Fuzzy geoprobe and method of use thereof
By constructing fuzzy spatial stratification and fuzzy statistics, the problem of information loss in spatial stratification of geographic detectors is solved, achieving higher analytical stability and accuracy, and is applicable to complex geographic analyses such as urban patterns, soil properties, infectious disease transmission, and environmental pollution.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF GEOGRAPHICAL SCI & NATURAL RESOURCE RES CAS
- Filing Date
- 2026-03-11
- Publication Date
- 2026-07-03
AI Technical Summary
Existing geographic detectors suffer from information loss during spatial stratification, leading to a decrease in the stability and accuracy of analysis results. In particular, they are unable to effectively capture micro-changes and inter-layer gradient characteristics when dealing with continuous explanatory variables.
A fuzzy spatial stratification method is adopted. By calculating the membership degree of each spatial unit to each stratum, fuzzy statistics are constructed to reconstruct the continuous estimate of the target variable. Furthermore, the interaction of explanatory variables is identified through fuzzy intersection operations, thereby enhancing the sensitivity to spatial distribution.
It improves the adaptability and accuracy of the geographic detector in complex geographic analysis, enables more granular quantification of the driving forces of explanatory variables, reduces sensitivity to stratification thresholds, and maintains backward compatibility.
Smart Images
Figure CN122333009A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of geographic information science and spatial intelligent computing technology, and in particular to a fuzzy geographic detector and its usage method. Background Technology
[0002] Spatial heterogeneity is a common characteristic of geographic data. Geographical detectors (GD), as a classic spatial statistical method for detecting spatial heterogeneity, have advantages such as not requiring the assumption of independent and identical distribution, being able to identify nonlinear coupling relationships, and being computationally simple. They have been widely used in various natural and social system studies, including urban patterns, soil properties, infectious disease transmission, environmental pollution, and climate response, providing effective support for geographic modeling and policy making.
[0003] Spatial attribution analysis and interaction detection constitute the two core functions of a geospatial detector. They are used to evaluate the explanatory power of single explanatory variables and their combinations on the target variable, respectively. Both rely on the homogeneity of the target variable within spatial strata and its heterogeneity between strata. Their metrics are as follows: Statistical measure. Traditional The calculation of statistics relies on deterministic spatial stratification with "unique attribution," meaning each spatial unit is assigned to only one stratum. The explanatory power of the explanatory variables for the target variable is measured by comparing the spatial distribution relationship between the strata assigned to the explanatory variables and that of the target variable. However, this process is highly sensitive to the stratification method, which may affect the stability of the analysis results and the reliability of the conclusions.
[0004] To improve the stability and adaptability of geographic detectors, researchers have proposed various spatial layering optimization strategies in recent years. The basic idea behind these strategies is to maximize... The statistical measure serves as the objective function, automatically searching for the optimal stratification result to fully explore the explanatory power of explanatory variables on the objective variable. For example, the Optimal Parameter Geographic Detector (OPGD) method integrates multiple univariate stratification methods such as the natural breakpoint method and the isometric method, and selects the corresponding... The stratified result with the largest statistical value. The Robust Geographic Detector (RGD) method searches using a dynamic programming algorithm. The optimal solution of the statistic improves the stability of spatial attribution analysis results in univariate scenarios. For multivariate scenarios, the Locally Interpretable Hierarchical Heterogeneous (LESH) method improves the stability of spatial attribution analysis results by constructing a system based on... The decision tree with optimal statistics achieves spatial stratification, and the Shapely method is combined to quantify the marginal contribution of each variable, effectively identifying and characterizing the interaction between explanatory variables.
[0005] Although existing studies have optimized stratification strategies from different perspectives, optimized geographic detectors still essentially rely on deterministic spatial stratification. This stratification strategy leads to information loss in two ways: First, continuous differences between variables within a stratum are smoothed out, weakening the ability to characterize spatial distribution details and thus masking the micro-variable characteristics of explanatory variables within a stratum. Second, continuous geographic processes in inter-stratum transition regions are discretized into inter-stratum abrupt changes, resulting in the inability to effectively represent the gradual characteristics of these transition regions. These two levels of information loss not only weaken the ability of explanatory variables to represent real geographic processes but also significantly increase the sensitivity of geographic detection results to stratification thresholds, thereby affecting the robustness and accuracy of attribution analysis.
[0006] For example, Figure 1 When continuous explanatory variables are discretized, the fine-grained continuous changes within a stratum are smoothed out, and the gradual transitions between strata become abrupt changes, resulting in information loss and weakening the accuracy of the description of the spatial distribution of explanatory variables. Therefore, how to mitigate the information loss caused by spatial stratification has become one of the key challenges in improving the attribution analysis capabilities of geographic detectors.
[0007] Therefore, there is a need to provide an improved technical solution that addresses the shortcomings of the existing technology. Summary of the Invention
[0008] The purpose of this application is to provide a fuzzy geographic detector and a method for using it, so as to solve or alleviate the problems existing in the prior art.
[0009] To achieve the above objectives, this application provides the following technical solution: This application provides a fuzzy geographic detector, which is applied to a computer device and includes: The fuzzy spatial stratification unit is configured as follows: the spatial units of the study area are stratified using the fuzzy spatial stratification method, the membership degree of each spatial unit to each stratification is calculated, and the fuzzy spatial stratification result is obtained. The spatial attribution analysis unit is configured to: calculate representative values of target variables for each layer based on membership degrees, and accordingly calculate reconstructed values of target variables for each spatial unit; and construct fuzzy attribution analysis based on the estimation error between the reconstructed values and the observed values. Statistics are used to measure the explanatory power of explanatory variables on the spatial differentiation of the target variable; Wherein, the target variable represents the value in the same stratum. Within, the weighted mean of the target variable with the membership degree as the weight, the reconstructed value of the target variable in different strata. The following is a weighted summation of the target variables, with the membership degree as the weight; The interaction identification unit is configured to: superimpose the fuzzy spatial layering results of multiple explanatory variables using fuzzy intersection operations, and compare the fuzzy layers before and after superposition. Changes in statistics can help identify the types of interactions between explanatory variables.
[0010] Preferably, the formula for calculating the representative value of the target variable within each stratum is: , In the formula, For layering The weighted mean of the internal target variable. This represents the total number of spatial units within the study area. For the first Each spatial unit belongs to a stratification membership degree For the first The observed values of the target variable for each spatial unit.
[0011] Preferably, the formula for calculating the reconstructed value of the target variable is: , In the formula, For the first Reconstructed values of the target variables for each spatial unit This represents the total number of layers.
[0012] Preferably, the fuzziness The formula for calculating the statistic is: , , In the formula, Indicates ambiguity Statistic, This represents the squared error generated by reconstructing the target variable using fuzzy spatial hierarchies. This represents the total variance of the target variable.
[0013] This application provides a method for using a fuzzy geographic detector, including: Acquire geospatial data of the study area, wherein the geospatial data includes a target variable and at least one explanatory variable; The geospatial data is input into the fuzzy geographic detector described in any of the above embodiments, and the detection results are output. The detection results include the membership degree of each spatial unit to each layer, fuzziness... The fuzziness before and after the fuzzy spatial layering of statistics and different explanatory variables Changes in statistics; Based on the detection results, the explanatory power of a single explanatory variable and a combination of multiple explanatory variables on the target variable is analyzed.
[0014] This application provides a computer device, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the method for using the fuzzy geographic detector described in the above embodiments.
[0015] This embodiment provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the method for using the fuzzy geographic detector described in the above embodiment.
[0016] This embodiment provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the method for using the fuzzy geographic detector described in the above embodiment.
[0017] Beneficial effects: The fuzzy geographic detector provided in this application, through fuzzification of the spatial stratification of continuous explanatory variables, maps each explanatory variable to a continuous membership degree corresponding to the total number of strata, capturing the microscopic continuous differences within spatial units and the gradual characteristics of transitional regions between strata. Based on the classic geographic detector, it calculates representative values of target variables and generates reconstructed values of target variables, and reconstructs new fuzzy geographic detectors based on the estimation errors of the two. The statistical measures reduce the sensitivity of the detection results to the stratification threshold and discretization scheme. Fuzzy intersection operations are performed on the fuzzy spatial stratification to compare the fuzziness. The statistical changes identify the interaction of explanatory variables, fully consider the semantic overlap and attribute fusion of spatial units in different dimensions, and can identify the driving force contributions of intermediate or mixed functional areas that cannot be captured by traditional hard stratification (i.e., deterministic spatial stratification), providing a more granular quantitative means to explain the interaction effects of complex geographic systems.
[0018] Meanwhile, when the membership degree is 0 or 1, the fuzzy geographic detector can degenerate into a classic geographic detector, ensuring the detector's backward compatibility. It also inherits the advantages of classic geographic detectors in handling spatial heterogeneity, exhibits higher detection capabilities in the spatial attribution of explanatory variables, and demonstrates stronger adaptability in the mechanism analysis of complex geographic analysis processes such as urban patterns, soil properties, infectious disease transmission, environmental pollution, and climate response, providing more accurate scientific basis for geographic decision support. Attached Figure Description
[0019] Figure 1 This diagram illustrates the information loss caused by the discretization of explanatory variables.
[0020] Figure 2 This is a logical diagram of a fuzzy geographic detector.
[0021] Figure 3 Fuzzy simulation for permutation test The probability density distribution of the statistic.
[0022] Figure 4 For the fuzzy code corresponding to each explanatory variable The ranking results of the statistics.
[0023] Figure 5 The analysis results explain the types of interactions between variables.
[0024] Figure 6 The differences in stratification within the layer between the traditional geographic detector and the fuzzy geographic detector are shown in the following: (a) is the spatial distribution of actual road density in the study area, (b) is the spatial distribution of actual NO2 concentration in the study area, (c) is the deterministic stratification result of road density generated by the traditional geographic detector, and (d) is the fuzzy spatial stratification result of road density generated by the fuzzy geographic detector.
[0025] Figure 7 The differences in stratification between traditional and fuzzy geographic detectors in the transition area are shown in the figures: (a) is the spatial distribution of actual road density in the study area, (b) is the spatial distribution of actual NO2 concentration in the study area, (c) is the deterministic stratification result of road density generated by the traditional geographic detector, and (d) is the fuzzy spatial stratification result of road density generated by the fuzzy geographic detector.
[0026] Figure 8 This is a schematic diagram of the structure of a computer device. Detailed Implementation
[0027] The following explains some of the relevant terms used in this application.
[0028] Spatial heterogeneity refers to the uneven distribution of geographical phenomena in space, and it is the core object of study for geographic detectors.
[0029] A q-statistic is an indicator used in geospatial detectors to measure the explanatory power of an independent variable for the spatial diversity of a dependent variable. Its value ranges from [0,1]. This indicates that the independent variable has no explanatory power for the dependent variable; This indicates that the independent variable completely determines the spatial differentiation of the dependent variable.
[0030] The dependent variable / target variable (Y) refers to the target variable in the study, or the explained variable, such as: land use change intensity, surface temperature, soil moisture content, environmental pollution indicators (such as NO2 concentration), etc.
[0031] Explanatory variables / driving factors (X) are factors that may affect the spatial distribution of the dependent variable Y. They can be natural or anthropogenic factors, such as elevation, slope, precipitation, population density, distance from roads, etc.
[0032] The embodiments of this application will now be described with reference to the accompanying drawings.
[0033] This embodiment provides a fuzzy geographic detector (FGD) applied to a computer device, comprising: a fuzzy spatial stratification unit configured to: stratify the spatial units of the study area using a fuzzy spatial stratification method, calculate the membership degree of each spatial unit to each stratum, and obtain fuzzy spatial stratification results; and a spatial attribution analysis unit configured to: calculate the representative value of the target variable for each stratum based on the membership degree, and accordingly calculate the reconstructed value of the target variable for each spatial unit; and construct a fuzzy spatial attribution analysis based on the estimation error between the reconstructed target variable value and the observed value. The statistical measure is used to assess the explanatory power of explanatory variables on the spatial differentiation of the target variable; where the target variable represents values within the same stratum. Within, the weighted mean of the target variable with the membership degree as the weight, the reconstructed value of the target variable in different strata. The following is a weighted summation of the target variables with the membership degree as the weight; the interaction identification unit is configured to: superimpose the fuzzy spatial layering results of multiple explanatory variables using fuzzy intersection operation, and compare the fuzzy values before and after superposition. Changes in statistics can help identify the types of interactions between explanatory variables.
[0034] The fuzzy geographic detector provided in this application is applied to computer equipment. Specifically, the fuzzy geographic detector can be converted into computer instructions through programming, so that when these computer instructions are executed by the computer's processor, they can realize the technical logic of the fuzzy geographic detector provided in this embodiment.
[0035] Fuzzy set theory is an important mathematical tool for dealing with uncertainty, fuzziness, and gradual change. By changing the binary logic in classical set theory, it allows elements to belong to a set to different degrees (membership), thus more realistically depicting the many phenomena in the real world with unclear boundaries and semantic ambiguity.
[0036] Traditional spatial stratification discretizes continuous explanatory variables and then definitively assigns spatial units to a certain stratum (classification / gradation). This stratification approach is based on the premise that explanatory variables within the same stratum are relatively homogeneous, while there are significant differences between strata.
[0037] Classical geographic detectors calculate target variables based on spatial stratification results. Statistics are methods for measuring the relationships and interactions between variables.
[0038] The fuzzy geodetector constructed in this embodiment is an extension based on the classic geodetector. Deterministic spatial stratification is a prerequisite for classic geodetectors, where each explanatory variable in each spatial unit has only a unique stratification assignment. Furthermore, existing geodetector software (such as the Excel version of Geodetector and the geodetector package in R) all require the input of discretized values for each explanatory variable. In other words, existing geodetector software assumes the discretization of explanatory variables by default. Therefore, for a long time, the research direction of scholars in the field of geodetectors has generally focused on how to find the optimal discretization segmentation point, while ignoring the fact that boundaries in the real world may be fuzzy and gradual. Existing geodetectors also fail to provide a method for handling continuous explanatory variable inputs.
[0039] The preliminary step of the fuzzy geographic detector proposed in this application is fuzzy spatial layering. For example... Figure 2 As shown, fuzzy spatial stratification, under fuzzy set theory, involves spatial units not being uniquely assigned to any particular stratum. Instead, they can simultaneously belong to multiple strata (stratum 1, stratum 2, ..., stratum n) with different membership degrees. This allows the model to more realistically express the spatial continuity and gradual changes of variables, preserving more spatial distribution information while maintaining flexibility. In other words, fuzzy geographic detectors no longer forcibly discretize continuous explanatory variables into strata (labels). Instead, through fuzzy spatial stratification, they convert continuous explanatory variables into continuous membership degrees for each spatial unit. These membership degrees serve as the basis for detection, solving for fuzzy... Statistical data was used to create a new type of geographic detector. The specific implementation is as follows: First, using the fuzzy spatial hierarchical method, the membership degree of a spatial unit to each hierarchy can be obtained, expressed as: (1) in, Indicates the first Each spatial unit belongs to a stratification membership degree For the number of layers, Indicates the first Explanatory variables for the stratification of spatial units The method for fuzzy spatial hierarchies can be any method for calculating membership, such as fuzzy C-means clustering (FCM) or Gaussian membership methods. This application... The specific method is not limited.
[0040] In particular, since membership degree is the probability of a spatial unit belonging to a stratum, the sum of the membership degrees of each spatial unit in each stratum is 1. That is to say, the membership degrees of the same spatial unit to each stratum satisfy the following constraint: (2) Classic geographic detectors employ The basic idea behind using statistical measures to measure the explanatory power of explanatory variables on the target variable is that if an explanatory variable can explain the spatial heterogeneity of the target variable, then the spatial distributions of the two are similar. Specifically, this means that the within-stratum variance after stratification should be significantly smaller than the population variance. The formula for calculating the statistic is: (3) (4) (5) in, It is the sum of the variances within the layers. It is the sum of total variances. and They are layered The number and variance of spatial units, It is the total number of spatial units within the study area. It is layered Internal space unit The observed values of the target variable.
[0041] from The calculation method of statistics shows that traditional geographic detectors require spatial units to be uniquely assigned to a layer for intra-layer variance, making it difficult to perform calculations within a fuzzy spatial layering framework, thus limiting its application in such scenarios. Furthermore, The calculation of statistics is based on the premise that each spatial unit is assigned to a certain stratum. Since it relies on deterministic spatial stratification, it ignores the fuzziness and continuity of the spatial differentiation process. Especially in areas where the boundaries of geographical units are fuzzy and the changes in variables are gradual, it is easy to cause spatial information loss and reduce the accuracy and stability of attribution analysis.
[0042] To address this issue, some scholars have proposed using the fuzzy rough set method. By introducing fuzzy stratification of the target variable, this method quantifies the confidence that units with similar attributes within a window belong to the same stratum, thus improving the flexibility of stratification to some extent. In the calculation process, this method first constructs a fuzzy similarity matrix to measure the similarity between spatial units, and then uses the lower approximation operation of fuzzy rough sets to determine the boundary of spatial unit affiliation.
[0043] However, in the application of this scheme, it was found that the lower approximation operation is essentially to first calculate the minimum membership degree of all similar spatial units in the neighborhood in each layer, as the probability of these spatial units belonging to that layer; then select the maximum probability to determine the most likely single layer affiliation of the spatial unit. In essence, it still follows the "single affiliation" judgment logic, which cannot fully capture the multiple affiliations of spatial units and may lead to deviations in the detection results.
[0044] This application does not follow the aforementioned fuzzy rough set method, but rather extends the classic geographic detector by incorporating the concept of fuzzy spatial layering. Expand and reconstruct the statistics. The definition of statistics and the introduction of fuzzy statistics The purpose of this statistical approach is to capture the fuzziness of spatial differentiation by utilizing the membership degree of spatial units to multiple strata, and thereby reconstruct a continuous estimate of the target variable, achieving a more robust spatial attribution analysis.
[0045] Therefore, the problem faced by this application is: classical geographic detectors The intra-stratum variance in the statistics requires that spatial units belong to a unique stratum, which is why it cannot be calculated based on fuzzy spatial stratification. Traditional statistical measures are ill-suited for attribution analysis and interaction detection in fuzzy spatially layered scenarios. This application addresses this by fuzzily extending the statistical measures of classic geographic detectors, enabling them to construct fuzzy spatial layers based on continuous explanatory variables. Furthermore, this application aims to construct a statistical measure that is backward compatible with classic geographic detectors, given a membership degree representation. The statistically compatible explanatory power mechanism enables it to perform attribution analysis and interaction detection in fuzzy hierarchical scenarios where there is no unique attribution.
[0046] Specifically, the solution in this embodiment will adopt the traditional The intra-level variance in the statistic is expanded to the squared error between the reconstructed value of the target variable and the observed value of the target variable, forming a new fuzzy error. This application constructs a fuzzy statistical measure to effectively integrate fuzzy attribution information within a stratification and transitional features at stratification boundaries, enhancing sensitivity to continuous changes in explanatory variables and reducing information loss caused by deterministic stratification. Statistics can adapt to spatial relationship detection methods in fuzzy spatial stratification, supporting more accurate and effective attribution analysis in the context of complex spatial distribution.
[0047] In fuzzy geographic detectors, fuzziness The specific steps for constructing the statistics are as follows: After fuzzy stratification of spatial units, the spatial attribution analysis unit uses the membership degree of each spatial unit to different strata as a weight, calculates the weighted sum of the weighted means within each stratum, and uses this sum as the representative value of the target variable. Then, it is applied to different strata... The continuous estimates of the target variable (i.e., the reconstructed values of the target variable) are reconstructed. Then, the fuzzy logic is calculated using the squared error between the reconstructed values and the observed values of the target variable. Statistics. A detailed explanation follows: ① Calculate the mean value within the fuzzy layer (fuzzy spatial layering).
[0048] In fuzzy spatial stratification, spatial units It can be assigned to multiple strata with different membership degrees simultaneously, therefore the intra-stratum mean of the target variable is expanded to a membership-weighted mean. The calculation formula is as follows: (6) In the formula, For layering The weighted mean of the target variable, i.e., the value represented by the target variable. This represents the total number of spatial units within the study area. For the first Each spatial unit belongs to a stratification membership degree For the first The observed values of the target variable for each spatial unit.
[0049] ② Reconstruct the estimated value of the target variable (calculate the reconstructed value of the target variable).
[0050] In traditional geographic detectors, the intra-layer mean is typically used as an estimate of the target variable, and the intra-layer variance is calculated accordingly to measure the dispersion of the target variable across different layers. However, this estimation method, represented by the mean, implicitly assumes homogeneity within layers and abrupt changes between layers, which may lead to information loss. Considering that fuzzy spatial stratification preserves the intra-layer spatial distribution of explanatory variables and the spatial structure of transition regions through the continuous spatial variation of membership degrees, this application introduces a membership degree-based approach. The weighting strategy involves calculating a weighted sum of the weighted means for each stratum to reconstruct the spatially continuously varying estimates of the target variable. This reduces the impact of information loss on the detection results. The specific calculation method is as follows: (7) In the formula, For the first The estimated value of the target variable for each spatial unit. This represents the total number of layers.
[0051] ③ Construction fuzzy Statistics.
[0052] Under fuzzy spatial stratification, due to the estimated value of the target variable... It is a weighted sum of the in-layer means with membership degrees as the weight, and therefore its sum is related to the observed values. The squared error reflects the degree to which the spatial variation of membership explains the spatial distribution of the target variable, thus measuring the coupling relationship between the explanatory and target variables. (The definition is fuzzy.) The statistics are as follows: (8) (9) In the formula, Indicates ambiguity Statistic, This represents the squared error generated by reconstructing the target variable using fuzzy spatial hierarchies. This represents the total variance of the target variable.
[0053] The following is about fuzziness. The principles of statistics and their compatibility are explained.
[0054] In this application, ambiguity In the context of fuzzy spatial stratification, the statistical measure... The statistics have been expanded, and this fuzzy expansion is theoretically similar to... The statistics exhibit good consistency: when the membership degree degenerates to a 0–1 variable, fuzzy spatial stratification is formally equivalent to deterministic spatial stratification, meaning each spatial unit uniquely belongs to a particular stratum. In this case, the weighted mean of the fuzzy stratification simplifies to the arithmetic mean of the deterministic stratification, and the fuzzy error is equivalent to the in-stratum variance in the classical method. Correspondingly, the fuzzy... Statistical transformation into classical Statistical measure. Therefore, while enhancing the ability to represent spatial structure, the fuzzy geographic detector maintains its theoretical inheritance from classical methods. The mathematical expression of this transformation relationship is as follows: (10) (11) (12) Vague The magnitude of the statistic reflects the explanatory power of the fuzzy spatial structure defined by the explanatory variables on the spatial distribution of the target variable. A larger value indicates a smaller error between the estimated value of the target variable reconstructed using fuzzy spatial hierarchies and the original observation value, meaning a stronger spatial coupling relationship exists between the explanatory and target variables. Due to the error term ( ) is non-negative, fuzzy The theoretical range of values for the statistic is: When fuzzy spatial layering can completely restore the spatial distribution of the target variable, that is, when the estimated value is completely consistent with the observed value, the error is 0. At this time, the fuzzy... A statistic reaching its theoretical upper limit of 1 indicates that the explanatory variables can adequately explain the spatial heterogeneity of the target variable. Conversely, when fuzzy... When the statistic is less than or equal to 0, it indicates that the fuzzy spatial stratification cannot explain the spatial structure of the target variable, and there is no significant spatial coupling relationship between the explanatory variable and the target variable.
[0055] Furthermore, in practical applications, to ensure fuzziness... Statistics have statistical inference significance and require systematic testing for significance. If the fuzzy spatial stratification of the explanatory variables cannot effectively reconstruct the spatial distribution of the target variable, it can be considered that there is no spatial coupling relationship between the explanatory and target variables, and the statistical results should be regarded as randomly generated. Therefore, fuzzy... The significance test of a statistic can be formalized into the following hypothesis testing framework: Null hypothesis Current blur The statistics are derived from the results generated by a completely random fuzzy hierarchical structure; Alternative Hypothesis Current blur The statistic is significantly higher than that produced by a random stratified structure, reflecting the true spatial coupling relationship between the explanatory variables and the target variable.
[0056] To avoid blurring To make strong assumptions about the distribution of the statistics, this application employs a permutation test for nonparametric significance testing. The specific procedure is as follows: First, while maintaining the fuzzy hierarchical structure generated by the explanatory variables, the observations of the target variable are randomly permuted between spatial units. Each permutation involves random exchange... The target variable values for each spatial unit are used to simulate the spatial distribution characteristics of the target variable under the condition that the null hypothesis holds. This process is repeated. Each time (the experiment was set to 9999 times), the fuzzy permutation was recalculated. The statistic is then used to construct its empirical distribution under the null hypothesis. Then, the fuzzy logic to be tested is... Statistic and permutation test simulation generation Compare several fuzzy statistics to calculate the permutation test. Value. Specifically, the simulated value. The fuzzy statistics are sorted from smallest to largest. If the fuzzy statistic to be tested is... The statistic is greater than the first one. If there are a value, then The value can be represented as: (13) when When the value is less than the preset significance level (e.g., 0.05), the null hypothesis is rejected, and the fuzzy spatial structure defined by the explanatory variables is considered to have statistically significant explanatory power for the target variable, i.e., fuzzy... The statistic is significant.
[0057] To verify the reliability of the permutation test, this application calculated the permutation test simulation fuzzy logic. The probability density distribution of a statistic, such as Figure 3 As shown in the figure. It can be seen from the figure that in and In the case of random distribution, fuzzy The statistics are mainly concentrated in the range of 0-0.002. When the significance levels are set to 0.1, 0.05 and 0.01 respectively, if the values in equation (10) are... If the value is less than the preset significance level, then it is fuzzy. The statistics are greater than 0.00069, 0.00085 and 0.0012, respectively.
[0058] In geospatial analysis, the influence of multiple explanatory variables on the target variable is often not independent, but may interact to affect the spatial distribution of the target variable. Classic geospatial detectors use spatial overlay methods to identify interaction effects: two explanatory variables are spatially layered and overlaid, and the results are compared before and after overlay. Statistics are used to determine whether an interaction exists and its type.
[0059] After introducing fuzzy spatial layering, spatial superposition is extended to the intersection operation of fuzzy sets to identify the interaction effects of multiple explanatory variables. Specifically, fuzzy spatial layers are constructed for each explanatory variable, the membership degree of each spatial unit to each layer is calculated, and the fuzzy spatial layers of multiple explanatory variables are superimposed using the product rule of fuzzy intersection.
[0060] With two explanatory variables (like (for soil type) and (like Taking slope and two strata (stratum 1 and stratum 2) as examples, the explanatory variables are... Divided into two fuzzy layers , Explanatory variables Divided into two fuzzy layers , Therefore, when there are two layers and two explanatory variables, the fuzzy spatial stratification result is four layers. , and , To distinguish it from traditional spatial stratification, it is called a fuzzy layer. The value of each spatial unit in the layer represents the membership degree of the spatial unit to a certain stratum under a single explanatory variable. Note that in classic geographic detectors, the number of layers is the same as the number of explanatory variables; that is, the deterministic stratification result of two explanatory variables is two layers, and the spatial units in each layer are represented by the labels corresponding to stratum 1, 2, etc., indicating their stratification affiliation. In probing explanatory variables... and When interacting, four combined layers can be constructed according to the fuzzy intersection operation rules: , , , For any spatial unit Its intersection layering The membership degree in (m, n=1,2) can be calculated using the following formula: (14) in, and Representing spatial units Fuzzy layering and The degree of membership.
[0061] Based on the interaction criteria of classic geographic detectors, the interactions between interpreting factors can be classified into five types: nonlinear attenuation, single-factor nonlinear attenuation, two-factor enhancement, independent interaction, and nonlinear enhancement. The specific discrimination methods are shown in Table 1 below. Table 1. Types and determination methods of interactions
[0062] In summary, the fuzzy geographic detector proposed in this embodiment, such as Figure 2 As shown, this fuzzy geographic detector takes continuous observations of explanatory and target variables as input and includes three core modules: The first module is a fuzzy spatial stratification unit, which calculates the membership degree of each spatial unit to each stratum for each explanatory variable by introducing a fuzzy spatial stratification method (such as FCM). The second module is a spatial attribution analysis unit, which calculates the weighted mean within each stratum using fuzzy membership degrees as weights. The weighted sum is used to obtain the estimated value of the target variable (i.e., the reconstructed value of the target variable). Then, the squared error between the estimated value and the observed value is used to replace the traditional... Intra-layer variance in statistics, constructing fuzzy Statistics are used to enhance sensitivity to continuous changes in explanatory variables. Finally, fuzzy logic is tested using permutation tests. The significance of the statistics. The third module is the interaction identification unit, which uses fuzzy intersection operation to superimpose the fuzzy spatial layering results of multiple explanatory variables, and compares the fuzzy values before and after superposition. By analyzing changes in statistical parameters, the type of interaction between explanatory variables can be identified. This fuzzy geodetector, by allowing spatial units to simultaneously belong to multiple strata with different membership degrees, more realistically expresses the spatial continuity and gradual processes of variables, avoids the information loss of continuous explanatory variables (such as slope) in the geodetection process caused by stratification strategies, and improves the robustness and accuracy of geoattribution analysis.
[0063] Based on the same inventive concept, this embodiment also provides a method for using a fuzzy geographic detector, including: Acquire geospatial data of the study area, wherein the geospatial data includes a target variable and at least one explanatory variable; The geospatial data is input into the fuzzy geographic detector provided in any of the foregoing embodiments, and the output includes the membership degree of each spatial unit to each layer, fuzzy... The fuzziness of the statistics and the fuzziness before and after the layering of each fuzzy space Results of detecting changes in statistical measures; Based on the detection results, we analyze the explanatory power of a single explanatory variable and a combination of multiple explanatory variables on the target variable.
[0064] The method for using the fuzzy geographic detector provided in this embodiment can perform all the technical steps of the fuzzy geographic detector and achieve the same technical effect, which will not be elaborated here.
[0065] Verification Example Taking the study and geographical analysis of the driving mechanism of NO2 concentration in Guangdong Province as an example, the study of the driving mechanism of NO2 concentration is one of the typical studies of geographical analysis and mechanism explanation of environmental pollution. The specific method of using the fuzzy geographic detector in this scenario is as follows: First, spatial data was collected. POIs, population density, land use, and road density were used as explanatory variables, and NO2 concentration as the target variable. This spatial data was acquired through remote sensing data products, the Gaode Map API, and OpenStreetMap. The collected raw data was then uniformly converted into raster data with a spatial resolution of 2 kilometers. The conversion method involved averaging the values within each 2-kilometer grid cell to obtain representative characteristic values. Specific data sources are shown in Table 2.
[0066] Table 2. Case Data Sources
[0067] Secondly, using the fuzzy C-means clustering method, clustering was performed based on POI density, population density, land use, and road density respectively. A fuzzy spatial hierarchy is constructed using a kilometer-scale raster to obtain the fuzzy hierarchy corresponding to these explanatory variables. For each explanatory variable, the fuzzy hierarchy result is a raster representation of the membership degree of each raster to each hierarchy.
[0068] Then, based on the fuzzy stratification results, the fuzzy logic corresponding to each explanatory variable is calculated respectively. Statistics.
[0069] Figure 4 The fuzzy code corresponding to each explanatory variable is given. The statistical ranking results show that road density has the highest explanatory power for NO2 concentration, indicating that traffic emissions dominate the spatial differentiation of NO2; built-up areas are next, consistent with the pattern that they significantly influence NO2 concentration as carriers of human activities; shrubs and grasslands have a weaker explanatory power. Furthermore, the explanatory power varies among different types of POI density, indicating that different human activities correspond to different NO2 emission intensities.
[0070] Finally, these explanatory variables are combined in pairs, and corresponding fuzzy spatial layers are selected for fuzzy superposition. The fuzziness after superposition is then compared with that before superposition. Statistics are used to determine the type of interaction between these variables, such as... Figure 5 As shown in the figure, most interactions between variables are of the two-factor enhancement type, while a few are of the single-factor weakening, independent, or non-linear enhancement type.
[0071] To illustrate the fuzzy geographic detector (especially the fuzzy one) in this embodiment (Statistical measures), compared to the advantages of traditional geographic detectors in attribution accuracy, Figure 6 The differences in stratification between traditional and fuzzy geographic detectors in intra-layer and transitional regions were compared. Figure 7 The differences in stratification between traditional and fuzzy geographic detectors in transitional regions were compared.
[0072] like Figure 6 As shown in (a) and (b), the spatial distribution of NO2 concentration in the actual mesosphere is largely consistent with the spatial distribution of road density. Layering was performed using both a traditional geographic detector and the fuzzy geographic detector proposed in this application. The results show that the traditional geographic detector classifies most areas into stratum 3 (e.g., ...). Figure 6 As shown in (c)), ignoring fine-grained variations in road density within layers may result in lower explanatory power. In contrast, fuzzy geographic detectors utilize continuous variations in membership (such as...) Figure 6 As shown in (d) in the figure, the characteristics of intra-layer variation are more refined, which improves the accuracy of the judgment of the consistency between road density and NO2.
[0073] like Figure 7 As shown in (a) and (b), road density and NO2 concentration exhibit similar distributions in the transition zone. The deterministic stratification of traditional geographic detectors uniquely classifies the spatial units of the transition zone to stratum 2 or 3, simplifying the gradual change in road density. Figure 7 (c) leads to a decrease in the spatial matching degree of variables, thereby affecting the coupling relationship detection results of the geographic detector. In contrast, the fuzzy geographic detector characterizes the gradual process of road density through continuous changes in membership degree. Figure 7 (d) reduces the disruption of the coupling relationship between road density and NO2 concentration in the transition area by deterministic stratification, and improves the accuracy of interpreting quantitative results.
[0074] Since it is difficult to obtain the true value of the correlation strength between geographic variables in real-world scenarios, this embodiment also designed a simulation experiment to generate three sets of fully coupled relationships ( , and The explanatory variable X and the target variable Y are compared under the condition that the true value of the association strength is 1, thus verifying the detection advantage of the fuzzy geographic detector. Tables 3 to 5 respectively give the following... , and Under three fully coupled relationships, with different numbers of layers (2, 3, 4, and 5), deterministic and fuzzy spatial layering were performed using the K-means method and fuzzy C-means clustering (FCM method), thereby calculating... Statistics and Fuzzy Statistic The size of the statistic.
[0075] Table 3 Down Statistics and Fuzzy Statistic Comparison of statistics
[0076] Table 4 Down Statistics and Fuzzy Statistic Comparison of statistics
[0077] Table 5 Down Statistics and Fuzzy Statistic Comparison of statistics
[0078] As can be seen from the table, under the three fully coupled relationships, the fuzzy A statistic closer to 1 indicates that the detection results are more accurate.
[0079] This application provides a computer device, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the method for using the fuzzy geographic detector provided in the foregoing embodiments.
[0080] Specifically, the embodiments of this application can be applied to Figure 8 The electronic devices (computer devices) shown may be, but are not limited to, mobile terminals such as mobile phones, tablets, handheld computers, and personal digital assistants (PDAs), smart home devices such as smart TVs and smart cameras, wearable devices such as smart bracelets, smartwatches, and smart glasses, or other desktop, laptop, notebook, ultra-mobile personal computer (UMPC), netbook, and smart screen computer devices.
[0081] like Figure 8 As shown, the electronic device 200 may include one or more of the following components: a processor 201, a memory 203, a communication interface 202, and a communication bus 204. The memory 203 can be connected to the processor 201 via the bus 204. The bus can transfer data between the processor 201 and the memory 203. The bus can be divided into an address bus, a data bus, a control bus, etc.
[0082] Processor 201 may include one or more processing cores. Processor 201 can connect to various parts within the electronic device 200 using various interfaces and lines. It performs various functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory 203, and by calling data stored in memory 203. For example, processor 201 may include an application processor (AP), a modem processor, a CPU, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a video codec, a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic array (PLA), and / or a neural network processing unit (NPU). The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed; the NPU implements artificial intelligence (AI) functions; and the modem handles wireless communication. Different processing units can be independent devices or integrated into one or more processors. For example, the multiple processing units shown above are all integrated into a single SoC, or the AP is a separate semiconductor chip, while other processing units are integrated into a single SoC. This application does not limit this to any particular type.
[0083] The memory 203 may include random access memory (RAM), read-only memory (ROM), or non-transitory computer-readable storage medium. The memory 203 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 203 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function, such as the usage method of a fuzzy geographic detector; the data storage area may store geospatial data collected based on the use of the electronic device 200, etc.
[0084] In addition, those skilled in the art will understand that the structure of the electronic device 200 shown in the above figures does not constitute a limitation on the electronic device 200. The electronic device may include more or fewer components than shown, or combine certain components, or have different component arrangements. For example, the electronic device 200 may also include components such as a microphone, speaker, radio frequency circuit, sensor, audio circuit, power supply, and Bluetooth module, which will not be described in detail here.
[0085] This application provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the method for using the fuzzy geographic detector provided in the foregoing embodiments.
[0086] This application provides a computer program product, including a computer program / instructions, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of the method for using the fuzzy geographic detector provided in the foregoing embodiments.
[0087] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A fuzzy geographic detector, wherein the fuzzy geographic detector is applied to computer equipment, characterized in that, include: The fuzzy spatial stratification unit is configured as follows: the spatial units of the study area are stratified using the fuzzy spatial stratification method, the membership degree of each spatial unit to each stratification is calculated, and the fuzzy spatial stratification result is obtained. The spatial attribution analysis unit is configured to: calculate the representative value of the target variable for each layer based on the membership degree, and calculate the reconstructed value of the target variable for each spatial unit accordingly; Based on the estimation error between the reconstructed value and the observed value of the target variable, a fuzzy model is constructed. Statistics are used to measure the explanatory power of explanatory variables on the spatial differentiation of the target variable; Wherein, the target variable represents the value in the same stratum. Within, the weighted mean of the target variable with the membership degree as the weight, the reconstructed value of the target variable in different strata. The following is a weighted summation of the target variables, with the membership degree as the weight; The interaction identification unit is configured to: superimpose the fuzzy spatial layering results of multiple explanatory variables using fuzzy intersection operations, and compare the fuzzy layers before and after superposition. Changes in statistics can help identify the types of interactions between explanatory variables.
2. The fuzzy geographic detector according to claim 1, characterized in that, The formulas for calculating the representative values of the target variables within each stratum are as follows: ， In the formula, For layering The weighted mean of the internal target variable. This represents the total number of spatial units within the study area. For the first Each spatial unit belongs to a stratification membership degree For the first The observed values of the target variable for each spatial unit.
3. The fuzzy geographic detector according to claim 2, characterized in that, The formula for calculating the reconstructed value of the target variable is: ， In the formula, For the first Reconstructed values of the target variables for each spatial unit This represents the total number of layers.
4. The fuzzy geographic detector according to claim 3, characterized in that, The ambiguity The formula for calculating the statistic is: ， ， In the formula, Indicates ambiguity Statistic, This represents the squared error generated by reconstructing the target variable using fuzzy spatial hierarchies. This represents the total variance of the target variable.
5. A method for using a fuzzy geographic detector, characterized in that, include: Acquire geospatial data of the study area, wherein the geospatial data includes a target variable and at least one explanatory variable; The geospatial data is input into any one of the fuzzy geodetectors described in claims 1 to 4, and the detection results are output. These results include the membership degree of each spatial unit to each layer, and the fuzziness... The fuzziness before and after the fuzzy spatial layering of statistics and different explanatory variables Changes in statistics; Based on the detection results, the explanatory power of a single explanatory variable and a combination of multiple explanatory variables on the target variable is analyzed.
6. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of using the fuzzy geographic detector as described in claim 5.
7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of using the fuzzy geographic detector as described in claim 5.
8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method of using the fuzzy geographic detector as described in claim 5.