Spectral clustering / minimum spanning tree fusion-based earthquake emergency zoning method

Abstract

The application discloses a spectrum clustering / minimum spanning tree fusion earthquake emergency zoning method, which comprises the following steps: step one, constructing an earthquake emergency zoning capability correlation network model; step two, performing similarity calculation optimization on the earthquake emergency zoning network model according to step one, including index factor screening, geographical space information and network similarity weight operation; step three, fusing spectrum clustering and a minimum spanning tree algorithm, including minimum spanning tree correction and regional division based on a spectrum clustering improved algorithm; and step four, establishing an earthquake emergency decision application according to the result of the earthquake emergency regional division, so as to realize earthquake emergency zoning division and earthquake emergency decision making of each region. According to the earthquake emergency regional characteristics, the application describes the application of the earthquake emergency zoning in emergency auxiliary decision making, explores an earthquake emergency auxiliary method suitable for the types of earthquake emergency regions, and provides a theoretical basis for earthquake emergency command decision making and rescue action scheme countermeasures.

Description

Technical Field

[0001] This invention relates to an earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion, belonging to the field of geographical regionalization. Background Technology

[0002] Post-earthquake emergency response and rescue are crucial methods for effectively mitigating earthquake disaster losses. However, given my country's vast territory and distinct geographical and disaster characteristics across different regions, it is necessary to explore regional earthquake emergency characteristics and establish different earthquake emergency zoning systems. This facilitates targeted earthquake emergency preparedness and rescue, thereby enhancing the effectiveness of earthquake emergency response and disaster reduction. Therefore, this paper explores an earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion, and applies this method to establish a hierarchical earthquake emergency zoning system for my country.

[0003] For a long time, people have conducted extensive exploration and practice in earthquake prevention and disaster reduction, gradually developing and forming three major countermeasure systems: earthquake monitoring and forecasting system, earthquake disaster prevention system, and earthquake emergency rescue system. However, in the specific construction, development, and application of these three systems, there are often differences and emphases due to the actual conditions of different countries and regions. To reduce the losses caused by earthquakes to humans and society, countries around the world have focused their research on the spatial analysis of earthquake disasters, the formulation of earthquake emergency plans, and the implementation of emergency rescue. The concept of spatial analysis can be traced back to the revolution in geography and regional science. In the early stages, it mainly introduced statistical methods into geographical research to quantitatively describe the spatial distribution patterns of points, lines, and areas. In later stages, it gradually focused on the characteristics of geographical space itself, spatial decision-making processes, and the spatiotemporal evolution of spatial systems, providing a convenient way to conduct research on geospatial issues. Currently, spatial analysis has wide applications in natural disaster risk assessment, natural disaster database construction, disaster mapping, and decision analysis.

[0004] Regionalization, or the division of regions, is not merely a data analysis tool but also a representation of the analytical results. Regionalization must be compatible with and support the sustainable development of a region. By dividing regions, the attributes and connections of various components within the geographical environment can be visually expressed, leading to a better understanding and exploration of their occurrence, development, distribution, and structure—the underlying geographical laws. Exploring the regional differentiation patterns of the geographical environment has always been a crucial topic in geosciences, especially geographical research. In this process, the theory and methods of "geographical regionalization" have matured. Geographical regionalization is the process of dividing a comprehensive geographical environment into several spatial regions based on its similarities and differences. It summarizes complex regional differences into a scientific system and spatial network. However, in the comprehensive division of geographical regions, the role of human beings in the regionalization system is rarely considered; that is, the natural and human elements are not organically combined. Furthermore, the theoretical and methodological system of geographical regionalization is not yet perfect. A deeper understanding of human geography systems and regional differentiation patterns is needed to establish a more rigorous and comprehensive regionalization system that meets the needs of sustainable regional development.

[0005] Regarding earthquake emergency response, my country currently relies primarily on peacetime earthquake emergency plans to guide pre-earthquake preparation and post-earthquake rescue efforts. These plans fall into two categories: the first is national-level plans and countermeasures, and the second is emergency plans formulated under regulations such as the "Regulations on Emergency Response to Destructive Earthquakes" and the "National Emergency Response Plan for Destructive Earthquakes." While these plans reflect some regional differences in earthquake emergency response, they are often too simplistic and lack a comprehensive description and analysis of regional variations, particularly failing to address specific socio-economic issues and key technical aspects under local earthquake conditions. Therefore, these plans generally suffer from a disconnect from the natural and socio-economic conditions of specific regions. In fact, both types of earthquake emergency plans are primarily empirical and descriptive regulations and rules, still in their early stages compared to dynamic, scientific, computer-modeled, and systematic emergency decision-making. Therefore, strengthening research on regional division of earthquake emergency response and systematically reflecting and applying this in my country's emergency work is of paramount practical importance. Summary of the Invention

[0006] The purpose of this invention is to provide an earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion, for use in pre-earthquake emergency prevention and preparedness and post-earthquake emergency command and rescue. It measures the earthquake emergency type of each county-level city based on earthquake emergency zoning, understanding the emergency response capabilities, emergency characteristics, and local emergency features of each county-level city. This further helps to understand the organizational structure, action measures, resource guarantees, and psychological qualities necessary for regions with different characteristics in China, and the performance and preparedness of various factors currently affecting earthquake emergency response capabilities, before and after an earthquake.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: an earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion, comprising the following steps:

[0008] Step 1: Construct a network model for earthquake emergency zoning capabilities;

[0009] Step 2: Based on Step 1, optimize the earthquake emergency zoning network model by calculating similarity, including the selection of indicator factors, geospatial information, and network similarity weight calculation.

[0010] Step 3: Integrate spectral clustering with the minimum spanning tree algorithm, including minimum spanning tree correction and region partitioning based on the improved spectral clustering algorithm;

[0011] Step four: Based on the results of the earthquake emergency zone division, establish an earthquake emergency decision-making application to realize the division of earthquake emergency zones and the formulation of earthquake emergency decisions in various regions.

[0012] Furthermore, in step two, the selection of indicator factors specifically includes the selection of factors that are influenced by regional factors such as the level of earthquake emergency response capabilities, and the selection of interrelated factors as the basis for determining regional division.

[0013] Furthermore, in the selection of earthquake emergency zoning indicators, the selection principles of "scientific, comparable, operable, independent, and representative" for earthquake emergency response are followed, and the four major methods of indicator screening are compared, theoretical analysis, experience-based learning, and realistic deduction to select earthquake emergency zoning indicator factors.

[0014] Furthermore, in step two, geospatial information is one of the characteristics affecting earthquake emergency response. The node location of each county is determined according to its own geographical location and latitude and longitude. By processing the geographical distance between counties and obtaining the normalized distance between all county-level cities, the geographical information between each county-level city can be obtained.

[0015] Furthermore, in step two, the network similarity weight calculation is divided into geospatial calculation, earthquake emergency zoning index dataset calculation, and earthquake emergency similarity optimization. Geospatial information calculation uses ArcGIS to convert latitude and longitude data into XY coordinate data. Distance calculation between county-level cities is performed using any two county nodes, and the resulting geographic data needs to be represented using distance data with unified dimensions. In the earthquake emergency zoning index dataset calculation, the weights between counties and cities represent the strength of the relationship between them in the construction of the regional earthquake emergency correlation network. The correlation degree between earthquake emergency capabilities in different regions is directly proportional to the correlation degree of earthquake emergency index factors and inversely proportional to geographic location information. Earthquake emergency similarity optimization, in the earthquake emergency zoning correlation network, uses the final ratio between the correlation coefficient of each county node and the normalized node as a standard to measure the strength of the node relationship.

[0016] Furthermore, the geospatial information calculation involves using ArcGIS to convert latitude and longitude data into XY coordinate data, and then applying the formula C = sin(LatA)*sin(LatB)*cos(LngA-LngB) + cos(LatA)*cons(LatB), d(V i V j =R*Arccos(C)*π / 180, which is the spatial distance between counties after processing with latitude and longitude.

[0017] The earthquake emergency zoning index dataset is calculated as follows: Treating each of the n indicators as independent points, the similarity between samples is calculated to obtain a similarity matrix S, where S is a symmetric matrix with diagonal elements of 0.

[0018] The earthquake emergency similarity optimization refers to the strength of the connection between county-level cities within a geospatial information region at the level of earthquake emergency zoning, measured by the optimized similarity of the complex network, using the following formula: The final similarity matrix W is obtained.

[0019] Furthermore, in step three, the minimum spanning tree correction specifically includes converting the earthquake emergency zoning network graph into an adjacency matrix, then using the minimum spanning tree to correct the adjacency matrix, removing edges with large network weights, and treating the corrected adjacency matrix as a spatial relationship matrix between sample points.

[0020] Furthermore, the instance process of the minimum spanning tree correction matrix is ​​as follows:

[0021] 1) Find the longest edge in the minimum spanning tree G. If this edge is removed, the minimum spanning tree will be divided into two segments, G1 and G2. The similarity distance is then equal to the distance between any sample point x in G1. iBetween any sample point in G2, use (x i ,x j )=d ij express;

[0022] 2) Cut tree G1 and tree G2, and repeat step 1) until there are no more subtrees to cut; the matrix obtained after the cutting is completed is used to measure the similarity between sample points;

[0023] The above two steps complete the correction of the similarity matrix. In the similarity matrix obtained before and after the operation, "0" indicates that there is no spatial attribute between the two counties; "1" indicates that there is a spatial relationship between the two counties; and " / " indicates that the connection between the two counties is severed after the cut.

[0024] Furthermore, in step three, the region partitioning based on the improved spectral clustering algorithm uses graph theory to characterize the data. Based on the principle of graph segmentation, spectral clustering is used to transform the problem to be solved into a graph partitioning solution. This characteristic of spectral clustering is applied to the earthquake emergency response capability association network transformed into a graph form, and finally the clustering partitioning result is completed.

[0025] Furthermore, the specific process of clustering is as follows:

[0026] 1) After obtaining the similarity matrix W and the adjacency matrix T, perform an exponential transformation on the similarity matrix W to obtain the final similarity matrix W'.

[0027]

[0028] 2) Construct a normal Laplace matrix from the similarity matrix W' obtained after correcting the adjacency matrix:

[0029]

[0030] 3) Calculate the eigenvalues ​​of matrix L, sort them in ascending order, take the first k smallest eigenvalues ​​and calculate the corresponding eigenvectors, and then cut them using the standard cut algorithm (NCut); the normalized Laplacian matrix D... -1 / 2AD -1 / 2;

[0031] 4) Obtain D -1 / 2AD -1 / 2. Find the first k1 (1≤k1<11) smallest eigenvalues ​​and their corresponding eigenvectors f, and finally normalize the matrix f to obtain the eigenma matrix H. The eigenma matrix H can be regarded as a sample set. Finally, perform cluster analysis on the matrix H.

[0032] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0033] (1) This invention realizes the construction of an earthquake emergency zoning method based on the fusion of spectral clustering and minimum spanning tree. Graph theory algorithm is selected as the clustering method for earthquake emergency zoning in this paper. Spectral clustering algorithm is suitable for the requirements of earthquake emergency zoning in this paper, but problems occur in the clustering process. Therefore, this paper improves the traditional spectral clustering algorithm. By establishing an earthquake emergency capability association network model and optimizing the similarity calculation, the earthquake emergency zoning association network matrix is ​​combined with the adjacency matrix corrected by the minimum spanning tree to finally realize the clustering and division of earthquake emergency areas. Moreover, the division result of the algorithm meets the regional division requirements of earthquake emergency in this paper.

[0034] (2) This invention, based on the massive amount of indicator data and geographic information data on earthquake emergency response in my country, classifies secondary regional types with different earthquake emergency response characteristics. This paper standardizes the earthquake emergency zoning indicator factor data and, combined with spectral clustering / minimum spanning tree algorithms, delineates my country's secondary earthquake emergency zoning. The primary earthquake emergency zoning consists of eight earthquake emergency zones, including those in the Northeast and Southeast, while the secondary emergency zoning includes 59 regional types.

[0035] (3) This invention discusses the characteristics of my country's Level II earthquake emergency zoning and introduces its application in earthquake emergency decision support. It analyzes the characteristics of earthquake emergency zoning and its impact on earthquake emergency rescue from the perspectives of natural geographical environment, economic and human geography, and disaster characteristics. Based on the characteristics of earthquake emergency zones, it elaborates on its application in emergency decision support and explores earthquake emergency support methods suitable for different earthquake emergency zone types. This provides a theoretical basis for the scientific formulation and effective implementation of earthquake emergency command decisions and rescue action plans. Attached Figure Description

[0036] Figure 1 This is a diagram illustrating the architecture of a spectral clustering method for earthquake emergency zoning.

[0037] Figure 2 This is a structural diagram of a spectral clustering method for earthquake emergency zoning.

[0038] Figure 3 This is a content structure diagram of earthquake emergency zoning similarity calculation optimization.

[0039] Figure 4 The diagram shows the network model of earthquake emergency response capabilities; (a) dataset of county-level cities in Yunnan Province, and (b) constructed network connectivity graph.

[0040] Figure 5 It is an indicator system for establishing earthquake emergency zoning.

[0041] Figure 6 Examples of some county-level cities in Yunnan Province: (a) Map of some counties in Yunnan Province, (b) Latitude and longitude data of some counties in Yunnan Province.

[0042] Figure 7 This is the clustering algorithm process after fusing spectral clustering and minimum spanning tree: (a) dataset, (b) constructing connected graphs, (c) MST correction, and (d) graph slicing and clustering. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0044] Example 1.

[0045] like Figure 1 As shown, an architecture design for an earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion is presented. Based on the architecture design diagram, the structure of the spectral clustering method is designed, as follows: Figure 2 As shown, it is mainly divided into the following three parts:

[0046] (1) Similarity calculation optimization. In order to obtain the adjacency matrix representing the vertices, it is necessary to obtain the similarity matrix between samples. By optimizing the similarity, and combining the geographical information and indicator data of county-level cities in the region, the weights of the complex network of earthquake emergency response capability are finally constructed.

[0047] (2) Minimum spanning tree correction. A transfer matrix is ​​constructed using the minimum spanning tree. An exponential transformation is performed on the transfer matrix to obtain the matrix with the best similarity to itself. This avoids problems such as unstable clustering results and repeated calculations due to the presence of the scaling factor in the Gaussian measure. The indicator data and geographic information data of various provinces and cities in my country are extracted as a sample set, and a similarity map is constructed. At this time, the division of earthquake emergency areas becomes a problem of dividing the map.

[0048] (3) Regional division based on spectral clustering method. The earthquake emergency zone was divided according to the relevant division criteria of spectral clustering, and the experimental results were obtained.

[0049] In summary, the structure of the spectral clustering method for earthquake emergency zoning consists of similarity calculation optimization, minimum spanning tree correction, and region division based on the spectral clustering method.

[0050] Example 2.

[0051] Figure 3 The optimized content structure for similarity calculation using spectral clustering methods divides the similarity in the graph into the following four parts:

[0052] (1) Constructing an earthquake emergency response capability correlation network model. When establishing the earthquake emergency response capability network model, firstly, all county-level cities in my country are set as a set of nodes, and the data of each node represents the multidimensional earthquake emergency response index data of each county-level city; secondly, a comprehensive index reflecting the correlation between earthquake emergency response capabilities between two sample points is established, and this comprehensive index is calculated according to relevant rules; finally, in order to effectively measure the weight of each side index of the earthquake emergency response network, the correlation between earthquake emergency response capabilities between two nodes is expressed.

[0053] (2) Screening of Indicator Factors. For earthquake emergency zoning, the establishment of earthquake emergency response cities and counties in each region should be multi-dimensional in terms of time and space. The interaction between these influencing factors and the regional indicator factors and earthquake emergency response capabilities over time and space is crucial. Regional earthquake emergency response capabilities are strongly related to various indicator factors; changes in these indicator factors directly affect the correlation of earthquake emergency response capabilities.

[0054] (3) Constructing an earthquake emergency zoning indicator system. The construction of the indicator system is the basis for the division of earthquake emergency zones. It mainly includes the classification, quantification and screening of indicators. Through appropriate indicator selection methods, indicators that can comprehensively and scientifically reflect the level of earthquake emergency response capabilities are made. Natural environment, regional seismic activity and regional socio-economic conditions are used as the measurement criteria for earthquake emergency zone division. In this way, evaluation indicators are established to establish the relationship between these factors and earthquake emergency zoning. Specific research is also conducted on the factors that affect earthquake emergency zoning.

[0055] (4) Network Similarity Weight Calculation. Network similarity weight calculation is divided into geospatial calculation, earthquake emergency zoning index dataset calculation, and earthquake emergency similarity optimization. Among them, geospatial information calculation uses ArcGIS to convert latitude and longitude data into XY coordinate data. The distance calculation between county-level cities is performed by calculating the distance between any two county nodes. The resulting geographic data also needs to be represented by distance data with unified dimensions. In the construction of the regional earthquake emergency correlation network, the weight between counties and cities represents the strength of the relationship between them. The correlation degree between earthquake emergency capabilities in various regions is directly proportional to the correlation degree of earthquake emergency index factors and inversely proportional to geographic location information. Earthquake emergency similarity optimization is to use the correlation coefficient of each county node and the final ratio between the normalized nodes as a standard to measure the strength of the relationship between nodes in the earthquake emergency zoning correlation network.

[0056] The earthquake emergency zoning method is described in further detail below, with the specific steps as follows:

[0057] Step 1: Construct an earthquake emergency response capability correlation network model. Figure 4 The earthquake emergency response capability network diagram is represented as G=(V,E,W), and the division is defined as follows:

[0058] 1) V represents the set of nodes within the earthquake emergency zone;

[0059] 2) E represents the set of edges within the earthquake emergency zone;

[0060] 3) W represents the set of weights of each side within the earthquake emergency zone, and the magnitude of the weight value represents the correlation between the earthquake emergency response capabilities of any two counties (cities);

[0061] In summary, the above three levels together constitute the earthquake emergency response capability correlation network model.

[0062] Step two involves screening indicator factors. In selecting earthquake emergency zoning indicators, based on the principles of "scientific rigor, comparability, operability, independence, and representativeness" for earthquake emergency response, and combined with indicator screening reference methods, four main methods are used: comparative method, theoretical analysis method, experience-based method, and realistic extrapolation method. These methods are used to screen earthquake emergency zoning indicator factors, including:

[0063] 1) Indicator Selection Principles. The level of earthquake emergency response in a region is reflected in multiple aspects and is influenced by numerous factors, often requiring the selection of highly representative indicators. Therefore, certain principles must be followed when assessing earthquake emergency zoning. Thus, the following six principles, including scientific rigor and comparability, are used to select earthquake emergency indicators. The following explains each principle:

[0064] i. Scientific principle: When determining the assessment indicators, objective facts must be respected and the designed indicators must be consistent with the actual situation of earthquake emergency zoning capabilities, so as to better reflect the current status of earthquake emergency zoning capabilities;

[0065] ii. Comparability principle: In order to conduct comparative analysis of different earthquake emergency response areas, the evaluation index system should be able to reflect regional differences, and the selected index data should be complete and comparable;

[0066] iii. Operational Principles: All evaluation indicators must be based on evidence, facilitate quantitative analysis, and reflect the characteristics and actual conditions of the region. Furthermore, to facilitate work, measurement, and calculation, the evaluation indicators should be interconnected and kept as consistent as possible within the current statistical framework in my country. Operational feasibility also means that decision-makers can use easily accessible results to better assist in earthquake disaster prevention and mitigation efforts, thereby further improving local earthquake emergency response capabilities. Because data on emergency plans for county-level cities is fragmented and incomplete, it is essential to fully utilize existing data and extract relevant information from it.

[0067] iv. The principle of independence: In the set of evaluation indicators, each indicator should not only be scientifically sound but also concise and clear. Furthermore, the indicators may be interrelated; if duplicate information is not excluded, these interrelated details will be amplified, thus affecting the rationality of the evaluation results. Therefore, ensuring that the characteristics reflected by the indicators are not duplicated is crucial to guaranteeing the independence of each indicator.

[0068] v. Representativeness Principle: When conducting earthquake emergency zoning, it is essential to consider various factors such as geographical environment, climate, earthquake conditions, human factors, and economic factors. Including all elements in the assessment is neither realistic nor necessary. Therefore, the selected indicators must be representative, reflecting earthquake emergency zoning from various perspectives, as well as the role and specific content of each dimension.

[0069] ⅵ. Accessibility principle: There are many indicators for evaluating earthquake emergency response, but data for some indicators may be missing due to reasons such as the age of the data or the remoteness and sparse population of the region. Therefore, the data for earthquake emergency response indicators should be as accessible as possible, and data for indicators that are available in the study area for a certain period of time should be selected.

[0070] 2) Indicator Selection Reference Methods. When selecting evaluation indicators, a certain reference basis is necessary. Therefore, methods such as comparison, theoretical analysis, empirical reference, and real-world deduction were adopted.

[0071] i. Comparative method: Compare my country's earthquake emergency response process with that of other countries in the world;

[0072] ii. Theoretical analysis method: drawing on or citing classic theoretical viewpoints from authoritative institutions;

[0073] iii. Experience-based approach: Review and statistically analyze frequently occurring indicators in relevant literature on historical earthquake disasters and the evaluation of emergency zoning development levels, and incorporate them into the indicator system as widely recognized influencing factors;

[0074] iv. Reality extrapolation method: Based on strategic plans in the earthquake emergency database, earthquake emergency response reports from provincial, municipal and county governments, and some real-world socio-economic and earthquake disaster indicators collected when my country faces earthquake disasters.

[0075] Based on the above six principles and four screening methods, factors and indicator factors that influence earthquake emergency zoning were selected.

[0076] Step 3: Construct an earthquake emergency zoning indicator system. The level of earthquake emergency zoning capability is influenced by numerous regional factors. Therefore, this step begins by examining the factors affecting regional earthquake emergency zoning to assess its indicator capability. Based on the above analysis, the earthquake emergency zoning indicator system is divided into three levels: target layer, element layer, and indicator layer. Figure 5 For earthquake emergency response indicator system.

[0077] 1) Target Layer. The target layer A of the earthquake emergency zoning index system is the highest level, referring to the magnitude of the region's earthquake emergency response capability;

[0078] 2) Element Layer. The element layer consists of three elements: natural environment, seismic activity, and socio-economic conditions;

[0079] 3) Indicator Layer. The indicator layer consists of 15 secondary indicators;

[0080] In summary, the earthquake emergency zoning indicator system has been established. Let the overall objective factor set A be the overall objective of earthquake emergency zoning evaluation, A = {B1, B2, B3} = {natural environment, regional seismic activity, regional socio-economic conditions}. The framework of the main influencing factors of the earthquake emergency indicator system is shown in Table 1.

[0081] Table 1. Framework of Major Influencing Factors in Earthquake Emergency Response Index System

[0082]

[0083] Step four, network similarity weight calculation, mainly consists of the following three parts:

[0084] 1) Geospatial Information Calculation. Geographic information between county-level cities requires distance calculation. Taking any two county nodes as an example, ArcGIS is used to convert latitude and longitude data into XY coordinate data. Then, the formula C = sin(LatA)*sin(LatB)*cos(LngA-LngB) + cos(LatA)*cons(LatB) is used, where d(V i V j =R*Arccos(C)*π / 180, which is the spatial distance between counties after processing with latitude and longitude.

[0085] 2) Calculation of earthquake emergency zoning index dataset. Treating the n indicators as independent points, the similarity between each sample is calculated to obtain a similarity matrix S, where S is a symmetric matrix with diagonal elements of 0.

[0086] 3) Earthquake Emergency Response Similarity Optimization. The strength of the connection between county-level cities within a geospatial information region at the level of earthquake emergency response zoning is measured by the optimized similarity of the complex network, using the following formula: The final similarity matrix W is obtained.

[0087] The above three steps complete the calculation and optimization of earthquake emergency zoning similarity.

[0088] Example 3

[0089] Figure 6 This is the minimum spanning tree correction process. After obtaining the similarity matrix W for each county-level city, the next step is to obtain the adjacency matrix T. The adjacency matrix, also known as the transitive matrix, provides spatial attributes for the similarity matrix. To reduce the impact of the adjacency matrix on the spectral clustering algorithm, the minimum spanning tree is used to correct the adjacency matrix. The following is an example of using the minimum spanning tree to correct the matrix.

[0090] 1) Find the longest edge of the minimum spanning tree G. If this edge is removed, the minimum spanning tree will be divided into two segments, G1 and G2. The similarity distance, which is the distance between any sample point xi in G1 and any sample point in G2, is represented by (xi,xj) = dij.

[0091] 2) Cut trees G1 and G2, and repeat step 1) until there are no more subtrees to cut. The resulting matrix is ​​used to measure the similarity between sample points.

[0092] The above two steps complete the correction of the similarity matrix. In the similarity matrix obtained before and after the operation, "0" indicates that there is no spatial attribute between the two counties; "1" indicates that there is a spatial relationship between the two counties; " / " indicates that the connection between the two counties is severed after the cut; see Table 2-4.

[0093] Table 2. Unimproved adjacency matrix T (transfer matrix)

[0094]

[0095] Table 3 shows the improved complete adjacency matrix T (transfer matrix).

[0096]

[0097] Table 4 shows the final adjacency matrix T (transit matrix) after graph-cutting clustering.

[0098]

[0099] In summary, the minimum spanning tree correction for earthquake emergency zoning is achieved.

[0100] Example 4

[0101] Figure 7 The flowchart shows the clustering algorithm that combines spectral clustering and minimum spanning tree. Graph theory is used to characterize the data, find the minimum spanning tree G'(V,E), and then partition G'(V,E). This method is based on the principle of graph partitioning, using spectral clustering to transform the problem into a graph-partitioned solution. This characteristic of spectral clustering is well-suited for use in the earthquake emergency response capability association network, which is transformed into a graph form. The specific process is as follows:

[0102] 1) After obtaining the similarity matrix W and the adjacency matrix T, perform an exponential transformation on the similarity matrix W to obtain the final similarity matrix W'.

[0103] I.

[0104] 2) Construct a normal Laplace matrix from the similarity matrix W' obtained after correcting the adjacency matrix:

[0105] II.

[0106] 3) Calculate the eigenvalues ​​of matrix L, sort them in ascending order, take the first k smallest eigenvalues ​​and calculate their corresponding eigenvectors, then perform slicing using the standard cut algorithm (NCut). The normalized Laplacian matrix D is then obtained. -1 / 2 AD -1 / 2 ;

[0107] 4) Obtain D -1 / 2 AD -1 / 2 The smallest k1 (1≤k1<11) eigenvalues ​​and their corresponding eigenvectors f are obtained. Finally, the matrix f is normalized to obtain the eigenma matrix H. The eigenma matrix H can be regarded as a sample set. Finally, cluster analysis is performed on the matrix H.

[0108] The above four steps realize the division of earthquake emergency areas using the improved spectral clustering method. Table 5 shows the pseudocode of the spectral clustering method based on minimum spanning tree.

[0109]

[0110] The meanings of each formula are as follows:

[0111] Ⅰ: Calculation results of the earthquake emergency zoning similarity matrix;

[0112] II: Normal Laplace matrix;

[0113] The meanings of the parameters in the formula are as follows:

[0114] LngA,LatA: Represents the latitude and longitude of node Vi;

[0115] LngB,LatB: Represents the latitude and longitude of node Vj;

[0116] R: Represents the Earth's radius, approximately 6356.76 km;

[0117] d(Vi,Vj): Spatial distance between county-level cities i and j;

[0118] Si,Sj: Index of county-level city indicator factors;

[0119] x in : Indicates the parameter magnitude of index n in county-level city i;

[0120] Sij: represents the set of distances between all index clusters and county-level cities i and j;

[0121] REL(Si,Sj): Represents the weight of the indicator factors between county-level cities i and j;

[0122] Xnorm(i,j): represents the normalized geographical distance between county-level cities;

[0123] w ij : Indicates the similarity of earthquake emergency response capabilities by combining indicator factors and geographical information factors;

[0124] D: Denotes the degree matrix;

[0125] exp(T): Represents the function of exponential transformation;

[0126] W': Represents the similarity matrix obtained after correcting the adjacency matrix;

[0127] L: represents the normal Laplace matrix

[0128] In summary, the improved spectral clustering method for earthquake emergency zoning was achieved, and the secondary regional division of earthquake emergency zoning was completed.

[0129] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the scope of protection of the present invention in any way, and all technical solutions obtained by equivalent substitution or other means fall within the scope of protection of the present invention.

[0130] All parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A method for earthquake emergency zoning based on spectral clustering / minimum spanning tree fusion, characterized in that... Includes the following steps: Step 1: Construct a network model for earthquake emergency zoning capabilities; Step 2: Based on Step 1, optimize the earthquake emergency zoning network model by calculating similarity, including the selection of indicator factors, geospatial information, and network similarity weight calculation. Step 3 involves integrating spectral clustering with the minimum spanning tree algorithm, including minimum spanning tree correction and improved region partitioning based on spectral clustering. Specifically, minimum spanning tree correction involves transforming the earthquake emergency zoning network graph into an adjacency matrix, then using the minimum spanning tree to correct the adjacency matrix, removing edges with large network weights. The corrected adjacency matrix is ​​then considered as the spatial relationship matrix between sample points. An example of the minimum spanning tree correction matrix is ​​provided below. 1) Find the longest edge in the minimum spanning tree G. If this edge is removed, the minimum spanning tree will be divided into two segments, G1 and G2. The similarity distance is then equal to the distance between any sample point x in G1. i Between any sample point in G2, use (x i ,x j )=d ij express; 2) Cut tree G1 and tree G2, and repeat step 1) until there are no more subtrees to cut; the matrix obtained after the cutting is completed is used to measure the similarity between sample points; The above two steps complete the correction of the similarity matrix. In the similarity matrix obtained before and after the operation, "0" indicates that there is no spatial attribute between the two counties; "1" indicates that there is a spatial relationship between the two counties; and " / " indicates that the connection between the two counties is severed after the cut. The improved spectral clustering algorithm for region partitioning uses graph theory to characterize the data. Based on the principle of graph segmentation, spectral clustering is used to transform the problem into a graph partitioning solution. This characteristic of spectral clustering is applied to the earthquake emergency response capability association network, which is transformed into a graph form, to finally complete the clustering results. The specific process of clustering is as follows: 1) After obtaining the similarity matrix W and the adjacency matrix T, perform an exponential transformation on the similarity matrix W to obtain the final similarity matrix W'. ； 2) Construct a normal Laplacian matrix from the similarity matrix W' obtained after correcting the adjacency matrix: ； 3) Calculate the eigenvalues ​​of matrix L, sort them in ascending order, take the first k smallest eigenvalues ​​and calculate the corresponding eigenvectors, then perform a standard cut algorithm to cut the matrix; the normalized Laplacian matrix... ; 4) Obtain The smallest k1 eigenvalues ​​and their corresponding eigenvectors f are obtained, where 1 ≤ k1 < 11; finally, the matrix f is normalized to obtain the eigenma matrix H, which can be regarded as a sample set. Finally, cluster analysis is performed on the matrix H. Step four: Based on the results of the earthquake emergency zone division, establish an earthquake emergency decision-making application to realize the division of earthquake emergency zones and the formulation of earthquake emergency decisions in various regions.

2. The earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion according to claim 1, characterized in that, In step two, the selection of indicator factors specifically includes the influence of regional factors such as the level of earthquake emergency response capability, and the selection of interrelated factors as the basis for determining regional division.

3. The earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion according to claim 1 or 2, characterized in that, In selecting earthquake emergency zoning indicators, the selection principles of "scientific, comparable, operable, independent, and representative" for earthquake emergency response are followed. The selection is combined with four major methods for indicator screening: comparative method, theoretical analysis method, experience reference method, and reality extrapolation method.

4. The earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion according to claim 1, characterized in that, In step two, geospatial information is one of the characteristics that affects earthquake emergency response. The node location of each county is determined according to its own geographical location and latitude and longitude. By processing the geographical distance between counties and obtaining the normalized distance between all county-level cities, the geographical information between each county-level city can be obtained.

5. The earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion according to claim 1, characterized in that, In step two, the network similarity weight calculation is divided into geospatial calculation, earthquake emergency zoning index dataset calculation, and earthquake emergency similarity optimization. The geospatial information calculation utilizes ArcGIS to convert latitude and longitude data into XY coordinate data. The distance calculation between county-level cities is performed by calculating the distance between any two county nodes. The resulting geographic data also needs to be represented using distance data with unified dimensions. In the construction of the regional earthquake emergency correlation network, the weights between counties and cities represent the strength of the relationship between them. The correlation between earthquake emergency capabilities and earthquake emergency index factors in various regions is directly proportional to the correlation between earthquake emergency index factors and inversely proportional to geographic location information. The earthquake emergency similarity optimization uses the correlation coefficient of each county node and the final ratio between the normalized nodes as a standard to measure the strength of the relationship between nodes in the earthquake emergency zoning correlation network.

6. The earthquake emergency zoning method based on spectral clustering / minimum spanning tree fusion according to claim 5, characterized in that, The geospatial information calculation involves using ArcGIS to convert latitude and longitude data into XY coordinate data, and then using formulas... , The spatial distance between counties is obtained after processing latitude and longitude. The earthquake emergency zoning index dataset is calculated as follows: Treating n indicators as independent points, the similarity between samples is calculated to obtain a similarity matrix S, where S is a symmetric matrix with diagonal elements of 0. ; The earthquake emergency similarity optimization refers to the strength of the connection between county-level cities within a geospatial information region at the level of earthquake emergency zoning, measured by the optimized similarity of the complex network, using the following formula: Finally, the similarity matrix W is obtained.

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