Key node identification method in combination with multi-dimensional features of group target

Abstract

The invention discloses a key node identification method in combination with group target multi-dimensional features. According to the method, the optimal communication distance of each target is estimated according to the connectivity and redundancy of the network if the target is in a fully connected state, and the group target is constructed into the complex network based on the optimal communication distance. Secondly, providing a key node identification method combined with the multi-dimensional features of the group target, and constructing and calculating the position features, the speed features, the density features and the appearance features of the group target; and finally, carrying out importance evaluation on the features by using an analytic hierarchy process, allocating weights for the feature values, and calculating the importance of the targets in the group, thereby identifying key nodes in the group targets. Based on the key node identification method provided by the invention, the identification precision and accuracy of the key node in the group target network can be effectively improved, and a decision basis can be provided for accurately countering and hitting the group target.

Description

Technical Field

[0001] The present application relates to the technical field of group target tracking and identification, and in particular to a key node identification method combining multi-dimensional features of group targets. Background Art

[0002] Swarm targets refer to multiple targets with similar movement characteristics and in the form of a cluster. For example, drone swarms play an increasingly important role in modern warfare due to their advantages such as low cost, zero casualties, and high mobility. Identifying key nodes in swarm targets can help us quickly locate strategic targets, optimize resource allocation, and quickly disintegrate the enemy's combat effectiveness with less losses.

[0003] The identification of key nodes in group targets requires treating each target as a node, transforming the group targets as a whole into a complex network, and using the key node identification method of the complex network. At present, the network structure is usually represented in the form of graph theory, and the edges in the network are stored through the adjacency matrix. The calculation of the adjacency matrix requires a threshold to determine whether there is a corresponding edge between two points. Considering that the communication between group targets is an important factor in maintaining its group target characteristics, the communication distance of the target is used as the threshold for calculating the adjacency matrix. However, since the enemy group targets are in a non-cooperative state with us, the communication threshold is often unknown, and how to accurately estimate the communication threshold is a difficult point. The current method of judging the network structure based on communication monitoring has low accuracy. Even if the information is captured, it is difficult to determine the sender and receiver of the information. Therefore, it is currently a more mainstream method to reverse the communication threshold through some network indicators under reasonable assumptions.

[0004] The key node identification methods in complex networks have been developed and accumulated a lot. They can be divided into local structure-based methods, global structure-based methods, and community structure-based methods, including degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, k-shell, LeaderRank, HITs, etc. The above methods all measure the key nodes in the network from different angles, and can achieve relatively ideal estimation results in some applicable networks, but there are still some shortcomings: 1) Using a single indicator or part of the centrality indicator as the identification criterion is easy to ignore some important information of the node, resulting in an imbalance in the estimation result; 2) The identification criterion is too simple, which may cause the importance of some nodes in the network to be the same, that is, the recognition accuracy is low; 3) As a moving target, the group target has potential motion characteristics. In addition to the target's position distribution information F, the speed information V reflecting the target's mobility, the density information f reflecting the target's density, and the shape information r reflecting the target's boundary area are all changing with the target's movement, but this part of information has not been fully utilized in the key node identification. Therefore, it is of great research significance to design a high-precision key node identification method with sufficient discrimination and full use of the characteristics of the group target. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the node features in the key node identification of group targets are not fully utilized and the recognition accuracy is low, and a key node identification method combining the multi-dimensional features of group targets is proposed. The overall calculation process of this method is complete, and it can comprehensively consider the characteristics of the nodes in the network structure and its own motion characteristics to improve the precision and accuracy of identification. This application uses the target state obtained after tracking the group target with a cardinalized probability hypothesis density (CPHD) filter and the group target shape estimated by an elliptical random hyperplane model (RHM) as the input parameters of the method, assuming that the target is in a fully connected state, to construct a complex network.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present application provides a key node identification method combining multi-dimensional features of group targets, the method comprising:

[0008] Step 1: After inputting the target state, the optimal transmission radius of the target is estimated based on the connectivity and redundancy of the network, and the network is constructed;

[0009] Step 2: Based on the adjacency matrix and node status of the complex network, construct and calculate the position index, speed index, density index and shape index of each node;

[0010] Step 3: Use the hierarchical analysis method to measure the importance of each indicator and assign weights, calculate the importance of each node, and identify the key nodes.

[0011] Optionally, the optimal transmission radius of the target is estimated and the network is constructed based on the connectivity and redundancy of the network, including:

[0012] Let the transmission radius of the nodes in the network satisfy the following formula:

[0013]

[0014] Where a and b represent the lengths of the major and minor semi-axes of the ellipse area under consideration, N represents the number of nodes, and the k value is increased with a fixed step size to make the transmission radius r c Gradually increase, and calculate the connectivity and redundancy of the current network at each radius. Network connectivity (NE) and redundancy (C) are expressed as follows:

[0015]

[0016] Among them, E represents the adjacency matrix of the network, l ij Represents the path distance between node i and node j. If there is no path between two nodes, the path distance l jk The reciprocal of is considered to be 0. i represents the degree of node i, that is, the number of other nodes connected to node i; the denominator represents the maximum number of edges that may exist between all nodes connected to node i, m i It represents the actual number of edges between these nodes.

[0017] The difference between normalized network connectivity and redundancy is used as the objective function. When a certain redundancy is reached, the transmission radius corresponding to the peak value of the objective function is taken as the communication threshold. The objective function is expressed as:

[0018]

[0019] Wherein, K represents the value range set of k.

[0020] Determine the transmission radius r c After that, it is used as the communication threshold to calculate the adjacency matrix E of the network. The calculation formula of the elements in E is as follows:

[0021]

[0022] Optionally, based on the adjacency matrix and node status of the complex network, construct and calculate the location index, speed index, density index and shape index of each node, including:

[0023] (1) Position indicator

[0024] The location index consists of two parts: the initial information of the node and the information collected from its neighboring nodes, expressed as:

[0025]

[0026] Among them, I i Represents the initial information of the node, N i and N j represents the neighbor set of nodes i and j, D k-＞j Represents the information transmitted from node k to node j. The calculation formula for initial information and transmitted information is:

[0027]

[0028] D k-＞j =I k JS jk ·(1-C k )·KS(j,k) (8)

[0029] Among them, ksi represents the k-shell value of node i, d max and max_ks represent the maximum node degree and k-shell value in the network respectively. JS jk and KS(j,k) represent the similarity and transmission efficiency between nodes j and k respectively, which can be expressed as:

[0030]

[0031] Among them, ψ j =N(j)∪{j} represents the circle composed of the node's neighbors and the node itself, and min_ks represents the minimum k-shell value among all nodes.

[0032] (2) Speed ​​index

[0033] The speed of a node represents its mobility. When a node fails, its original task may be transferred to a node that is similar to it and has high mobility among its neighbors. The speed index is expressed as:

[0034]

[0035] Among them, v i Represents the speed of each node, obtained from the state input.

[0036] (3) Density index

[0037] The density index is used to measure the degree of aggregation and distribution of individuals in a group. The density index of a node is expressed as:

[0038]

[0039] Among them, x i represents the position of the i-th node, h represents the estimated bandwidth, σ represents the standard deviation of the node position, K(·) represents the kernel function, and Gaussian kernel function is used.

[0040] (4) Appearance index

[0041] The shape index is used to measure the area where the group target is located. An ellipse is used to represent the shape of the group target, and its shape parameters are:

[0042] X=[a,b,m x ,m y ,φ] (14)

[0043] Among them, a and b represent the major and minor semi-axes of the ellipse, respectively, and m x and m y represents the coordinates of the center of mass of the ellipse, and φ represents the angle between the major axis of the ellipse and the positive semi-axis of the x-axis.

[0044] The shape index of the node is:

[0045]

[0046] Among them, rd i represents the radial distance from the node to the centroid, Indicates the distance from the ellipse boundary at this angle.

[0047] Optionally, use the analytic hierarchy process to measure the importance of each indicator and assign weights, calculate the comprehensive indicators of each node, and identify the key nodes, including:

[0048] The analytic hierarchy process consists of three layers: the top layer is the target layer, which outputs key nodes; the middle layer is the criterion layer, which is composed of four indicators of the nodes; and the bottom layer is the solution layer, which includes each node.

[0049] The indicator set is recorded as S = {F, V, f, r}, and the decision matrix constructed by the indicators is:

[0050]

[0051] Since the dimensions of each indicator are different, each column in the decision matrix needs to be normalized. The normalized decision matrix is ​​expressed as:

[0052]

[0053] Compare the four indicators in pairs and construct a judgment matrix by comparing the importance of the indicators. Let the constructed four-dimensional judgment matrix be W = (w ij ) 4×4 , w ij The value represents the importance ratio of the i-th indicator to the j-th indicator. The normalized weight vector of the judgment matrix is ​​obtained by the geometric mean method as ω = [ω1, ω2, ω3, ω4] T ,satisfy:

[0054] W·ω=λ max ·ω (18)

[0055] Among them, λ max Represents the maximum eigenvalue of the judgment matrix W.

[0056] Since the judgment matrix is ​​constructed subjectively, a consistency test is required.

[0057] The formula for the sex test is:

[0058]

[0059] in, RI is obtained by looking up Table 1, where n is the order of the comparison matrix. If the consistency index CR is less than 0.1, it means that the consistency test has passed, that is, the constructed judgment matrix is ​​reasonable, and the final comprehensive index value of each node is:

[0060]

[0061] Table 1 Consistency Index RI

[0062]

[0063] Finally, the nodes are sorted according to their comprehensive index values ​​S_V(i), and some of the top nodes are selected as key nodes according to the network scale.

[0064] Compared with the existing key node identification method, the advantages of this application are:

[0065] (1) Under the premise of only estimating the state of the group target, the transmission range of the node is estimated through reasonable assumptions, the group target is transformed into a network structure, and the overall process of identifying the key nodes of the group target is improved.

[0066] (2) It makes full use of the properties of nodes in the network structure and the movement characteristics of the nodes themselves, and comprehensively considers multi-dimensional characteristics such as node location, movement speed, density within the group, and group appearance information, thereby improving the recognition precision and accuracy of key nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flowchart of a key node identification method combining multi-dimensional features of group targets provided in an embodiment of the present application.

[0068] Figure 2 This is a distribution diagram of the estimated state of a group of targets at a certain moment provided in an embodiment of the present application.

[0069] Figure 3 A network topology diagram after the group target is constructed into a network provided in an embodiment of the present application.

[0070] Figure 4 This is a graph of infection results of the SIR infectious disease model provided in an embodiment of the present application.

[0071] Figure 5 This is a graph showing the change in node degree distribution entropy for each method provided in the embodiments of the present application.

[0072] Figure 6 This is a graph showing the network efficiency changes of the various methods provided in the embodiments of the present application.

[0073] Figure 7 A diagram showing the key node identification results provided in an embodiment of the present application. DETAILED DESCRIPTION

[0074] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0075] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0076] The present invention discloses a key node identification method combining the multi-dimensional characteristics of group targets. First, the group target state is used as input, assuming that the targets in the group are in a fully connected state, and the optimal communication distance of each target is estimated according to the connectivity rate and redundancy of the network, and the group targets are constructed as a complex network based on this. Secondly, a key node identification method combining the multi-dimensional characteristics of group targets is proposed, and the position characteristics, speed characteristics, density characteristics and shape characteristics of the group targets are constructed and calculated. Finally, the importance of the above characteristics is evaluated by the hierarchical analysis method, and weights are assigned to each indicator, the importance of each target is calculated, and the key nodes therein are identified. The steps are further explained below based on specific examples:

[0077] Step 1: After inputting the target state, the optimal transmission radius of the target is estimated based on the connectivity and redundancy of the network, and the network is constructed.

[0078] Specifically, referring to formula (1), when the k value is in the range of 0 to 16, the transmission radius r is calculated with a step size of 0.05. c , and for each r c Refer to equations (2)-(4) to calculate the connectivity and redundancy of the network, and take the r when the redundancy is greater than 0.35 and the objective function reaches the maximum value. c As the transmission radius. Finally, the transmission radius r c As the threshold of formula (5), the adjacency matrix of the network is calculated.

[0079] Step 2: Based on the adjacency matrix and node status of the complex network, construct and calculate the position index, speed index, density index and shape index of each node.

[0080] Specifically, for the location index, firstly, according to the adjacency matrix E obtained in step 1, the degree d, k-shell value and neighbor set neighbor of each node are calculated; secondly, the clustering coefficient, initial information, similarity and transmission efficiency of the node are calculated according to formulas (3), (7), (9) and (10) respectively; finally, the location index F of the node is calculated according to formulas (6) and (8).

[0081] For the speed index, the speed index V of the node is calculated according to formula (11), where the speed of each node is derived from the node state input.

[0082] For the density index, we first calculate the mean μ and standard deviation σ based on the node state input, then calculate the bandwidth h of the kernel density estimation according to formula (13), and finally substitute it into formula (12) to calculate the kernel density value of each node. The kernel function in the formula is The two-dimensional Gaussian kernel function of the distribution.

[0083] For the shape index, the basic ellipse equation is constructed according to the ellipse parameters of formula (14), and the shape index calculation of formula (15) can be realized by substituting the position of each node into the basic ellipse equation.

[0084] Step 3: Use the hierarchical analysis method to measure the importance of each indicator and assign weights, calculate the importance of each node, and identify the key nodes.

[0085] Specifically, firstly, the four indicators of each node calculated in step 2 are constructed into a normalized decision matrix according to equations (16) and (17); secondly, each indicator is compared pairwise to construct a comparison matrix as follows:

[0086]

[0087] According to formula (18), the normalized weight vector is w = {0.533, 0.133, 0.267, 0.067}, the RI of the 4th order judgment matrix is ​​0.89, and the consistency index CR is calculated according to formula (19). If the consistency test passes, the comprehensive index of each node is calculated according to formula (20):

[0088] The nodes are ranked according to the comprehensive index values, and some nodes with the highest ranking are selected as key nodes according to the network scale.

[0089] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments. The formulas mentioned in this section are all formulas in the content of the invention, and the serial numbers correspond to the formulas in the content of the invention, and are not repeated here.

[0090] Example

[0091] The advantages of the present application are further described below by comparing specific embodiments with other methods. The input of this embodiment is the state estimation obtained by tracking a group of targets using a CPHD filter. The number of targets in the group is 30, and the positions of the targets are distributed as follows: Figure 2 As shown, Figure 2 The ellipse in represents the outline boundary of the group target. The center of mass of the ellipse is located at [14.67, 42.67] m, the major and minor semi-axes are 176 m and 113 m respectively, and the deflection angle is -0.105 rad. After calculating the target input in step 1, it is found that when k is 0.3, the objective function value of formula (4) is the largest, thus determining the node transmission radius r cis 58.73m. Based on this calculation, the adjacency matrix E of the network is obtained, and the connection topology of the network is obtained. Figure 3 .

[0092] After calculation in steps 2 and 3, the comprehensive index of each node can be obtained as shown in Table 2.

[0093] Table 2 Comprehensive indicators of each node

[0094]

[0095]

[0096] To verify the effectiveness of the method in this paper, the method provided in this application is compared with the degree centrality method, the closeness centrality method, the k-shell method, the PageRank method and the ECRM method, and the recognition results and various network indicators are shown in Table 3. In Table 3, the resolution represents the discrimination of all nodes; the two values ​​in the number of subgraphs represent the number of subgraphs of the network after removing the first 5 important nodes and the first 10 important nodes; the two values ​​in the network entropy represent the node degree distribution entropy of the network after removing the first 5 important nodes and the first 10 important nodes; the two values ​​in the network efficiency represent the network efficiency after removing the first 5 important nodes and the first 10 important nodes.

[0097] Table 3 Comparison of recognition results of different methods

[0098]

[0099] When verifying key nodes in the network, the SIR model simulates the infection process and uses nodes as infection sources. It can accurately identify nodes that have a significant impact on network propagation without relying on the degree centrality of nodes or other traditional network indicators, and helps to discover some hidden key nodes. Therefore, analysis based on the SIR model can be used to verify the effectiveness of key node identification algorithms. Figure 4 In order to identify the importance of nodes according to this method, the SIR model is used to take each node as the infection source in turn, and the infection results are obtained after 1000 Monte Carlo experiments. It is not difficult to see that the number of infections of each node in the figure basically presents a power law distribution, that is, the more important the node is, the more nodes it can infect, which means that the node has a stronger ability to spread information. Combined with the top 10 node numbers in Table 2, this method believes that 9 of the 10 most important nodes have appeared in the top 10 nodes of other methods many times. Combining the above two points, the effectiveness of the method proposed in this application can be preliminarily explained.

[0100] The method of this application has a significant advantage in node resolution. It can fully identify the importance of each node, and will not have the situation where multiple nodes have the same importance as in the degree centrality method. From the perspective of network entropy and network efficiency, the method of this application also has certain advantages. Network entropy represents the distribution entropy of the degree of each node in the network. The larger the network entropy, the more chaotic the network. Figure 5 It is not difficult to see that the method of this application, k-shell and ECRM methods perform better in network entropy indicators. Deleting some of the corresponding nodes in turn according to the identification results of these methods can quickly make the network chaotic. Network efficiency is linked to the connectivity of the network. The lower the network efficiency, the more serious the network damage. Figure 6 It is not difficult to see that this method, degree centrality and PageRank methods perform more prominently in this indicator. Deleting some of the corresponding nodes in turn according to the identification results of these methods can quickly reduce network efficiency and connectivity and destroy the structure of the network.

[0101] From the above analysis, it can be seen that the method proposed in this application can effectively identify the key nodes in the group target network with high resolution. From the two indicators of network entropy and network efficiency, the method proposed in this application has obvious advantages over other methods, which proves the effectiveness and accuracy of the method proposed in this application.

[0102] Compared with the existing key node identification method, the advantages of this application are:

[0103] (1) Under the premise of only estimating the state of the group target, the transmission range of the node is estimated through reasonable assumptions, the group target is transformed into a network structure, and the overall process of identifying the key nodes of the group target is improved.

[0104] (2) It makes full use of the properties of nodes in the network structure and the movement characteristics of the nodes themselves, and comprehensively considers multi-dimensional characteristics such as node location, movement speed, density within the group, and group appearance information, thereby improving the recognition precision and accuracy of key nodes.

[0105] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A key node identification method combining multi-dimensional features of group targets, characterized in that: The method comprises the following steps: Step 1: After inputting the target state, the optimal transmission radius of the target is estimated based on the connectivity and redundancy of the network, and the network is constructed; Step 2: Based on the adjacency matrix and node status of the complex network, construct and calculate the position index, speed index, density index and shape index of each node; Step 3: Use the hierarchical analysis method to measure the importance of each indicator and assign weights, calculate the importance of each node, and identify the key nodes.

2. According to claim 1, a key node identification method combining multi-dimensional features of group targets is characterized in that: The target transmission radius is estimated by: In a two-dimensional plane, an ellipse is used to represent the shape of a group target. Therefore, in an ellipse region R containing all group targets and with a major axis a and a minor axis b, let the transmission radius of each target be r. c are the same, and assume that there exists a constant k>0, satisfying: Where N represents the number of targets, and the k value can be used to adjust the connectivity and redundancy of the network. On the basis of achieving a certain redundancy, the k value with the largest difference between connectivity and redundancy is selected to calculate the transmission radius r c ; The connectivity of the network is measured by the network efficiency NE, which is expressed as: Among them, E represents the adjacency matrix of the network, l ij Represents the path distance between node i and node j. If there is no path between two nodes, the reciprocal of the path distance is set to 0; The redundancy of the network is measured by the local clustering coefficient of the nodes, which is expressed as: Among them, d i represents the degree of node i, that is, the number of other nodes connected to node i; the denominator represents the maximum number of edges that may exist between all nodes connected to node i, m i It represents the actual number of edges between these nodes.

3. According to claim 1, a key node identification method combining multi-dimensional features of group targets is characterized in that: The calculation methods of each indicator are as follows: Position indicators: From the perspective of information volume, the node position index is expressed as: Among them, I i Represents the initial information of the node, N i and N j represents the neighbor set of nodes i and j, D k-＞j Represents the information transmitted from node k to node j; Speed ​​index: The speed of a node represents its mobility. Nodes with strong mobility in the group take on more tasks. The speed index of a node is expressed as: Among them, v i Indicates the speed of each node, JS ij Represents the similarity between nodes i and j; Density index: The density of group targets is used to measure the degree of aggregation and dispersion of individuals in a group and their distribution in a specific area. The density of each node is expressed in the form of a probability density function in the area. The density index of the node is expressed as: Among them, x i represents the position of the i-th node, h represents the estimated bandwidth, σ represents the standard deviation between target positions, and K(·) represents the kernel function; Appearance index: The shape of the group target refers to the outline of all nodes, which is used to measure the area where the group target is located. The shape of the group target is represented by an ellipse, and the shape parameters are: X=[a,b,m x ,m y ,φ](8) Among them, a and b represent the major and minor semi-axes of the ellipse, respectively, and m x and m y represents the coordinates of the centroid of the ellipse, φ represents the angle between the major axis of the ellipse and the positive semi-axis of the x-axis; The shape index of the node is: Among them, rd i represents the radial distance from the node to the centroid, Indicates the distance from the ellipse boundary at this angle.

4. According to claim 1, a key node identification method combining multi-dimensional features of group targets is characterized in that: The importance of each indicator is measured and weighted using the analytic hierarchy process, the importance of each node is calculated, and the key nodes are identified, including: The top layer is the target layer, which outputs key nodes; the middle layer is the criterion layer, which consists of four indicators of the nodes; the bottom layer is the solution layer, which includes each node; The indicator set is recorded as S = {F, V, f, r}, and the decision matrix constructed by the indicators is: The normalized decision matrix is ​​recorded as: Compare the four indicators in pairs and construct a judgment matrix by comparing the importance of the indicators. Let the constructed four-dimensional judgment matrix be W = (w ij ) 4×4 , w ij The value of represents the importance ratio of the i-th indicator to the j-th indicator; the normalized weight vector of the judgment matrix is ​​obtained by the geometric mean method as ω=[ω1,ω2,ω3,ω4] T ,satisfy: W·ω=λ max ·oh (12) Among them, λ max Represents the maximum eigenvalue of the judgment matrix W; The formula for consistency test of judgment matrix is: in, RI is obtained by looking up the consistency index table as shown in Table 1 , where n is the order of the comparison matrix; Table 1 Consistency Index RI If the consistency index CR is less than 0.1, it means that the consistency test has passed, that is, the constructed judgment matrix is ​​reasonable, then the final comprehensive index value of each node is: Finally, the nodes are sorted according to their comprehensive index values ​​S_V(i), and some of the top nodes are selected as key nodes according to the network scale.

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