A spatial multi-level structure extraction method for spatial stream data

Abstract

The application discloses a kind of space multilayer structure extraction methods for space stream data, including three stages, the generation stage of initial population, maximum spanning tree is generated based on stream data and neighbor information, initial population is generated based on maximum spanning tree by the way of selecting edge from maximum spanning tree;New population is generated based on initial population by crossing and mutation operation, and the optimal population of a generation is selected from new population based on fitness evaluation standard;Optimal individual is selected from the optimal population of a generation based on fitness, and the edge and node of it are filtered, and the final network structure is obtained.The application solves the problems existing in the existing space network structure extraction technology, such as the adjacent nodes with strong interaction being divided into different areas, the adjacent nodes with weak interaction being combined into the same area, the relationship between the nodes with strong interaction but not adjacent being filtered, etc., so that the extracted space network structure cannot completely reflect the actual network situation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of grid structure extraction, in particular to a spatial multi-level structure extraction method for spatial flow data. BACKGROUND

[0002] Extracting the hierarchical structure of nodes and edges and their relationships from complex and large-scale spatial social flow data helps to more clearly understand and recognize the correlation patterns between geographical elements and the structural characteristics contained in the flow space.

[0003] However, the current spatial network structure extraction method mainly uses complex network clustering with spatial constraints, user-specified spatial unit OD flow statistics aggregation, etc. But these methods have some problems, for example: the interaction of adjacent nodes is divided into different regions, the interaction of adjacent nodes is combined into the same region, the relationship between the nodes with strong interaction but not adjacent is filtered, etc. (due to non-adjacent, the strong interaction between nodes is also directly ignored, etc.), which may affect the accuracy of the results, so that the extracted spatial network structure cannot fully reflect the actual network situation. SUMMARY

[0004] The purpose of the present application is to build a spatial multi-level structure extraction method for spatial flow data that takes into account the spatial position of the nodes, the spatial relationship between the nodes, and is not affected by the variable MAUP effect, so that the analysis of the spatial network structure from large-scale spatial complex network data can accurately reflect the actual network situation.

[0005] Technical scheme: To achieve the above purpose, the spatial multi-level structure extraction method for spatial flow data comprises three stages, the first stage: the generation stage of the initial population, the task of the first stage is to generate a maximum spanning tree (MST) based on flow data and neighbor information, and to generate an initial population based on the maximum spanning tree by selecting edges from the maximum spanning tree. This stage needs to focus on how to create a maximum spanning tree and how to generate an initial population; the second stage: generating a new population based on the initial population through crossover and mutation operations, this stage needs to focus on the operation mode of crossover and mutation and the selection of individual fitness function; the third stage: selecting the optimal individual from the optimal generation population based on fitness, and filtering the edges and nodes of the optimal individual to obtain the final network structure, the visualization of the results can assist the developer to more conveniently analyze the extracted structure information; specifically comprising the following steps:

[0006] Step S1: the generation stage of the initial population, that is, generating a maximum spanning tree (MST) based on flow data and neighbor information, and generating an initial population by selecting edges from the maximum spanning tree;

[0007] Step S2: generating a new population based on the initial population through crossover and mutation operations;

[0008] Step S3: selecting an optimal population from the new population based on the fitness evaluation criteria;

[0009] Step S4: selecting an optimal individual from the optimal population based on the fitness evaluation criteria, visualizing the optimal individual, filtering the edges and nodes of the optimal individual, and obtaining a final network structure.

[0010] In step S1, a maximum spanning tree (MST) is generated based on flow data and neighbor information, and an initial population is generated by selecting edges from the maximum spanning tree. An edge is a line segment connecting two nodes, and a network structure describes the organizational relationship between nodes and edges. Through the connection of edges, nodes form a kind of association and interaction in the network. A network structure is an individual, and multiple individuals form a population. The initial population generation stage includes the following sub-steps:

[0011] Step S101: calculating the flow and strength between any two nodes;

[0012] Step S102: creating a flow matrix and a strength matrix between nodes based on the flow and strength;

[0013] Step S103: constructing a flow-based and strength-based maximum spanning tree based on the flow matrix and the strength matrix using the Kruskal algorithm;

[0014] Step S104: shuffling the order of edges in the flow-based or strength-based maximum spanning tree (MST) so that the order of edges connected to each node is different, creating selected_nodes_list and gene_list to save the selected nodes and edge sets for creating individuals, and creating candidate_edges_list to save candidate edges during the generation of individuals;

[0015] Step S105: traversing the edges in the maximum spanning tree (MST), if neither of the two nodes of the current edge is in selected_nodes_list, adding the two nodes of the edge to selected_nodes_list and adding the edge to gene_list, otherwise adding the edge to candidate_edges_list;

[0016] Step S106: If selected_nodes_list does not contain all the node objects in the MST, then traverse the edges in candidate_edges_list, and when a node of an edge is not in selected_nodes_list, add it to selected_nodes_list, and add the edge to gene_list, and then delete the edge from candidate_edges_list;

[0017] Step S107: After performing step S106, selected_nodes_list contains all the nodes in the MST, and if the number of edges in gene_list is less than the value of (|MST|-finalGroupNum+1), then randomly select a certain number of edges from candidate_edges_list, so that the number of edges in gene_list is equal to (|MST|-finalGroupNum+1); |MST| represents the number of edges contained in the maximum spanning tree, and finalGroupNum represents a threshold value set by the user, i.e., the number of final node groups;

[0018] Through the above operations, an individual can be obtained, i.e., all original nodes are aggregated into a network structure containing finalGroupNum node groups, in which the interaction between nodes in the same node group is stronger, and the interaction between nodes in different node groups is weaker;

[0019] Step S108: Repeat steps S104-S107 Y times to obtain an initial population containing Y individuals.

[0020] In step S101, the formula for calculating the flow between node N i and node N j is:

[0021] SE i，j = SE j，i = f i，j +f j，i ;

[0022] In the formula, f i，j represents the flow size from node N i to node N j , and f j，i represents the flow size from node N j to node N i ;

[0023] The formula for calculating the strength between two nodes is:

[0024]

[0025] where N represents all nodes in the data set, SE i，t represents the flow between node N i and node N t , SE j，k represents the flow between node N j and node N k .

[0026] The step S2 of generating a new population based on the initial population through the crossover and mutation operations comprises the following sub-steps:

[0027] Step S201: The order of individuals in the current population is shuffled to increase the randomness of edge exchange between different individuals, and an empty set crossed_population is created to store new individuals generated through parent edge crossover;

[0028] Step 202: A new individual is generated through edge crossover between two individuals by replacing an edge in any individual individual_1 in the current population with an edge in any other individual individual_2 in the current population, and the new individual is added to the crossed_population. One crossover operation can obtain two new individuals, and (Y / 2) crossover operations can obtain a new population containing Y individuals;

[0029] Step S203: A new population containing individuals is obtained through mutation operation on the new population obtained in step S202. For an individual, the difference set (mutate_set) between all edges in the maximum spanning tree and the edges of the current individual is used as the edge set that can be replaced during mutation. For each edge in the mutate_set, if any randomly obtained value is less than the mutation threshold, a randomly selected edge in the mutate_set is replaced with a randomly selected edge in individual.genes, which represents the set of all edges contained in the individual;

[0030] The step S3 of selecting the optimal population from the new population based on the fitness evaluation standard comprises the following steps: Y individuals in the last population and Y individuals in the new population generated after the crossover and mutation operations are combined into a set containing 2Y individuals, where the current population is the last population and the new population is the current population. Modularity is used as the fitness evaluation standard of individuals in the set to calculate the modularity of each individual. According to the sorting of each individual according to the modularity, Y individuals with higher modularity are selected to form a new population of the current generation;

[0031] Steps S2-S3 are repeated until there is no change in the individuals in the last generation and the current generation, thereby obtaining an optimal generation of populations.

[0032] The formula for calculating the individual fitness evaluation criterion is:

[0033]

[0034]

[0035] a i =∑ j e i，j ;

[0036] wherein m is the sum of all edge weights in the original network, i.e., the flow size or flow intensity, and v and w represent any two nodes in the network; when the two nodes v and w are directly connected, A vw represents the weight between nodes v and w, otherwise A vw =0; e i，i represents the ratio of the sum of weights between all child nodes in the node group c i to the sum of weights of the entire network; a i represents the ratio of the sum of edge weights between all child nodes in the node group c i and all child nodes in the network to the sum of weights of the entire network; the greater the value of the module Q, the better the effect of node aggregation.

[0037] The optimal individual is selected from the optimal generation of populations based on the fitness in step S4, specifically:

[0038] The optimal individual is selected from the optimal generation of populations based on the module, i.e., the individual with the highest module; when multiple nodes are aggregated into finalGroupNum node groups to form the optimal individual, the spatial positions of the new node groups are re-determined; if the set of nodes in a node group is {N1, N2,..., N n}, the set of weights corresponding to the nodes in the node group is {w1, w2,..., w n}, and the coordinates of the i-th node N i are (x i , y i ), then the coordinates of the new node generated by the node group are:

[0039]

[0040] wherein the weight w i represents the total number of nodes in the node group, the total degree of the node group, the sum of the in-degree and out-degree with other node groups, or the sum of the interaction intensity between the nodes in the node group;

[0041] By using different weight measurement methods, the connotations of the sizes of nodes in the finally generated spatial network structure are different.

[0042] The different connotations of the sizes of the nodes refer to that the size of a node represents the number of original nodes combined by the node, and the more the number, the larger the node, or represents the flow value between the nodes combined in the node, and the larger the internal flow value, the larger the node. The weights include flow or intensity, and users can select different weights according to analysis targets.

[0043] The visualization of the optimal individual in step S4 refers to the visualization of the edges and nodes in the optimal individual. Since each node in the optimal individual contains a plurality of original nodes, three different connotations are reflected through the relationships between the original nodes, which are: the total intensity value of the flow intensity between the nodes in the original network contained in the node; the sum of the out-degree and the in-degree of the node; and the total number of nodes in the original network contained in the node.

[0044] The edges between the nodes contain two different connotations: the interaction flow between the nodes and the interaction intensity between the nodes.

[0045] The filtering of the edges and nodes of the optimal individual in step S4 to obtain the final network structure refers to filtering the edges and nodes of the optimal individual according to the threshold values of the flow or intensity of the edges and the threshold values of the total flow and the total intensity of the nodes, removing the nodes smaller than the threshold values or the new nodes, and thus obtaining the final network structure.

[0046] Advantages: the present application has the following advantages:

[0047] 1. The method of the present application incorporates the spatial positions and spatial relationships of nodes into the network analysis process, thereby more accurately reflecting the distribution and interaction mode of nodes in space, and solving the problem of ignoring the spatial positions and spatial relationships of nodes in the logic of traditional complex network analysis algorithms.

[0048] 2. The method of the present application allows adjacent nodes across administrative boundaries to be combined into the same node group through a new node combination strategy, thereby making up for the deficiency of the node combination mode in the traditional method that ignores the fragmentation of adjacent nodes across administrative regions by using known spatial unit constraints such as administrative divisions.

[0049] 3. The method of the present application realizes a high generalization of the strength of the interaction relationships between adjacent nodes in a spatial network.

[0050] 4. The method provides an effective solution for exploring and deeply mining the spatial structure hidden in large-scale and complex spatial networks, and can be applied to the extraction and analysis of spatial network structure of any network composed of OD flow with weight, and can also be used as an effective map generalization method for spatial OD flow data. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is the network structure extraction flowchart of the method of the present application;

[0052] Figure 2 is the node interaction flowchart of the method of the present application;

[0053] Figure 3 is the maximum spanning tree construction flowchart of the method of the present application;

[0054] Figure 4 is the individual generation schematic diagram of the method of the present application;

[0055] Figure 5 is the schematic diagram of the generation of a new individual by the cross of two individuals in the method of the present application;

[0056] Figure 6 is the schematic diagram of the generation of a new individual by mutation of an individual in the method of the present application;

[0057] Figure 7 is the schematic diagram of the construction of network structure based on the optimal individual in the method of the present application. DETAILED DESCRIPTION

[0058] The technical solutions of the present application will be described in detail below in combination with embodiments and drawings.

[0059] The spatial multi-level structure extraction method for spatial flow data according to the present application, as shown in Figure 1 , includes three stages:

[0060] First stage: initial population generation stage

[0061] Step 1: as shown in Figure 2 (a)-(d), it is assumed that the target of the present embodiment is to calculate the interaction intensity ST 10 between N 14 and N 10，14 ; the flow size SE 10 between N 14 and N 10，14 is known to be 140;

[0062] Step 2: the total flow of N 10 and N 14 with other nodes is calculated to be 310 and 230 respectively; based on this, ST 10，14= 140 2 (310*230) = 0.275;

[0063] Step 3: According to the flow or strength calculation formula between two nodes, the flow matrix and strength matrix between nodes can be created; based on the flow matrix and strength matrix, and combined with the adjacent matrix between nodes, the maximum spanning tree based on flow and the maximum spanning tree based on strength are constructed by using Kruskal algorithm, such as Figure 3 (a)-(c) shown;

[0064] Step 4: Assuming that the order of the edges in the maximum spanning tree after the disorder operation is MST = {E 3-2 , E 4-1 , E 5-6 , E 13-8 , E 7-14 , E 12-11 , E 1-10 , E 9-5 , E 11-13 , E 10-12 , E 2-4 , E 11-9 , E 8-7}, as shown in Figure 4 (a);

[0065] By traversing the edges in the maximum spanning tree, we can get

[0066] gene_list = {E 3-2 , E 4-1 , E 5-6 , E 13-8 , E 7-14 , E 12-11},

[0067] candidate_edges_list = {E 1-10 , E 9-5 , E 11-13 , E 10-12 , E 2-4 , E 11-9 , E 8-7},

[0068] selected_nodes_list = {N1, N2, N3, N4, N5, N6, N7, N8, N 11 , N 12 , N 13 , N 14}, as shown in Figure 4 (b);

[0069] Step 5: Two edges {E1-10 , E 9-5} is added to gene_list, at this time:

[0070] gene_list = {E 3-2 , E 4-1 , E 5-6 , E 13-8 , E 7-14 , E 12-11 , E 1-10 , E 9-5},

[0071] candidate_edges_list = {E 11-13 , E 10-12 , E 2-4 , E 11-9 , E 8-7},

[0072] selected_nodes_list = {N1, N2, N3, N4, N5, N6, N7, N8, N9, N 10 , N 11 , N 12 , N 13 , N 14}, as shown in (a) ; Figure 4 c

[0073] Step 6: Assuming that the randomly taken edges are {E 11-13 , E 10-12}, the updated gene_list = {E 3-2 , E 4-1 , E 5-6 , E 13-8 , E 7-14 , E 12-11 , E 1-10 , E 9-5 , E 11-13 , E 10-12}, as shown in (d) ; Figure 4

[0074] Step 7: An individual can be created by the above operation. The method produces different individuals by different combinations of edges, and ingeniously avoids the problem of a node group containing only a single node. Steps 1 to 6 are repeated Y times to obtain an initial population containing Y individuals;

[0075] Second stage: iteration of the population to produce a new population stage

[0076] ​​​Step 1: This step is to produce two new individuals by crossing the edges of two individuals. The two individuals, individual_1 and individual_2, contain edges as shown in Figure 5 (a) 1 and Figure 5 (a) 2, respectively. The rule of edge crossing is to exchange the edges that do not exist in each other. Therefore, not any two edges can be exchanged for two individuals. The following describes three cases:

[0077] Case 1: Exchange the same edges of two individuals. Obviously, it is meaningless, such as exchanging the edge E 11-12 in individual_1 with the edge E 11-12 in individual_2. It will not produce any new individual, as shown in Figure 5 (b) 1 and Figure 5 (b) 2;

[0078] Case 2: Some nodes are only contained by one edge. The edge crossing operation can cause some nodes to be unable to form a node group, such as exchanging the edge E 8-13 in individual_1 with the edge E 5-6 in individual_2. It will cause N8 in individual_1 and N6 in individual_2 to be unable to form a node group, as shown in Figure 5 (c) 1 and Figure 5 (c) 2;

[0079] Case 3: Therefore, the edge crossing can only select the edges that are not contained by each other and the nodes contained by the edges are also contained by other edges. By exchanging the edge E 2-4 in individual_1 with the edge E 10-12 in individual_2, two new individuals are obtained, as shown in Figure 5 (d) 1 and Figure 5 (d) 2.

[0080] Step 2: This step is to produce one new individual by deleting the edge of one individual and adding a new edge, as shown in Figure 6 . For example, Figure 6 (a) represents all edges gene_list of an individual; and Figure 6 (b) represents the solid edges (E 2-4 , E 7-8 , E 11-13) represents the difference set between the maximum spanning tree MST and the edge set gene_list, denoted as mutate_set, which represents the edges in the maximum spanning tree MST that are not included in the current individual; from as Figure 6 (b) randomly select an edge E 7-8 , assuming that the obtained random number satisfies the mutation probability of the edge of the individual, it is added to the gene_list of the current individual, as shown in as Figure 6 (c); after adding, a random edge (E 1-10 ) that meets the conditions needs to be deleted from the edge set gene_list; because edge (E 1-4 ) also contains N1, edge (E 10-12 ) also contains N 10 , deleting edge (E 1-10 ) will not cause the omission of nodes, then the same operation is performed on the remaining edges E 2-4 and E 11-13 of mutate_set; as Figure 6 (d) represents the merging of points in a node group.

[0081] Step 3: Based on the last generation population and the new individual set generated by the crossover and mutation operations, the modularity of each individual is calculated as the fitness evaluation standard of the individual, and the individuals are sorted according to the modularity, and the half of the individuals with higher modularity are selected to form a new population of the generation.

[0082] Step 4: Repeat steps 1-3 of step 2 until the last generation and this generation of individuals do not change.

[0083] Third stage: selection and display of optimal solution

[0084] After multiple nodes are aggregated into node groups, the spatial positions of the new node groups need to be determined again. As shown in as Figure 7 (a) is the optimal solution obtained in the second stage; as shown in as Figure 7 (b) is the network structure obtained by merging the nodes in the optimal solution; as shown in as Figure 7 (c) is the result obtained by filtering the edges of the network structure; as shown in as Figure 7 (c) is the result obtained by filtering the points of the network structure according to the edge threshold, as shown in as Figure 7 (d) is the result obtained by filtering the points of the network structure according to the node threshold.

[0085] This paper proposes a method for extracting spatial multi-level network structure, which solves the problems of merging and integrating strategies of flow nodes, measurement of interaction value and interaction intensity between node groups after merging, and further feature filtering of extracted spatial network structure, thereby improving the accuracy and reliability of the analysis results.

[0086] This example based on the case analysis of the population flow dataset between cities, demonstrates the effectiveness and practical value of this method, which can be applied to any spatial network structure extraction and analysis problem with weighted OD flow composed network. Meanwhile, this method can be used as an effective map generalization method for spatial OD flow data.

Claims

1. A method for extracting the spatial multi-level structure of spatial stream data, characterized in that, Includes the following steps: Step S1: The initial population generation stage, which involves generating the maximum spanning tree (MST) based on the streaming data and neighbor information, and generating the initial population by selecting edges from the maximum spanning tree; Step S2: Generate a new population based on the initial population through crossover and mutation operations; Step S3: Select the optimal first-generation population from the new population based on fitness evaluation criteria; Step S4: Select the best individual from the best generation population based on the fitness evaluation criteria, visualize the best individual, and filter the edges and nodes of the best individual to obtain the final network structure. The edge mentioned in step S1 is a line segment connecting two nodes. The initial population generation stage includes the following sub-steps: Step S101: Calculate the flow and intensity between any two nodes; Step S102: Create a flow matrix and a strength matrix between nodes based on flow and strength; Step S103: Based on the flow matrix and intensity matrix, construct the maximum spanning tree based on flow and intensity using the Kruskal algorithm; Step S104: Shuffle the order of edges in the maximum spanning tree (MST) based on flow or intensity so that the order of edges connected to each node is different. Create selected_nodes_list and gene_list to store the sets of nodes and edges selected to create individuals, respectively. Create candidate_edges_list to store candidate edges in the process of generating individuals. Step S105: Traverse the edges in the maximum spanning tree MST. If neither of the two nodes of the current edge is in the selected_nodes_list, add the two nodes of this edge to the selected_nodes_list and add this edge to the gene_list. Otherwise, add this edge to the candidate_edges_list. Step S106: If selected_nodes_list does not yet contain all the node objects in MST, then traverse the edges in candidate_edges_list. When an edge has a node that is not in selected_nodes_list, add it to selected_nodes_list, add the edge to gene_list, and then remove the edge from candidate_edges_list. Step S107: After executing step S106, selected_nodes_list already contains all nodes in MST. If the number of edges in gene_list is still less than (|MST| - finalGroupNum+1), then a certain number of edges are randomly selected from candidate_edges_list to make the number of edges in gene_list equal to (|MST| - finalGroupNum+1); |MST| represents the number of edges contained in the maximum spanning tree, and finalGroupNum represents a threshold set by the user, i.e., the number of final node groups; The above operations result in an individual, which aggregates all the original nodes into a network structure containing finalGroupNum node groups. In this network structure, the stronger the interaction between nodes in the same node group, the better, and the weaker the interaction between nodes in different node groups, the better. Step S108: Repeat steps S104-S107 Y times to obtain an initial population containing Y individuals; Calculate the node in step S101 and nodes The formula for the flow rate between them is: ； In the formula and All indicate and nodes The flow between, Represents a node To the node The amount of traffic, Represents a node To the node The volume of traffic; The formula for calculating the strength between two nodes is: ， In the formula and All indicate and nodes The strength between them, where N represents the total number of nodes in the dataset. Represents a node and nodes The flow between, Represents a node and nodes The flow between them.

2. The method for extracting spatial multi-level structures from spatial stream data according to claim 1, characterized in that, Step S2, which describes generating a new population based on the initial population through crossover and mutation operations, includes the following sub-steps: Step S201: Shuffle the order of individuals in the current population to increase the randomness of edge exchanges between different individuals, and create an empty set crossed_population to store new individuals generated by the crossing of parent edges; Step 202: By replacing an edge of any individual_1 in the current population with an edge of any other individual_2 in the current population, a new individual is generated through the intersection of the edges between the two individuals. The new individual is then added to the crossed_population. One intersection operation yields two new individuals. Through (Y / 2) intersection operations, a new population containing Y individuals is obtained. Step S203: The new population obtained in step S202 is mutated to obtain a new population containing Y individuals. For an individual, the difference set of all edges in the maximum spanning tree and the edges of the current individual is used as the set of edges to be replaced during mutation. For each edge in the mutate_set, if any randomly obtained random value is less than the mutation threshold, a randomly selected edge in mutate_set is used to replace a randomly selected edge in individual.genes, where individual.genes represents the set of all edges contained in the individual.

3. The method for extracting spatial multi-level structures from spatial stream data according to claim 1, characterized in that, Step S3, which involves selecting the optimal generation population from the new population based on fitness evaluation criteria, specifically involves merging the Y individuals from the previous generation population with the Y individuals from the new population generated through crossover and mutation operations to form a set containing 2Y individuals. The current population is the previous generation population, and the new population is the current generation population. Modularity is used as the fitness evaluation criterion for individuals in the set to calculate the modularity of each individual. Then, each individual is sorted according to its modularity, and the Y individuals with higher modularity are selected to form the new generation population. Repeat steps S2-S3 until there are no changes in the individuals in the previous generation and the current generation, thus obtaining the optimal generation population.

4. The method for extracting spatial multi-level structures from spatial stream data according to claim 3, characterized in that, The calculation formula for the individual fitness evaluation criteria is as follows: ， ， ； in, This represents the sum of all edge weights in the original network, i.e., the sum of flow magnitude or flow intensity. This represents the total number of node groups in the community division represented by the individual. and Represents any two nodes in the network; when two nodes and When directly connected, Represents a node and The weights between them, otherwise ; Represents a node group The ratio of the sum of weights among all child nodes to the sum of weights of the entire network; Represents a node group The ratio of the sum of the weights of all edges connecting all child nodes in the network to all child nodes in the network to the sum of the weights of the entire network; e i,j The modularity represents the ratio of the weights of all edges between node group i and node group j to the total weights of the entire network. The larger the value, the better the node merging effect.

5. The method for extracting spatial multi-level structures from spatial stream data according to claim 1, characterized in that, Step S4, which involves selecting the optimal individual from the optimal generation population based on fitness, specifically includes: Based on modularity, the optimal individual (i.e., the individual with the highest modularity) is selected from the optimal generation. After multiple nodes aggregate into a finalGroupNum node group, forming the optimal individual, the spatial location of the new node group is redefined. If the set of nodes in a node group is... The set of weights corresponding to the nodes in this node group is , No. Nodes The coordinates are ( If the coordinates of the new node generated by the node group are: ， Among them, weight It represents the total number of nodes in a node group, the total degree of the node group, the sum of the in-degree and out-degree of other node groups, or the sum of the interaction strength between nodes within a node group; By using different weighting methods, the meaning of node size in the final generated spatial network structure will differ.

6. The method for extracting spatial multi-level structures from spatial stream data according to claim 5, characterized in that, The meaning of node size varies. It refers to the number of original nodes merged into the node, with a larger number of merged nodes resulting in a larger node size. Alternatively, it can refer to the flow value between merged nodes within the node, with a larger internal flow value resulting in a larger node size. The weight can include flow or intensity, and users can select different weights based on their analysis objectives.

7. The method for extracting spatial multi-level structures from spatial stream data according to claim 1, characterized in that, The visualization of the optimal individual mentioned in step S4 refers to the visualization of the edges and nodes in the optimal individual. Since each node in the optimal individual contains multiple original nodes, the relationship between the original nodes reflects three different meanings: the total strength value of the flow intensity between the nodes in the original network contained in the node; the sum of the out-degree and in-degree of the node; and the total number of nodes in the original network contained in the node. The edges between nodes have two different meanings: the interaction flow between nodes and the interaction strength between nodes.

8. The method for extracting spatial multi-level structures from spatial stream data according to claim 1, characterized in that, Step S4, which involves filtering the edges and nodes of the optimal individual to obtain the final network structure, refers to filtering the edges and nodes of the optimal individual based on the set thresholds for edge flow or strength, as well as the thresholds for total flow and total strength in the nodes. This process removes nodes that are below the thresholds or new nodes, thereby obtaining the final network structure.

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