and space, and based on the spatiotemporal geographic weighted regression model, the analysis results are generated to describe the spatiotemporal distribution law of the response variables in the target geographic area. The analysis results are fed to the second terminal 103, and the second terminal 103 performs at least one of the following operations based on the analysis results: outputting prediction and early warning information or optimizing resource allocation strategy.

[0031] For example, observational data includes environmental pollution monitoring data, traffic accident record data, or regional land use change data; When the observed data is environmental pollution monitoring data, the data acquisition component 101 can specifically be an Internet of Things (IoT) consisting of air quality monitoring stations, water quality monitoring buoys, and online monitoring equipment for industrial emission outlets deployed in the target area. The first terminal 102 can be deployed on a cloud server or edge computing node of the environmental protection department, running the modeling algorithm of this application. The second terminal 103 can be a large-screen early warning system of the environmental protection command center, a mobile law enforcement terminal, or an air quality release platform for the public. In this scenario, the monitoring equipment collects and uploads pollutant concentrations and related meteorological data from each station in real time. The first terminal 102 dynamically generates a high-resolution spatiotemporal distribution map of pollution risk for the next few hours by fitting a GTWPR model. Based on this, the second terminal 103 pushes precise patrol instructions to law enforcement terminals in high-risk areas and issues tiered early warnings to the public, realizing the transformation from uniform control to precise spatiotemporal intervention, improving emergency response speed and resource utilization efficiency.

[0032] When the observed data specifically refers to traffic accident records, the data acquisition component 101 may include roadside traffic cameras, inductive loop detectors, millimeter-wave radar, floating car GPS data sources, and traffic police accident reporting systems. The first terminal 102 can be deployed in the city's traffic management system or the traffic police brigade's computing center. The second terminal 103 is the traffic police command center's dispatch platform, the vehicle-mounted intelligent terminal of a patrol car on the road, or a navigation and early warning system linked to a map service provider. In this scenario, multi-source data is fused and input into the first terminal 102. Through GTWPR or GTWLR models, not only are stable traffic accident black spots identified, but temporary high-risk road sections that may appear in future set weather and time periods (such as evening rush hour during heavy rain) can also be predicted. Based on this, the second terminal 103 generates dynamic duty plans to guide the forward deployment of police forces. Simultaneously, it pushes real-time warnings to drivers via a navigation app, indicating that the road section ahead is 500 meters away and urging them to slow down and drive cautiously. This shifts safety management from post-accident handling to pre-accident prevention, effectively reducing the accident rate.

[0033] When the observed data specifically refers to regional land use change data, the data acquisition component 101 may include remote sensing satellites, surveying drones, land survey mobile terminals, and socio-economic statistical databases. The first terminal 102 may be deployed on the land and space basic information platform of the natural resources department or the GIS analysis server of the planning institute. The second terminal 103 is a land and space planning auxiliary decision-making system or a single-map implementation supervision system. In this scenario, multi-period remote sensing images and ground survey data are processed by the first terminal 102, and the spatiotemporal variability of the impact of different natural geographical conditions and location economic factors on processes such as arable land conversion and construction land expansion is quantitatively analyzed using the model of this invention. The generated spatiotemporal heterogeneity map of driving forces is presented on the second terminal 103, allowing planners to intuitively see the dominant driving factors and their intensity changes in different zones and planning periods. This provides a scientific basis for delineating differentiated control zones and formulating time-precise land supply plans, realizing an upgrade from experience-based planning to data-driven, spatiotemporally precise planning, and improving the level of refinement in land and space governance.

[0034] Specifically, such as Figure 2 As shown, the spatiotemporal geographic weighted regression method for count data includes the following steps S10-S30.

[0035] S10: Acquire observation data collected at multiple spatiotemporal observation points within the target geographic area. The observation data includes the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable Response variable The count data is a non-negative integer or a binary data value of 0 or 1.

[0036] The implementation of step S10 essentially involves spatiotemporal alignment, attribute extraction, and business definition of monitoring, sensing, and survey data in specific fields, thereby constructing a standardized dataset that can be used for spatiotemporal geographic weighted regression model analysis.

[0037] In some embodiments, the observation data originates from a network of national and provincial automatic air quality monitoring stations deployed in the target city. Each monitoring station serves as an observation point, with its spatial coordinates... This refers to the longitude and latitude of the station. Time stamp. The data is represented by an hourly timestamp. The independent variable is... Data collected synchronously by sensors within the station may include, but is not limited to, concentrations of sulfur dioxide (SO2), nitrogen dioxide (NO2), ozone (O3), carbon monoxide (CO), wind speed, wind direction, temperature, and relative humidity at that moment. Response variables In this scenario, data is defined as count data. Specifically, taking PM2.5, the primary pollutant, as an example, a concentration limit is set according to the national "Ambient Air Quality Standard" (GB 3095-2012). For each monitoring station's hourly data, its 24-hour moving average concentration is calculated. If this value exceeds the set concentration limit, a PM2.5 exceedance event is counted for that hour. Response variable This refers to the cumulative number (non-negative integer) of PM2.5 exceedance events that occurred within the specified hourly timestamp of the day at which the monitoring station is identified. This data can be generated in real-time by the monitoring station's data platform through time window statistics.

[0038] In some embodiments, the observation data originates from the traffic accident database and road sensing equipment of the urban traffic management department. Pre-defined geographic grids or specific road segments within the urban road network are used as observation points, and their spatial coordinates... This refers to the latitude and longitude of the center point of the grid or road segment. Time stamp. This can be a date or a set time period within a day (e.g., morning rush hour 07:00-09:00). Independent variable Data was acquired by fusing multi-source data, including: average traffic volume passing through the road segment during the specified time period (from inductive loop detectors), average vehicle speed (from floating car GPS data), weather conditions (e.g., sunny, rainy, snowy, from meteorological bureau API), lighting conditions (day / night), and road type (highway, arterial road, etc.). Response variable Here defined as binary data (0 or 1), it indicates whether at least one recorded traffic accident has occurred in the specified spatiotemporal unit. Response variable This indicates that an accident has occurred within this spacetime unit; response variable This indicates that no accident has occurred. This variable is determined jointly by the traffic police accident response system records and the spatial-temporal matching function of the Geographic Information System (GIS).

[0039] In some embodiments, the observation data originates from the interpretation of multi-period remote sensing satellite imagery and national geographic census data. The smallest map patch or regular grid in the land survey is used as the observation point, and its spatial coordinates... These are the coordinates of the geometric center point of the patch. Time stamp. The year of observation. Independent variable. Potential factors driving land use change include natural factors such as slope, aspect, and elevation (extracted from the Digital Elevation Model, DEM), and socioeconomic factors such as the distance of the land parcel to the nearest highway entrance, distance to the municipal government, and population density of the administrative district (obtained from statistical yearbooks). Response variables Here, data is defined as count data. By comparing land use classification maps from two adjacent periods, changes in land use type for each map patch are identified. For example, focusing on the change type of conversion from arable land to construction land, the response variable... This is defined as the number of times a map patch undergoes a type conversion from cultivated land to construction land within two observation intervals. For most map patches, this value is 0 (no change) or 1 (one change); for a very small number of map patches that have undergone complex changes, this value may be greater than 1. This variable is determined through spatial overlay analysis using remote sensing change detection technology and Geographic Information System (GIS).

[0040] S20: Based on the spatiotemporal location information of the observation points, a spatiotemporal geographic weighted regression model is constructed through fitting to describe the response variable. With independent variable The local relationships between them that change with their spatiotemporal positions; wherein, the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. .

[0041] In this embodiment, the Poisson regression method is integrated into the geographically and temporally weighted regression (GTWR) framework to construct a geographically and temporally weighted Poisson regression (GTWPR) model to adapt to the characteristics of integer count data. At the same time, the logistic regression method is combined with GTWR to develop a geographically and temporally weighted logistic regression (GTWLR) model to handle binary discrete count data.

[0042] In some embodiments, the GTWPR model is specifically expressed as follows: ; In the formula, express Follows the principle that the mean and variance are both equal. The Poisson distribution; Regression point The spatiotemporal location, and These represent the spatial and temporal coordinates of the regression point, respectively. and Regression point The independent and dependent variables; Indicates the first The regression point is... The regression coefficients of the variables, which are about the regression point. For any function at a given location, as It changes with the changes.

[0043] In some embodiments, the iterative formula for the GTWPR regression coefficient estimate is as follows: ; In the formula, Indicates position First The estimated local regression coefficients for the next iteration; Represents the matrix of independent variables. yes Transpose of a matrix; Represents the spatiotemporal weight matrix. , Regression point For the regression point Influence weight; It is by The variance weight matrix formed It is a vector composed of the adjusted dependent variable.

[0044] In some embodiments, the weight matrix is ​​often expressed as a Gaussian kernel function, with the specific formula as follows: ; In the formula, Regression point Regression point The distance between them This is a bandwidth parameter used to adjust the relationship between weights and distance.

[0045] In some embodiments, in the GTWPR model and The calculation formulas are as follows: ; ; ; ; In the formula, Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. Indicates the first The regression point of the next iteration In position Adjusted dependent variable, Indicates the first The regression point of the next iteration In position Adjusted dependent variable, Indicates the first The regression point of the next iteration In position Adjusted dependent variable, This represents the estimated value of the regression coefficient for the local intercept term. Indicates the first The regression point of the next iteration The Estimates of the regression coefficients of the independent variables. Regression point The One independent variable, Indicates the first One dependent variable, Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. It is the first A linear predictor of each observation.

[0046] In some embodiments, the expression for the GTWLR model is as follows: ; In the formula, Indicates to conduct Transformation, express The probability of.

[0047] In some embodiments, the iterative formula for the GTWLR regression coefficient estimate is as follows: ; In some embodiments, GTWLR The calculation formula is as follows: ; In some embodiments, GTWPR and GTWLR are... The convergence criterion formula for the next iteration is as follows: ; ; ; In the formula, Indicates the first The numerator of the convergence criterion for the next iteration. Indicates the first The denominator of the convergence criterion for the next iteration. Indicates the first Regression point at the next iteration The Estimates of the regression coefficients of the independent variables. Indicates the first The estimated value corresponding to the next iteration. Indicates the first The convergence criterion value of the next iteration. When the value is less than a preset threshold, the iteration is considered to have converged. Typically, this is... The threshold is set to 10. -5 .

[0048] It should be noted that, in the specific application scenarios, each observation point mentioned in the above embodiments is directly used as the regression point for local estimation by the model.

[0049] S30: Based on the spatiotemporal geographic weighted regression model, generate analysis results to describe the spatiotemporal distribution patterns of response variables within the target geographic region, and perform at least one of the following operations based on the analysis results: output prediction and early warning information or optimize resource allocation strategies.

[0050] In some embodiments, the observation data includes environmental pollution monitoring data, traffic accident record data, or regional land use change data; When the observed data is environmental pollution monitoring data, the response variable The independent variable represents the number of events where pollutant concentrations exceed the standard. The analysis includes one or more meteorological parameters such as wind speed, wind direction, temperature, humidity, and air pressure, as well as industrial emission source information; the analysis result is a spatiotemporal distribution map of pollution risk, and the operation performed includes sending early warning information to environmental monitoring terminals in designated areas.

[0051] When the observed data is specifically traffic accident record data, the response variable The independent variable serves as an indicator of the number of accidents or whether an accident has occurred within a specified spatiotemporal unit. The analysis includes one or more traffic and environmental factors such as traffic flow, average vehicle speed, road type, weather conditions, and lighting conditions; the analysis results are a dynamic traffic safety heat map; and the operations performed include generating traffic diversion plans for high-risk road sections or pushing early warning prompts to in-vehicle navigation devices. When the observed data is specifically regional land use change data, the response variable The independent variable is used to define the number of land use type conversions or whether a conversion has occurred for a plot of land within a unit of time. The analysis includes one or more natural and socioeconomic factors such as administrative divisions, population density, slope, aspect, distance from major transportation routes, and distance from the city center; the analysis results are a spatiotemporal heterogeneity map of the driving forces of land use change, and the operation performed is to optimize regional land resource allocation and planning decisions based on the map.

[0052] In some embodiments, Figure 3 The overall presentation presents the complete technical route of the method proposed in this application, which includes four main research stages and their corresponding key technologies.

[0053] The first phase is the research and development phase. The core of this phase is to evolve from the classic geographic weighted regression model to a spatiotemporal geographic weighted regression model through the introduction of key technologies. Specifically, in this first phase, Poisson regression and logistic regression, two models designed for count data, are combined with the key technology of incorporating time scales. This introduces both spatial and temporal dimensions into the geographic weighted regression framework, ultimately constructing two core models: the spatiotemporal geographic weighted Poisson regression model and the spatiotemporal geographic weighted logistic regression model.

[0054] The second stage is the model fitting stage. This stage focuses on the model fitting process for a given dependent variable and... For the specific problem of multidimensional independent variables, the estimation process for model parameters is as follows: First, the optimal bandwidth is obtained according to the AICc criterion, a step involving efficient search using the golden section method. Then, locally weighted regression is used to estimate the coefficients, the core of which is the least squares method for the next iteration. This process is an iterative cycle, and after each iteration, a convergence test is performed to determine whether the iteration has converged. If it does not converge, the regression coefficients for this iteration are output and the iteration continues; if it converges, the final regression coefficients are output, thus completing the model fitting.

[0055] The third stage is the model evaluation stage using simulation experiments. To systematically verify the performance of the constructed model, this invention designed model experiments. The key to this experiment lies in setting the regression coefficients in the simulation data; that is, generating simulation data by designing multiple sets of known regression coefficient functions with complex spatiotemporal variation patterns. Subsequently, the generated simulation data is input into the constructed model for fitting, and the results are compared with the preset true coefficients for accuracy evaluation, thereby assessing the robustness and stability of the model.

[0056] The fourth stage is the data validation stage. This stage aims to apply the model to real-world data to verify its practical effectiveness. First, data is collected and preprocessed for different application scenarios. Specifically, in the analysis of property crime data, influencing factors are integrated with both human and natural factors, which are used as independent variables, and a spatiotemporally weighted Poisson regression model is used to study and analyze the property crime data. Similarly, in the study of land change, human and natural factors are integrated as influencing factors, and a spatiotemporally weighted logistic regression model is used to study and analyze the land change data. Finally, the modeling and analysis results of these two types of real-world data jointly complete the validation steps of the proposed model, confirming its effectiveness in solving practical problems.

[0057] To further illustrate the feasibility and advancement of the method presented in this application, a detailed explanation will be provided below using specific simulation examples. It is important to note that the data used below is simulated data. This embodiment employs simulated data to verify model performance, primarily based on the following two core considerations: First, the principle of confidentiality. The real core data upon which the method relies is not suitable for direct disclosure in published patent applications. Second, the rigor and universality of scientific verification. Through carefully designed simulated data, a test environment with known real answers can be systematically constructed under completely controllable conditions, thereby enabling unbiased and repeatable quantitative evaluation of the accuracy and stability of the model estimation. This provides a more comprehensive demonstration of the model's theoretical superiority than using a few limited real-world cases.

[0058] Specifically, this embodiment designs and implements a series of simulation experiments to reveal the differences between GTWPR and GWPR and the Poisson regression model (PRM), and between GTWLR and GWLR and the logistic regression model (LRM), and to verify the superiority of GTWPR and GTWLR.

[0059] This embodiment first constructs a three-dimensional coordinate system, wherein, Represents the coordinate axes of a plane. This is the time axis. The spatial coordinate system has its origin at the lower left corner, and the length of each coordinate axis is set to 12 units. ). The value range is from 0 to (i.e., 0, 1, 2, ..., 11), and the regression points are evenly distributed across... On a three-dimensional grid, 1,728 regression points are generated throughout the entire space. The formula for calculating the coordinates of the regression points is as follows: ; in, for Divide by The remainder after; for Divide by Round down.

[0060] This embodiment further designs three sets of simulation data to comprehensively explore the robustness and stability of the GTWPR and GTWLR models in complex spatiotemporal data environments. The independent variables... Through the standard normal distribution Generation; regression coefficients and The coefficient calculation formulas for the three sets of simulation experiments are shown below.

[0061] Group 1: ; Group 2: ; Group 3: ; It should be noted that the three sets of simulation data used in this embodiment are not designed arbitrarily, but rather highly abstract and reproduce the core spatiotemporal heterogeneity laws of the data generation process in the aforementioned three types of real application scenarios, so that the simulation verification and real application form a direct theoretical mapping.

[0062] The first set of simulation data uses regression coefficients designed to decay exponentially with distance, corresponding to the typical generation mechanism of environmental pollution monitoring data. It simulates the physical process by which the intensity of the impact of point pollution sources or instantaneous emission events on the surrounding environment rapidly decays with spatial distance and time, and is used to verify the model's ability to reproduce this type of diffusion-decay spatiotemporal process.

[0063] The second set of simulated data, with regression coefficients that integrate periodic fluctuations and linear trends, corresponds to the complex patterns inherent in traffic accident record data. It simulates the typical characteristics of traffic flow and risk exhibiting periodic distribution along roads in space (such as passing through commercial and residential areas), and being affected by morning and evening peak cycles in time, superimposed with long-term trends. It is used to evaluate the model's ability to analyze periodic spatiotemporal interaction effects.

[0064] The third set of simulated data exhibits local peaks in regression coefficients within a specific spatiotemporal range, corresponding to policy-driven or hotspot development patterns commonly found in regional land use change data. It simulates the strong and concentrated driving effects of policies such as economic development zones and large-scale infrastructure construction at specific times and geographical locations, and is used to test the model's ability to capture sudden or focused spatiotemporal heterogeneity.

[0065] This embodiment uses the root mean square error (RMSE) and the coefficient of determination (R²). 2 The statistical evaluation metrics, including the corrected version of the Akaike Information Criterion (AICc), comprehensively measure the estimation accuracy of the model, study the specific impact of different bandwidth settings on model performance, and analyze the estimation error of regression coefficients. By calculating the deviation between the true value and the estimated value of the regression coefficients of each model, the accuracy of the model in capturing complex relationships between variables is further evaluated. The statistical indicators used include root mean square error (RMSE) and coefficient of determination (R²). 2The corrected version of the Akaike Information Criterion (AICc), calculated using the following formula: ; ; ; In the formula, This represents the observed average value of the dependent variable. The trace of the hat matrix is ​​a function of the bandwidth.

[0066] Finally, using the model constructed with simulated data, and based on real environmental pollution monitoring data, traffic accident record data, or regional land use change data, the number of events is used as the response variable. The GTWPR and GTWLR models are introduced, comprehensively considering spatial location and temporal dimensions, to evaluate their fitting ability and predictive accuracy for count data in real-world scenarios. Comparison with traditional models verifies the improvements in explanatory power and applicability of the new model, further demonstrating its application potential in crime analysis and land management.

[0067] The equipment or devices used in the implementation of the above simulation case are as follows: a computer with an Intel i9-10900K CPU, an RTX 3090 graphics card, and 64GB of memory.

[0068] To evaluate the estimation performance of the proposed GTWPR and GTWLR models under different spatiotemporal heterogeneity conditions, this embodiment designed a systematic simulation experiment and compared it with existing GWPR, GWLR, PRM, and LRM models. All four models (GTWPR, GTWLR, GWPR, and GWLR) used the same kernel function form to generate the spatiotemporal weight matrix during the calibration process, and the spatiotemporal bandwidth parameter was optimized using the AICc criterion. Considering the randomness of the simulation data, each experiment was repeated 100 times. To ensure the stability and reliability of the results, all simulation experiments were conducted in the MATLAB R2022a environment.

[0069] Table 1 Comparison of R2, AICc, and RMSE for PRM, GWPR, GTWPR, LRM, GWLR, and GTWLR

[0070] Table 1 shows the performance of six models (PRM, GWPR, GTWPR, LRM, GWLR, GTWLR) on three key evaluation metrics—R. 2 Performance comparison results of RMSE and AICc. To maximize R... 2Minimizing RMSE and AICc were used as the model selection criteria. The results showed that among the three models PRM, GWPR, and GTWPR, GTWPR exhibited the best performance in all three sets of simulation data: its R... 2 The highest performance was achieved by GTWLR, while the lowest performance was achieved by RMSE and AICc. GWPR's performance was between that of GTWLR and PRM, indicating that it could only capture spatial heterogeneity and failed to consider the time factor. In binary discrete data modeling, GTWLR also outperformed GWLR and LRM, with GWLR outperforming LRM, further demonstrating its sensitivity and adaptability to spatiotemporal heterogeneity.

[0071] Table 2 Comparison of spatial and temporal bandwidths of GWPR, GTWPR, GWLR, and GTWLR

[0072] Table 2 further lists the optimal spatial and temporal bandwidths for GWPR, GTWPR, GWLR, and GTWLR in the three sets of simulation data. The results show that the spatial bandwidth estimates of GTWPR and GTWLR are similar to those of GWPR and GWLR, indicating that their spatial sensitivity is consistent. However, GTWPR and GTWLR additionally capture significant temporal heterogeneity through temporal bandwidth, which reflects their stronger adaptability in the spatiotemporal dimensions.

[0073] Table 3. Comparison of RMSE values ​​for each coefficient of GWPR, GTWPR, GWLR, and GTWLR

[0074] Table 3 records the RMSE of the regression coefficient estimates for GWPR, GTWPR, GWLR, and GTWLR in the three sets of simulated data. Except for the first coefficient in the second set of simulated data, GTWPR and GTWLR have the lowest RMSE on all regression coefficients, significantly outperforming GWPR and GWLR. This result indicates that GTWPR and GTWLR have significant advantages in estimation accuracy and model applicability. It is worth noting that GTWPR and GTWLR not only possess good estimation capabilities but can also accurately identify variable relationships with similar levels of spatiotemporal heterogeneity, further validating their effectiveness in modeling complex spatiotemporal processes. The model accuracy slightly decreased in the second set of simulated data, possibly due to the complexity of the data structure or high noise levels, suggesting that model performance may be affected by data quality.

[0075] To better illustrate the advantages of the GTWPR and GTWLR models, this example demonstrates three sets of simulation data in... The spatial distribution of the regression coefficients at different time points was compared with the actual values ​​in the simulated data to verify the accuracy and superiority of GTWPR and GTWLR. The comparison reveals that the GTWPR and GTWLR models... The regression coefficients of the time-time estimates are highly consistent with the true values ​​of the simulated data, indicating that the GTWPR and GTWLR models have excellent performance in capturing the dynamic characteristics of spatiotemporal data. In contrast, while the GWPR and GWLR models can also reflect spatial distribution characteristics to some extent, they have limitations in capturing temporal heterogeneity, leading to some deviation between the regression coefficients and the true values. Since PRM and LRM can only fit global regression coefficients (constants) and cannot reflect spatial differences, regression coefficient plots for PRM and LRM are not included in this comparison. Regression coefficients of the three sets of simulation experiments. exist Spatial distribution of time as Figure 4 , Figure 5 and Figure 6 As shown.

[0076] This application also provides a spatiotemporal geographic weighted regression device for counting data, such as... Figure 7 As shown, the spatiotemporal geographic weighted regression device for counting data includes: The data acquisition module 701 is configured to acquire observation data collected at multiple spatiotemporal observation points within a target geographic area, the observation data including the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable The response variable Count data that is a non-negative integer or binary data that takes the value 0 or 1; The model building module 702 is configured to construct a spatiotemporal geographic weighted regression model based on the spatiotemporal location information of the observation points to describe the response variable. With the independent variable The local relationships between them that change with their spatiotemporal positions; wherein, the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. ; The model application module 703 is configured to generate analysis results based on the spatiotemporal geographic weighted regression model to describe the spatiotemporal distribution pattern of the response variables within the target geographic region, and to perform at least one of the following operations based on the analysis results: outputting prediction and early warning information or optimizing resource allocation strategies.

[0077] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0078] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0079] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0080] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0081] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the spatiotemporal geographic weighted regression method for counting data described in the above embodiments.

[0082] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the spatiotemporal geographic weighted regression method for counting data described in the above embodiments.

[0083] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0084] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0085] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0086] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0087] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0088] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0089] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0090] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0091] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0092] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A spatiotemporal geographic weighted regression method for count data, characterized in that, The method includes: Acquire observational data collected at multiple spatiotemporal observation points within a target geographic area. This observational data may include environmental pollution monitoring data, traffic accident record data, or regional land use change data. The observational data includes the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable The response variable Count data that is a non-negative integer or binary data that takes the value 0 or 1; Based on the spatiotemporal location information of the observation points, a spatiotemporal geographic weighted regression model is constructed through fitting to describe the response variable. With the independent variable The local relationships between them vary with their spatiotemporal locations; the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. ; Based on the spatiotemporal geographic weighted regression model, generate analysis results to describe the spatiotemporal distribution pattern of the response variables within the target geographic region, and perform at least one of the following operations based on the analysis results: output prediction and early warning information or optimize resource allocation strategies; When the response variable When the count data are non-negative integers, the spatiotemporal geographic weighted regression model is a spatiotemporal geographic weighted Poisson regression model, and its expression is: ； In the formula, express Follows the principle that the mean and variance are both equal. The Poisson distribution, For the regression point number, The number of observation points. Indicates the first One variable, For the total number of variables, Indicates the first The spatiotemporal local intercept term of each regression point; Local regression coefficients The estimation is performed using the following iterative formula: ； In the formula, Regression point In the The estimated local regression coefficients for the next iteration; Represents the matrix of independent variables. It is an independent variable matrix transpose; Represents the spatiotemporal weight matrix; It is the first At the regression point in the next iteration The model applies to all observation locations. Predicted value The diagonal weight matrix formed It is a vector composed of the corresponding adjusted dependent variables; When the response variable When the data is binary data with values ​​of 0 or 1, the spatiotemporal geographic weighted regression model is a spatiotemporal geographic weighted logistic regression model, and its expression is: ； In the formula, Indicates to conduct Transformation, express The probability, For the regression point number, The number of sample points. as independent variable The first in One variable, For the total number of variables, Indicates the first The spatiotemporal local intercept term of each regression point; Local regression coefficients The estimation is performed using the following iterative formula: ； ； In the formula, Regression point In the The estimated local regression coefficients for the next iteration; Represents the matrix of independent variables. It is its transpose; Represents the spatiotemporal weight matrix; It is a vector composed of the adjusted dependent variables. Indicates the l-th iteration The predicted probability.

2. The spatiotemporal geographic weighted regression method for count data according to claim 1, characterized in that, The elements in the spatiotemporal weight matrix are calculated using the following formula: ； In the formula, Indicates the observation point For the regression point Influence weight; Indicates the observation point Regression point The spatiotemporal distance between them; This is a bandwidth parameter used to adjust the relationship between weights and distance; Represented by natural constant An exponential function with base 0; In the In the next iteration, with the regression point Related weighting matrix With the adjusted dependent variable vector The weighted matrix is ​​defined as follows: This is a diagonal matrix, where the diagonal elements are the predicted estimates of the number of events occurring at each location: ； Adjusted dependent variable vector Defined as a column vector of its components: ； Among them, the Each component Calculated by the following formula: ； In the formula, For the first During the next iteration The corresponding number Linear predicted values ​​for each observation point For the first Regression point at the next iteration The estimated values ​​of the intercept term coefficients, For the first Regression point at the next iteration The Estimates of the coefficients of the independent variables; Indicates the first At the observation location, the first Observed values ​​of the independent variables; For the first The actual observed number of events occurring at each observation location; Indicated based on regression coefficients For the The predicted estimate of the number of times an event will occur at a given location.

3. The spatiotemporal geographic weighted regression method for count data according to any one of claims 1 to 2, characterized in that, The spatiotemporal local regression coefficients at each observation point are solved using an iterative algorithm. At that time, the first The convergence criterion formula for the next iteration is as follows: ； ； ； In the formula, Indicates the first The numerator of the convergence criterion for the next iteration. Indicates the first The denominator of the convergence criterion for the next iteration. Indicates the first Regression point at the next iteration The Estimates of the regression coefficients of the independent variables. Indicates the first The estimated value corresponding to the next iteration. Indicates the first The convergence criterion value of the next iteration; when When the value is less than a preset threshold, the iteration is considered to have converged.

4. The spatiotemporal geographic weighted regression method for count data according to claim 1, characterized in that, The optimal spatiotemporal bandwidth parameter of the spatiotemporal geographic weighted regression model is adaptively determined by minimizing the Akaike Information Criterion (AICc); wherein, the formula for calculating AICc is: ； In the formula, Indicated based on regression coefficients For the Predicted estimates of the number of events occurring at each location. The trace of the hat matrix is ​​a function of the bandwidth.

5. The spatiotemporal geographic weighted regression method for count data according to claim 1, characterized in that, When the observed data is environmental pollution monitoring data, the response variable The independent variable represents the number of events where pollutant concentrations exceed the standard. The analysis includes one or more meteorological parameters such as wind speed, wind direction, temperature, humidity, and air pressure, as well as industrial emission source information; the analysis result is a spatiotemporal distribution map of pollution risk, and the operations performed include sending early warning information to environmental monitoring terminals in designated areas; When the observed data is specifically traffic accident record data, the response variable The independent variable serves as an indicator of the number of accidents or whether an accident has occurred within a specified spatiotemporal unit. The analysis includes one or more traffic and environmental factors such as traffic flow, average vehicle speed, road type, weather conditions, and lighting conditions; the analysis results are a dynamic traffic safety heat map; and the operations performed include generating traffic diversion plans for high-risk road sections or pushing early warning prompts to in-vehicle navigation devices. When the observed data is specifically regional land use change data, the response variable The independent variable is used to define the number of land use type conversions or whether a conversion has occurred for a plot of land within a unit of time. The analysis includes one or more natural and socioeconomic factors such as the administrative division where the land parcel is located, population density, slope, aspect, distance from major transportation routes, and distance from the city center; the analysis results are a spatiotemporal heterogeneity map of the driving forces of land use change, and the operation performed is to optimize the allocation of regional land resources and planning decisions based on the map.

6. A spatiotemporal geographic weighted regression apparatus for counting data, used to implement the method as described in any one of claims 1-5, characterized in that, The device includes: The data acquisition module is configured to acquire observation data collected at multiple spatiotemporal observation points within a target geographic area, the observation data including the spatial coordinates of each observation point. Time stamp At least one independent variable and a response variable The response variable Count data that is a non-negative integer or binary data that takes the value 0 or 1; The model building module is configured to construct a spatiotemporally weighted regression model based on the spatiotemporal location information of the observation points to describe the response variable. With the independent variable The local relationships between them that change with their spatiotemporal positions; wherein, the model fitting process uses an iterative algorithm to solve for the spatiotemporal regression coefficients at each observation point. ; The model application module is configured to generate analysis results based on the spatiotemporal geographic weighted regression model to describe the spatiotemporal distribution pattern of the response variables within the target geographic region, and to perform at least one of the following operations based on the analysis results: outputting prediction and early warning information or optimizing resource allocation strategies.

7. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the spatiotemporal geographic weighted regression method for count data as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the spatiotemporal geographic weighted regression method for count data as described in any one of claims 1-5.

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