Traffic safety district division method based on node attributes and spatial constraints

Abstract

The invention belongs to the technical field of traffic safety and urban traffic planning, and discloses a node attribute and spatial constraint-based traffic safety district division method, which comprises the following steps of: extracting an attribute value of a traffic safety index for each node by taking an urban minimum space unit as the node; constructing a node attribute matrix by utilizing the attribute values of the traffic safety indexes, constructing a side relationship between nodes by utilizing a spatial adjacent matrix, and further constructing a traffic map; constructing a joint similarity matrix based on the node attribute similarity, the node structure similarity and a space hop penalty function; inputting the node attribute matrix and the spatial adjacency matrix into a graph convolutional neural network model for node embedding training, and calculating a loss function by using a joint similarity matrix to obtain a node embedding vector; and grouping the nodes by using a hierarchical clustering method, generating clustering labels, and displaying a traffic safety district division result. According to the method disclosed by the invention, the division result is balanced among connectivity, shape regularity and attribute homogeneity.

Description

Technical Field

[0001] This invention belongs to the field of traffic safety and urban traffic planning technology, and relates to a method for dividing traffic safety zones based on node attributes and spatial constraints. Background Technology

[0002] The operation of an urban transportation system is the result of the accumulation of numerous travel behaviors. Each travel behavior has a starting point and a destination, and the number of travel behaviors is enormous. It is impossible to study each travel behavior individually. It is necessary to integrate travel behaviors into a relatively macroscopic area for analysis. These areas are called traffic zones, which are the basic spatial units for urban transportation planning research. Traffic zones can be divided into micro traffic zones, meso traffic zones, and macro traffic zones according to different application levels.

[0003] In traffic safety planning and management theories, quantitative prediction of macro-level (regional) traffic safety levels is crucial. This helps in developing more targeted and effective traffic safety improvement strategies and measures, thereby comprehensively enhancing the region's traffic safety situation. Traffic safety analysis needs to be conducted at the macro-level (regional). Research has found that during the zoning process, there exists a problem of malleable unit area (MAUP) in geographic information science. This is because macro-level traffic safety analysis requires aggregating data to a micro-scale for analysis, but the results of the safety analysis vary depending on the spatial unit division. Specifically, this manifests in the identification of accident black spots, the fit of the prediction model, and the identification of risk factors in the prediction model. These differences ultimately affect decision-makers' accurate judgment of road safety conditions. In summary, appropriate traffic analysis zoning is a necessary condition for macro-level safety analysis.

[0004] Existing traffic safety analysis zoning studies have established a core organizational principle. This principle relies on three key components: defining appropriate homogeneity criteria, selecting suitable basic spatial units, and applying effective spatial aggregation methods. Current methods for dividing traffic safety zones for macro-level traffic safety analysis fail to adequately consider complex accident causes and potential safety improvement opportunities due to limitations in the accuracy and efficiency of spatial aggregation methods. Accidents are related to multiple potential regional risk factors, and with the increasing prevalence and application of multi-source data in the field of traffic safety, constructing safety homogeneity criteria that can reflect various complex accident causes is crucial to solving the problem.

[0005] Currently, various zoning units, such as Traffic Analysis Zones (TAZs), census blocks, administrative divisions, artificial grid zones, and functional statistical zones, are used for macro-level safety analysis. Among them, TAZs are the most widely used. However, TAZs are usually divided by major roads, which reduces the accuracy of predictive models and creates potential redundancy in accident risk identification. These existing zoning units are the result of division according to certain standards, and some information may be lost during secondary division.

[0006] Traditional methods for dividing traffic safety zones based on graph theory, mathematical programming, heuristic algorithms, and clustering often fail to fully reflect the complex structural and functional relationships within the traffic system, neglecting the inherent connections between spatial proximity and safety characteristics. Furthermore, some methods suffer from insufficient fusion capabilities when handling multi-source heterogeneous data, resulting in division results that lack the ability to express actual risk patterns, thus limiting their potential application in precise traffic safety management. In recent years, the development of deep learning technologies such as graph neural networks has provided new approaches to fusing spatial structural information and attribute features. Graph neural network-based methods can learn higher-order relationships and potential similarities between traffic safety zones while preserving spatial topology, providing an effective technical path for achieving more scientific and accurate traffic safety zone division. Summary of the Invention

[0007] This invention addresses the technical problems of poor continuity in existing traffic safety zone division methods by providing a traffic safety zone division method based on node attributes and spatial constraints, which achieves a balance between connectivity, shape regularity, and attribute homogeneity in the division results.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention provides a method for dividing traffic safety zones based on node attributes and spatial constraints, comprising the following steps:

[0010] S1: Using the smallest urban spatial unit as a node, extract the attribute values ​​of traffic safety indicators for each node;

[0011] S2: Construct a node attribute matrix using the attribute values ​​of traffic safety indicators, construct the edge relationships between nodes using the spatial adjacency matrix, and then construct a traffic graph G = (V, E, X) containing nodes and edges, where: V is the node set, E is the edge set, X is the node attribute matrix, X is an n×d matrix, n is the number of nodes, and d is the number of traffic safety attribute indicators.

[0012] S3: Construct a joint similarity matrix based on node attribute similarity, node structure similarity, and spatial jump distance penalty function;

[0013] S4: Input the node attribute matrix and spatial adjacency matrix into the graph convolutional neural network model for node embedding training, and use the joint similarity matrix to calculate the loss function to obtain the node embedding vector;

[0014] S5: Using a bottom-up hierarchical clustering method, nodes are grouped, cluster labels are generated, and the results of traffic safety zone division are displayed.

[0015] In the above technical solution, the traffic safety attribute indicators include the frequency of historical traffic accidents, the severity of accidents and the total number of accidents, the density of road intersections, the total length of roads, the daily vehicle mileage, the proportion of road sections with different speed limits, the population density and the household economic income.

[0016] In the above technical solution, the spatial adjacency matrix is ​​A = [a ij ] n×n Let i and j be nodes, i = 1, 2, ..., n, j = 1, 2, ..., n. If node i and node j are adjacent, then a ij =1, otherwise a ij =0.

[0017] In the above technical solution, the node attribute similarity is The calculation formula is as follows:

[0018]

[0019] Where: X i and X j σ represents the attribute vectors of node i and node j obtained from the node attribute matrix X, respectively, and σ is the bandwidth parameter of the Gaussian kernel function.

[0020] In the above technical solution, the node structure similarity is: The calculation formula is as follows:

[0021]

[0022] Where: X i and X j These are the attribute vectors of node i and node j obtained from the node attribute matrix X, respectively.

[0023] In the above technical solution, the spatial jump penalty function is expressed as follows:

[0024]

[0025] Among them: hops ij d represents the shortest jump distance from node i to j in the traffic graph. max α is the maximum jump distance threshold; α is the node attribute similarity. Similarity to node structure The balance coefficient, α∈[0,1]; θ is the high similarity threshold.

[0026] In the above technical solution, the joint similarity matrix S = [S ij ] n×n S ij The calculation formula is as follows:

[0027]

[0028] In the above technical solution, the loss function is expressed as follows:

[0029]

[0030] Among them: po p p∈[0,N po ] represents regions with similarity, i.e., S ij≠0 N po This represents the number of regions with similar characteristics. The Euclidean distance between regions with similar characteristics; ne q ,q∈[0,N ne ] represents regions that do not have similarity, i.e., S ij＝0 N ne This represents the number of regions that are not similar. d represents the Euclidean distance between regions that are not similar; ε is a control condition; d ij Embed the Euclidean distance between the training outputs for the corresponding nodes.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] This invention first introduces a joint similarity matrix that integrates node attribute similarity and node structure similarity during graph convolutional neural network model training, and combines it with a spatial jump penalty mechanism to effectively enhance the model's ability to perceive changes in spatial topology and local attributes. Second, it extracts complex association features between nodes through graph convolutional embedding representation, and combines it with a hierarchical clustering method with spatial connectivity constraints to ensure that the partitioning results achieve a balance between connectivity, shape regularity, and attribute homogeneity. Finally, through map visualization of the clustering results and multi-dimensional index evaluation methods, the clustering effect of different safety homogeneity indices is evaluated from two levels: clustering quality and modeling support capability. This verifies the practicality and superiority of the method of this invention, and provides effective support for traffic safety community partitioning and spatial policy formulation. Attached Figure Description

[0033] Figure 1 This is a census district in Florida County, as described in this embodiment of the invention.

[0034] Figure 2This is a visualization of the aggregation results of each group in the embodiments of the present invention. Detailed Implementation

[0035] The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of protection of the present invention. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art. Unless otherwise specified, the test methods in the following embodiments are conventional methods.

[0036] Example 1

[0037] S1: Using the smallest spatial unit in the city as a node, extract traffic safety attribute values ​​for each node.

[0038] This embodiment selects Florida County, USA as the study area, using census tract units within the area as the smallest spatial unit of the city, and as nodes in the transportation map network (a total of 17,368 nodes), with each node corresponding to a spatial area. Census tracts are as follows: Figure 1 As shown.

[0039] This embodiment selects 11 traffic safety attribute indicators covering different attributes such as traffic accident characteristics, road characteristics, and socioeconomic characteristics: historical traffic accident frequency, accident severity, and total number of accidents; road intersection density, total road length, daily vehicle mileage (DVMT), and the proportion of road sections with speed limits of 25, 45, and 55-65 mph; population density, and annual household income. The collision risk data for traffic accidents comes from the state's Department of Transportation collision analysis reporting system from 2005 to 2007. Collision records are divided into five groups according to injury severity: property damage only (no injury), possible injury (minor injury), obvious injury without incapacity, incapacity injury, and fatal injury. By convention, accidents with only property damage and minor injury are defined as minor accidents, accidents without obvious incapacity injury are defined as serious injury accidents, and accidents with incapacity injury and death are defined as fatal accidents. Equivalent property damage is used to uniformly quantify the severity of traffic accidents, and the corresponding conversion standard is derived through verification. Using a single property damage accident (PDO) as the statistical unit, one fatal injury accident is equivalent to 1330 PDO accidents, one serious injury accident is equivalent to 949 PDO accidents, and one minor injury accident is equivalent to 11 PDO accidents each. This conversion relationship allows traffic accidents of different severity levels within a region to be quantified into a uniform PDO. The conversion results of the attribute values ​​for each traffic safety indicator are shown in Table 1.

[0040] Table 1 Attribute values ​​of different traffic safety attribute indicators

[0041]

[0042]

[0043] The attribute values ​​of traffic safety indicators are extracted for each node. The attribute values ​​of traffic safety indicators for the first 10 nodes in this embodiment are shown in Table 2.

[0044] Table 2 shows the attribute values ​​of traffic safety indicators for the first 10 nodes.

[0045] node A B C D E F G H I J K 0 0 0 0 0 0.039681 0.391091 1 0 0 10.71532 27.13 1 7 3239 0.004392 14.55731 0.206082 1.593978 0.643283 0 0 5.366005 33.182 2 17 6119 0.005123 0 0.287019 3.318302 0.871503 0 0 10.34536 31.953 3 0 33 0 0 0.133666 0.554734 1 0 0 8.487074 26.25 4 1 11 0.000539 0 0.188524 1.854335 1 0 0 10.3006 27.13 5 0 0 0 0 0.197681 1.944355 1 0 0 10.18036 27.13 6 0 0 0 0 0.244907 1.70391 1 0 0 6.274017 41.892 7 0 0 0 0 0.172171 0.714245 1 0 0 8.607585 26.25 8 3 22 0.000492 0 0.214154 6.098371 1 0 0 6.953698 38.295 9 0 0 0 4.966402 0.201353 1.063733 0.738454 0 0 6.645436 32.76 10 1 949 0.000197 0 0.163984 5.066736 0.669401 0 0 5.249156 35.313

[0046] To demonstrate the impact of homogeneity on region clustering performance, the regions were grouped according to different attributes as A, B, C, ABC, DEF, EFGHIJK, as shown in Table 3.

[0047] Table 3 shows the experimental group divisions considering different attributes.

[0048]

[0049]

[0050] S2: Construct a traffic graph containing nodes and edges.

[0051] S2.1: Construct a node attribute matrix X using the attribute values ​​of traffic safety indicators. X is an n×d matrix, where n = 17368. Based on the 6 groupings, with d taking values ​​of 1, 1, 1, 3, 3, 7, the node attribute matrix X corresponds to matrices of order 17368×1, 17368×1, 17368×1, 17368×3, 17368×3, and 17368×7, respectively.

[0052] S2.2: Construct edge relationships between nodes using a spatial adjacency matrix, where the spatial adjacency matrix A = [a ij ] n×n Let i and j be nodes, i = 1, 2, ..., n, j = 1, 2, ..., n. If a ij =1 indicates that node i and node j are adjacent; otherwise, it is a. ij =0; if two smallest spatial units share a boundary, they are considered to have a direct connection relationship.

[0053] S2.3: Finally, 6 traffic graphs G = (V, E, X) containing n nodes are formed, where: V is the node set, E is the edge set, and X is the node attribute matrix.

[0054] S3: Construct the joint similarity matrix.

[0055] S3.1: Calculate the similarity of node attributes and the similarity of node structure.

[0056] This embodiment uses the Gaussian kernel function (RBF) to measure the similarity of node attributes between any two nodes, based on the node attribute feature matrix X. To measure the implicit "structural commonality" relationship between nodes in the attribute space, a cosine similarity calculation method based on node attribute vectors is introduced, resulting in the node attribute similarity being: The calculation formula is as follows:

[0057]

[0058] Node structure similarity is The calculation formula is as follows:

[0059]

[0060] Where: X i and X j σ represents the attribute vectors of node i and node j obtained from the node attribute matrix X, respectively, and σ is the bandwidth parameter of the Gaussian kernel function.

[0061] S3.2: Construct the spatial jump penalty function.

[0062] Considering that nodes that are too far apart should not be grouped into the same cell even if they have similar attributes, a maximum hop distance threshold d is set. max Given a height similarity threshold θ, the spatial jump penalty function is expressed as follows:

[0063]

[0064] Among them: hops ij d represents the shortest jump distance from node i to j in the traffic graph. max d is the maximum jump distance threshold. max =5; α is the node attribute similarity. Similarity to node structure The balance coefficient is α∈[0,1]; θ is the high similarity threshold. In this embodiment, θ∈[0,1].

[0065] S3.3: Combining node attribute similarity and node structure similarity, construct a joint similarity matrix S = [S ij ] n×n S ij The calculation formula is as follows:

[0066]

[0067] The following is an excerpt from rows 11-21 and columns 11-21 of the joint similarity matrix S in this embodiment:

[0068]

[0069] This joint similarity matrix effectively combines the attribute homogeneity, structural similarity, and spatial distance constraints of nodes, providing accurate adjacency guidance information for subsequent graph convolutional neural network models and improving the connectivity and security interpretability of cell division.

[0070] S4: Using the node attribute matrix X and spatial adjacency matrix A as inputs, a graph convolutional neural network (GCN) model is introduced for node embedding training. The loss function is calculated using the joint similarity matrix to obtain the node embedding vector.

[0071] This embodiment employs a Graph Convolutional Neural Network (GCN) framework that integrates attribute information (node ​​features), spatial topology (adjacency / distance), and functional connections (similarity). It learns low-dimensional embeddings through GCN and explicitly aggregates adjacent node information using a graph Laplacian quadratic form. A loss function is calculated comprehensively, and attribute similarity and geographical distance are used as constraints to guide the learning process. Then, bottom-up agglomerative clustering is used to process the clusters and achieve traffic safety zone division. This framework adopts a robust "learn embeddings first → clustering later" process; to ensure geographical connectivity, clustering with connectivity constraints is used.

[0072] Z will be trained (1) and Z (2) Defined as the outputs of the first and second graph convolutional layers, and using W0 and W1 as the weights of the two layers, the forward propagation model can be formalized as the equation:

[0073]

[0074] in, A and I are the spatial adjacency matrix and the identity matrix, respectively. yes The degree matrix (i.e.) (a diagonal matrix).

[0075] The formula for calculating the loss function is as follows:

[0076]

[0077] Among them: po p p∈[0,N po ] represents regions with similarity, i.e., S ij≠0 N po This represents the number of regions with similar characteristics. The Euclidean distance between regions with similar characteristics; ne q ,q∈[0,N ne ] represents regions that do not have similarity, i.e., S ij＝0 N ne This represents the number of regions that are not similar. d represents the Euclidean distance between regions that are not similar; ε is a control condition; d ij The Euclidean distance between the embedded training outputs of the corresponding nodes is used. In this embodiment, 1 ≤ ε < 5.

[0078] S5: A bottom-up hierarchical clustering method (agglomerative clustering) is adopted. The merging criterion uses the link type "Ward" to measure the grouping of nodes and generate cluster labels. At the same time, it is ensured that the final partitioning results satisfy geospatial connectivity. After graph embedding and clustering are completed, the partitioning results are output and visualized.

[0079] This embodiment visualizes the maps obtained from different experimental groups in ArcGIS, intuitively displaying the boundaries, shapes, and distribution characteristics of the sub-areas, such as... Figure 2 As shown, by comparing the partition maps of different security homogeneity standard schemes, the advantages of the partitioning method of the present invention in terms of boundary clarity, connectivity, and shape regularity under different security homogeneity standards are demonstrated.

[0080] The following section evaluates the partitioning results obtained from different experimental groups using a multi-dimensional indicator system and compares them with the spectral clustering algorithm. The core idea of ​​the spectral clustering algorithm is to model the similarity structure of the data using the Laplacian matrix of the graph, obtain a low-dimensional embedding space through feature decomposition, and then perform traditional clustering in this space. This method can effectively characterize complex nonlinear structures and non-convex clusters, and is therefore widely used in graph data and spatial clustering tasks.

[0081] (1) Cluster evaluation

[0082] Intra-group attribute similarity is calculated using measures such as cosine similarity and Euclidean distance to measure the degree of similarity of attributes among nodes within the same traffic safety zone, reflecting whether the partitioning has created "homogeneous" regions. Intra-group inequality is assessed by calculating the dispersion of attribute distribution within each traffic safety zone and using indicators such as imbalance measures to evaluate the internal stability of the traffic safety zones. These indicators allow for a structural and multi-dimensional evaluation of the partitioning scheme, helping to verify whether the partitioning method achieves a balance between attribute consistency and spatial availability. The results are shown in Table 4.

[0083] Table 4 Clustering Evaluation Results

[0084] Group 1 2 3 4 5 6 Spectral clustering algorithm Median of inequality 0.696 0.710 0.656 0.670 0.673 0.589 0.692 Median cosine similarity 0.649 0.611 0.847 0.858 0.826 0.752 0.512 Euclidean distance median 0.196 0.293 0.031 0.373 0.244 1.166 0.440

[0085] (2) Evaluation of prediction models

[0086] Using the identified traffic safety zones as the spatial basis for the prediction model, a zero-inflated negative binomial regression (ZINB) model was chosen as the traffic accident prediction model. This model consists of two sub-processes: the first is the zero-inflated part, which uses a logistic regression function to characterize the generation mechanism of structural zero values, thereby identifying traffic safety zones where accidents are unlikely to occur under specific conditions; the second is the counting part, which uses negative binomial regression to describe unstructured zero values ​​and positive integer exponents, addressing the excessive dispersion problem caused by the variance of accident data exceeding the mean. The aggregated zone attributes are used as input. The dataset for traffic accident prediction includes zone ID, road and traffic-related data (DVMT, total road length, length of road segments with speed limits of 25 / 45 / 55-65 mph), and socioeconomic factors (median annual household income, population density, and intersection density). The total number of accidents in each zone is used as the dependent variable, and the remaining variables are preprocessed and used as explanatory features.

[0087] A traffic accident prediction model was trained using training data and its performance was validated using test data. Evaluation metrics for prediction performance (mean absolute error (MAE), median absolute error (MAD), and root mean square error (RMSE)) were calculated and compared.

[0088]

[0089] In the formula: y i and These represent the observed and predicted crash counts, respectively.

[0090] Calculate and compare the goodness-of-fit indices, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).

[0091]

[0092] The final results are shown in Table 5.

[0093] Table 5 Evaluation Results of the Prediction Model

[0094] Group 1 2 3 4 5 6 Spectral clustering algorithm MAE 80.66 92.88 111.66 917.02 102.13 239.20 1386.52 MAD 57.43 55.65 67.92 34.24 59.69 20.32 27.34 RMSE 191.45 638.57 435.01 13174.91 385.05 2757.33 34261.84 AIC 7797.87 7594.43 7127.87 7581.49 6791.63 7701.38 7951.84 BIC 7835.35 7627.22 7155.97 7628.33 6819.74 7748.23 7998.69

[0095] As can be seen from Tables 4 and 5, the evaluation results of the method of the present invention are better than those of the spectral clustering algorithm in all groups except for the MAD index.

[0096] (3) Ablation test

[0097] To demonstrate the contribution of each step in the partitioning method of this invention, ablation experiments were conducted, as shown in Table 6.

[0098] Table 6 Ablation Experiment Results

[0099]

[0100] The results show that removing any module degrades model performance. In particular, removing the model training module that utilizes the loss function leads to a rapid decrease in the accuracy of the accident prediction model, a significant drop in cosine similarity among the clustering metrics, and a slight decrease in the model's fit. Since the loss function calculation involves the similarity matrix, eliminating the model training component weakens the influence of the similarity matrix on the clustering results; therefore, removing the loss function has the greatest impact on model performance. In conclusion, the loss function calculated using the joint similarity matrix is ​​a key factor in the model's performance.

[0101] The embodiments described above are merely preferred embodiments of the present invention and are only used to explain the present invention. They are not intended to limit the scope of the present invention. For those skilled in the art, other implementation methods can be easily made by substitution or modification based on the technical content disclosed in this specification. Therefore, all changes and improvements made on the principle of the present invention should be included within the scope of the patent application of the present invention.

Claims

1. A method for traffic safety zone division based on node attributes and spatial constraints, characterized in that, The method comprises the following steps: S1: Taking the minimum space unit of the city as a node, attribute values of a traffic safety index are extracted for each node; S2: A node attribute matrix is constructed by using the attribute values of the traffic safety index, an edge relationship between nodes is constructed by using a spatial adjacency matrix, and a traffic graph G=(V, E, X) containing nodes and edges is constructed, wherein V is a node set, E is an edge set, X is a node attribute matrix, X is an nxd order matrix, n is the number of nodes, and d is the number of traffic safety attribute indexes; S3: A joint similarity matrix is constructed based on a node attribute similarity, a node structure similarity and a spatial hop distance penalty function; S4: The node attribute matrix and the spatial adjacency matrix are input into a graph convolutional neural network model for node embedding training, a loss function is calculated by using the joint similarity matrix, and a node embedding vector is obtained; S5: A bottom-up hierarchical clustering method is used to group nodes, a clustering label is generated, and a traffic safety subdistrict division result is displayed.

2. The traffic safety cell division method according to claim 1, characterized in that, The traffic safety attribute indexes include a historical traffic accident frequency, an accident severity and a total number of accidents, a road intersection density, a total road length, a daily vehicle driving mileage, a proportion of road sections with different speed limits, a population density and a household economic income.

3. The traffic safety cell division method of claim 1, wherein, The spatial adjacency matrix is A=[a ij ] n×n , i, j are nodes, i=1, 2, …, n, j=1, 2, …, n, if there is an adjacency relationship between node i and node j, then a ij =1, otherwise a ij =0.

4. The traffic safety cell division method of claim 1, wherein, The node attribute similarity is The calculation formula is as follows: where: X i and X j are the attribute vectors of node i and node j, respectively, obtained from the node attribute matrix X, and σ is the bandwidth parameter of the Gaussian kernel function.

5. The traffic safety cell division method of claim 1, wherein, The node structure similarity is The calculation formula is as follows: where: X i and X j are the attribute vectors of node i and node j, respectively, derived from the node attribute matrix X.

6. The traffic safety cell division method according to claim 1, 4 or 5, characterized by, The spatial hop distance penalty function is expressed as follows: where: hops ij is the shortest hop distance from node i to j in the traffic graph; d max is the maximum hop distance threshold; a is the balance coefficient of node attribute similarity and node structure similarity a∈[0,1]; θ is the high similarity threshold.

7. The traffic safety cell division method according to claim 6, characterized in that, The joint similarity matrix S = [S ij ] n×n where S ij is calculated as follows:

8. The traffic safety cell division method according to claim 7, characterized in that, The loss function is expressed as follows: where: po p , p e [0, N po ] is the similarity region, i.e. S ij≠0 ; N po is the number of similarity regions; is the Euclidean distance of the similarity region; ne q , q e [0, N ne ] is the non-similarity region, i.e. S ij＝0 ; N ne is the number of non-similarity regions; is the Euclidean distance of the non-similarity region; ε is the control condition; d ij is the Euclidean distance between the corresponding node embedding training output results.

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