An analysis method for high-level structure of heterogeneous combat networks based on spectral clustering of combat models

Abstract

The present invention provides a method for analyzing the high-level structure of a heterogeneous combat network based on spectral clustering of combat motifs. The method includes the following steps: using a subgraph pattern consisting of multiple equipment nodes connected in the combat network as a combat motif; converting the combat network into a combat motif adjacency matrix; dividing the corresponding combat network into a set of interconnected slices based on the combat motif adjacency matrix; performing spectral clustering on each interconnected slice in the set of interconnected slices, and gradually dividing the slice into clusters with a node size no greater than a set threshold; aggregating all clusters of combat motifs in the interconnected slices to obtain functional clusters of the combat motifs; and then aggregating the functional clusters of all combat motifs of interest to obtain a complete set of functional clusters of different combat motifs in the combat network. This method can be used to discover high-level functional clusters in the combat network based on the different combat motifs of interest.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-level analysis of combat networks, and in particular relates to an analysis method for the high-level structure of heterogeneous combat networks based on combat model spectral clustering. Background Art

[0002] The high-order organizational structure of complex networks is an effective way to understand and model the interactions between multiple individuals in complex systems. With the development of intelligent science, the scale and complexity of combat interactions between equipment in combat systems are increasing.

[0003] Combat network analysis is the analysis and evaluation of complex combat systems based on network science. Research on combat network analysis primarily focuses on network disruption strategies, combat link prediction, combat effectiveness assessment, and topological feature analysis. The theoretical foundation of combat networks is the OODA operational loop theory, which posits that the combat process is composed of multiple entities involved in reconnaissance, decision-making, influencing, and targeting. While the types of elements are limited, the OODA loop has multiple manifestations to achieve various combat functions for different missions.

[0004] Most existing combat network analysis research is based on low-order network topology, specifically, pairwise node connectivity patterns. To our knowledge, no research has examined the higher-order structure of combat networks. However, with the rapid increase in the scale and complexity of complex combat systems, higher-order structures are more suitable for modeling clustered collaboration patterns among multiple assets. Furthermore, studying the higher-order structure of combat networks facilitates deeper research into complex combat systems, including understanding system functional structures, exploring internal operational coordination mechanisms, identifying key combat clusters, and enhancing system robustness. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an analysis method for the high-order structure of heterogeneous combat networks based on combat model spectral clustering, so as to solve at least one of the above-mentioned problems existing in the prior art.

[0006] Based on the above objectives, one or more embodiments of the present application provide a method for analyzing the high-level structure of a heterogeneous combat network based on combat model spectral clustering, which includes the following steps:

[0007] Step 1: A subgraph pattern consisting of multiple synergistic equipment nodes in the combat network is used as the combat model;

[0008] Step 2: Convert the combat network into a combat model adjacency matrix based on the different combat models of interest;

[0009] Step 3: Divide the corresponding combat network into a set of interconnected segments according to the combat model adjacency matrix in step 2;

[0010] Step 4: For each interconnected patch in the interconnected patch set, perform spectral clustering on its combat model adjacency matrix and gradually divide it into clusters whose node size is no larger than the set threshold;

[0011] Step 5: Summarize all clusters of combat models in the interconnected slice to obtain the functional clusters of the combat models, and then summarize the functional clusters of all combat models of interest to obtain a set of functional clusters of different combat models in the complete combat network.

[0012] Based on the above technical solution of the present invention, the following improvements can also be made:

[0013] Optionally, define the adjacency matrix of the combat model as A OM , the combat model of interest is OM, the combat model adjacency matrix A OM Record the number of times each pair of nodes in the combat network appears in the same combat model instance of the combat model OM, indicating the frequency and intensity of each pair of equipment participating in the formation of a functional cluster in the combat system; set the model instance set of the combat model OM of interest to be I G (OM) = {I1, I2, ..., I p}; then the combat model adjacency matrix A OM The element in is defined as (A OM ) ij :

[0014]

[0015] Where 1(C) is the truth function of condition C. If C is true, the function value is 1, otherwise it is 0; V i 、V j For equipment nodes in the combat network, I k ∈{I1,I2,...,I p}.

[0016] Optionally, based on the operational model adjacency matrix A OM The high-order Laplace matrix of the combat network and the symmetric and normalized Laplace matrix of the combat model are calculated using the following formulas:

[0017] L OM =D OM -A OM (2),

[0018]

[0019] Among them, L OM is the Laplace matrix of the combat model, D OM is the combat model degree matrix of the combat model, expressed as (D OM ) ii=∑ j (A OM ) ij , is the symmetric and normalized Laplace matrix of the combat model, and I is the identity matrix.

[0020] Optionally, the spectral clustering process in step 4 includes:

[0021] Step 41: Perform eigendecomposition on the normalized combat model Laplace matrix to obtain the second smallest eigenvalue λ2 and its eigenvector ω2;

[0022] Step 42: Connect the slices C according to the elements in the eigenvector ω2 j Node sorting in ;

[0023] Step 43: Generate a network partitioning strategy for the interconnection slice based on the order of node arrangement, and divide it into two subgraphs S and Find a network partitioning strategy that minimizes the Conductance of the combat model;

[0024] Step 44: Repeat steps 41 to 43 until the number of nodes in all clusters is no greater than the set threshold.

[0025] Optionally, in step 42, all equipment nodes are sorted according to the corresponding values in the eigenvector ω2 of the eigenvalue λ2, with nodes with larger values being placed in front, and then a network partitioning strategy is generated according to the order of the nodes.

[0026] Optionally, in the network partitioning strategy of minimizing the Conductance of the operational model in step 43, the evaluation index φ OM Determine that the evaluation index is defined as:

[0027]

[0028] Among them, S and are two complementary subgraphs of the combat network; is the number of motif instances of the operational motif of interest OM that are destroyed by the partition, i.e., the motif instance has at least one node in S and another node in in;vol OM (S) is the total number of nodes of all motif instances in OM in S;

[0029] Select the one with the minimum The network partitioning strategy is taken as the optimal network partitioning strategy.

[0030] The present invention provides a method for analyzing the high-level structure of heterogeneous combat networks based on spectral clustering of combat motifs. It introduces the concept of combat motifs to describe high-level interactions between multiple pieces of equipment and proposes a framework for analyzing the high-level functional structure of heterogeneous combat networks based on spectral clustering of combat motifs. This framework can be used to discover high-level functional clusters in a combat network based on different combat motifs of interest. Specifically, it has the following significant benefits:

[0031] 1) High computational efficiency; it can achieve high-order functional clustering of different combat models in large-scale combat networks in a short time;

[0032] 2) High accuracy; accurately found the high-level functional structure centered on real high-frequency equipment nodes in the experimental combat network;

[0033] 3) Important combat models can be identified in the absence of prior knowledge; when the high-order interaction patterns in the combat network are unknown in advance, the importance of different combat models to the combat network can be analyzed from the perspective of the high-order organization of the combat network, and the key equipment coordination patterns in the combat system can be found.

[0034] The high-order functional structure analysis method proposed in this invention is of great significance to the analysis of large-scale complex combat systems of intelligent equipment. This technical achievement can promote the application of high-order network theory in combat network analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a basic structural diagram of a heterogeneous combat network according to an embodiment of the present invention, which illustrates a method for analyzing a high-order structure of a heterogeneous combat network based on combat model spectral clustering.

[0036] Figure 2 Schematic diagram of some common combat motifs in the method for analyzing high-level structures of heterogeneous combat networks based on combat motif spectral clustering according to an embodiment of the present invention.

[0037] Figure 3 This is a framework diagram of the combat motif spectral clustering of the combat network of the embodiment of the present invention, which is an analysis method of the high-order structure of the heterogeneous combat network based on the combat motif spectral clustering.

[0038] Figure 4 This is a schematic diagram of a network partitioning strategy based on the eigenvectors of the combat motif Laplace matrix of the analysis method of the high-order structure of a heterogeneous combat network based on combat motif spectral clustering in an embodiment of the present invention.

[0039] Figure 5 This is a schematic diagram of the average running time of simulated combat networks of different sizes using the high-order function clustering method of the analysis method of the high-order structure of heterogeneous combat networks based on combat model spectral clustering according to an embodiment of the present invention.

[0040] Figure 6 This is a schematic diagram of the high-level functional structure of the combat network 1 in the experiment of the analysis method of the high-level structure of the heterogeneous combat network based on the combat model spectral clustering according to an embodiment of the present invention.

[0041] Figure 7 Schematic diagram of comparison of different combat motifs in combat network 2 in an experiment of a method for analyzing high-order structures of heterogeneous combat networks based on combat motif spectral clustering according to an embodiment of the present invention.

[0042] Figure 8 Schematic diagram of the variation of motif conductance of different combat motifs with cluster size in the combat network 2 partitioning method of the heterogeneous combat network high-order structure analysis method based on combat motif spectral clustering according to an embodiment of the present invention.

[0043] Figure 9 For the embodiment of the present invention Figure 3 Amplified diagram of Figure 1 .

[0044] Figure 10 For the embodiment of the present invention Figure 3 Amplified diagram of Figure 2 . DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present disclosure more clearly understood, the present disclosure is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0046] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in one or more embodiments of the present application should have the usual meanings understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in one or more embodiments of the present application do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0047] One or more embodiments of the present application provide a method for analyzing the high-level structure of a heterogeneous combat network based on combat model spectral clustering, comprising the following steps:

[0048] Step 1: Based on the subgraph pattern composed of multiple equipment nodes with synergistic effects in the combat network as the combat model; define the adjacency matrix of the combat model as A OM , the combat model of interest is OM, the combat model adjacency matrix A OM Record the number of times each pair of nodes in the combat network appears in the same combat model instance of the combat model OM, indicating the frequency and intensity of each pair of equipment participating in forming a specific functional cluster in the combat system; set the model instance set of the combat model OM of interest to be I G (OM) = {I1, I2, ..., I p}; then the combat model adjacency matrix A OM The element is defined as (A OM ) ij :

[0049]

[0050] Where 1(C) is the truth function of condition C. If C is true, the function value is 1, otherwise it is 0; V i 、V j For equipment nodes in the combat network, I k ∈{I1,I2,...,I p}.

[0051] Step 2: Convert the combat network into a combat model adjacency matrix based on the different combat models of interest;

[0052] Based on the combat model adjacency matrix A OM The high-order Laplace matrix of the combat network and the symmetric and normalized Laplace matrix of the combat model are calculated using the following formulas:

[0053] L OM =D OM -A OM (2),

[0054]

[0055] Among them, L OM is the Laplace matrix of the combat model, D OM is the combat model degree matrix of the combat model, is the symmetric and normalized Laplace matrix of the combat model, and I is the identity matrix.

[0056] Step 3: Divide the corresponding combat network into a set of interconnected segments according to the combat model adjacency matrix in step 2;

[0057] Step 4: For each interconnected patch in the interconnected patch set, perform spectral clustering on its combat model adjacency matrix and gradually divide it into clusters whose node size is no larger than the set threshold;

[0058] Step 41: Perform eigendecomposition on the normalized combat model Laplace matrix to obtain the second smallest eigenvalue λ2 and its eigenvector ω2; Figure 4 shown.

[0059] Step 42: Connect the slices C according to the elements in the eigenvector ω2 j Node sorting in ;

[0060] Step 43: Generate a network partitioning strategy for the interconnection slice based on the order of node arrangement, and divide it into two subgraphs S and Find a network partitioning strategy that minimizes the Conductance of the combat model;

[0061] Step 44: Repeat steps 41 to 43 until the number of nodes in all clusters is no greater than the set threshold.

[0062] In step 42, all equipment nodes are sorted according to the corresponding values in the eigenvector ω2 of the eigenvalue λ2, with nodes with larger values being placed in front, and then a network partitioning strategy is generated according to the order of the nodes.

[0063] In the network partitioning strategy of minimizing the Conductance of the operational model in step 43, the evaluation index φ is used. OM Determine that the evaluation index is defined as:

[0064]

[0065] Among them, S and are two complementary subgraphs of the combat network; is the number of motif instances of the operational motif of interest OM that are destroyed by the partition, i.e., the motif instance has at least one node in S and another node in in;vol OM (S) is the total number of nodes of all motif instances in OM in S;

[0066] Select the one with the minimum The network partitioning strategy is taken as the optimal network partitioning strategy.

[0067] Step 5: Aggregate all clusters of the operational model in the interconnected slice to obtain the functional cluster of the operational model. Then aggregate the functional clusters of all the operational models of interest to obtain the complete set of functional clusters of different operational models in the operational network. Aggregation can be understood as the set of all clusters of the operational model in the network interconnected slice is the functional cluster of the operational model, and the set of functional clusters of all the operational models of interest is the functional cluster of different operational models in the operational network.

[0068] It can be understood that in this embodiment, a method for analyzing the high-level structure of a heterogeneous combat network based on the spectral clustering of combat motifs is provided, the concept of combat motifs is proposed to describe the high-level interactions between multiple equipment, and a framework for analyzing the high-level functional structure of a heterogeneous combat network based on the spectral clustering of combat motifs is proposed. Figure 3 As shown, through this framework, high-order functional clusters in the combat network can be discovered based on different combat models of interest. Specifically, it has the advantages of high computational efficiency; high-order functional clustering of different combat models in large-scale combat networks can be achieved in a short time; high accuracy; accurate discovery of high-order functional structures centered on real high-frequency equipment nodes in experimental combat networks; identification of important combat models in the absence of prior knowledge; and analysis of the importance of different combat models to the combat network from the perspective of the high-order organization of the combat network when the high-order interaction patterns in the combat network are unknown in advance, and finding the key equipment coordination patterns in the combat system. Among them, Figure 3 For the high-order Laplace matrix and spectral clustering process in the framework diagram, please refer to Figure 9-10 .

[0069] Specifically, Definition 1 (heterogeneous network): Given a network G = (V, E, ψ, ξ), where V = ∪ i V i Is a collection of various nodes, V = ∪ i E i is a set of edges. ψ is a mapping function from node to node type: V→T V , where T V is a set of node types. ξ is a mapping function from edges to edge types: E→T E , where T E is a set of edge types. V |>1 and |T E When |>1, the network is called a heterogeneous network.

[0070] The combat network is a typical heterogeneous network, and the nodes in the heterogeneous combat network represent combat equipment. According to the different combat functions of the equipment in the combat system, the nodes in the heterogeneous combat network are divided into reconnaissance nodes, decision nodes, interference nodes and attack nodes, that is, |T V |=4.

[0071] The nodes and their meanings are as follows:

[0072] Reconnaissance node (S): equipment with reconnaissance, surveillance and early warning capabilities during combat;

[0073] Decision-making node (D): equipment with combat decision-making, command and control capabilities in combat;

[0074] Interference node (I): equipment with electromagnetic interference capability during combat;

[0075] Strike Node (A): Equipment with firepower strike capability in combat;

[0076] The edges in the heterogeneous combat network represent the combat interaction relationship. Based on the node types defined above, 12 edge types are defined in the heterogeneous combat network, namely |T E |=12, as shown in Table 1. On this basis, the basic structure of the heterogeneous combat network can be summarized as follows: Figure 1 .

[0077] Table 1. Edge types in heterogeneous combat networks

[0078] Edge Type Combat implications S→D Uploading of reconnaissance intelligence S→S Collaborative reconnaissance S→I / A Reconnaissance intelligence sharing D→D Collaborative decision-making D→S / I / A Reconnaissance, jamming, and strike missions I→I Coordinated interference I→S / A Electromagnetic interference protection A→A Coordinated strike

[0079] Motifs are considered an effective method for describing high-order connectivity patterns in networks. They focus on the statistical frequency of subgraphs that appear in a network. The definitions of motifs and motif instances are shown in Definitions 2 and 3.

[0080] Definition 2 (Motif): Assume that the network G = (V G , E G , ψ G ,ξ G ) there exists a connected subgraph M=(V M , E M , ψ M ,ξ M ), so that If the probability that M appears in the random network more than or equal to the number of times it appears in G is lower than a predetermined threshold (such as P = 0.01), then M is called the motif of G. V |>1 and |T E When |>1, M is called a heterogeneous motif of G.

[0081] Definition 3 (Motif Instance): An instance of a motif M is a subgraph I in a network G = (V I , E I , ψ I ,ξ I ), so that (V I , E I ) is isomorphic to (V M , EM ), ψ I =ψ M ,ξ I =ξ M A motif instance is topologically identical to the corresponding motif.

[0082] The above definition allows for the extraction of statistically significant connectivity patterns, but only a subset of these patterns possesses practical functional significance within a complex combat network. Here, the concept of a combat model is defined by incorporating prior domain knowledge of the functional structure of combat systems. This allows analyses based on combat models to reflect the high-level functional structural characteristics of combat networks.

[0083] Definition 4 (Operational Motif): An Operational Motif (OM) is a subgraph pattern consisting of multiple connected equipment nodes in a combat network that is not only statistically frequent but also has practical operational functional significance. Clusters formed based on the connection pattern of the motif can realize specific combat functions.

[0084] The combat model has the following characteristics:

[0085] Heterogeneity: In the combat model, nodes and edges are heterogeneous and have specific semantic information.

[0086] Directionality: The edges in the combat model are directed, indicating directional relationships such as intelligence uploading, information transmission, task allocation, command and control.

[0087] Duplication: Generally, a combat model has multiple isomorphic instances in the combat network, and several types of combat models can coexist in the same combat network.

[0088] Structural complexity: Combat models are more complex in topology, and they describe the complex combat coordination relationships between multiple equipment.

[0089] Please refer to Figure 2 , Figure 2 This paper summarizes some common operational models consisting of three or four equipment nodes. The operational model describes the high-level functional structure pattern in the operational network. For example, the model OM2 is a feedforward loop consisting of one decision node, one jamming node, and one reconnaissance node. Its operational function is to achieve reconnaissance and early warning under the protection of electronic jamming. Specifically, the decision node issues a command, and the reconnaissance node completes the reconnaissance mission under the protection of the jamming node. Model OM 19 It is a four-equipment cluster that realizes the broadcast of reconnaissance situation information from two reconnaissance nodes to two strike nodes. 26 It forms a "decision-making-reconnaissance-interference-strike" cluster. The decision-making node issues instructions, and with the support of electromagnetic interference, the reconnaissance node transmits target intelligence to the strike node to achieve damage to the target.

[0090] Conductanceφ is an indicator widely used to evaluate the quality of network clustering. It focuses on finding a "sparse-balanced" network partitioning strategy from the perspective of low-order network topology. Sparse means that the number of edges between subgraphs is small enough, and balanced means that the total number of nodes in the two subgraphs is equivalent. In some studies on high-order network clustering, Conductance was improved to the motif Conductance from the perspective of high-order network structure. It is worth noting that the motif Conductance was originally proposed for the clustering problem of undirected homogeneous networks. In order to evaluate the quality of high-order functional clustering in directed heterogeneous combat networks, the embodiment improves Conductance to the "combat motif Conductance"φ OM , as shown in formula (4). For a specific type of combat motif, finding a clustering strategy that minimizes its "combat motif conductance" can ensure that there are sufficient motif instances within each combat cluster and that there are few motif instances across clusters. In this way, a combat cluster composed of closely connected motif instances can realize the specific combat function corresponding to the motif. By combining clusters of different combat motifs, the high-level functional structure of the combat network can be obtained.

[0091] In the combat model degree matrix, for a specific type of combat model OM, the combat model degree matrix D OM is a diagonal matrix whose elements (D OM ) ii Node V i The operational model degree of node V i The impact on the high-level functional structure of the network. Specifically, it records the impact of node V in the combat network. i The number of times the same motif instance appears in the combat motif OM at the same time as any other node. Its physical meaning is the frequency and strength of coordination between a specific equipment and any other equipment. OM Can be calculated as A OM The row sum is expressed as (D OM ) ii =∑ j (A OM ) ij .

[0092] Based on the above definition, in the formal description, it is assumed that in the heterogeneous combat network G, the set of all combat models is For the combat model OM i (i=1,...,m), its combat function is expressed as The set of motif instances is denoted as I G (OM iOn this basis, the high-order function clustering problem in the combat network is to divide G into n clusters, each cluster has a specific combat function, that is, G = G1∪...∪G n Each cluster G j (j=1, ..., n) is composed of a specific type of combat model OM i The motif instance of G j can be considered as fulfilling a combat function The optimal high-order function clustering strategy of the combat network makes the model Conductanceφ of each combat model OM minimize.

[0093] Based on this, the following experiments were conducted to verify the effectiveness and applicability of the method proposed in this embodiment:

[0094] Two combat network datasets were used in the experiment. The experimental networks were abstracted from real-world examples of joint combat systems composed of various equipment based on the heterogeneous combat network model. Table 2 shows the properties of the experimental combat networks.

[0095] Table 2. Attributes of the experimental combat network

[0096] Experimental Network 1 Experimental Network 2 Decision Node 292 326 Scouting Node 476 652 Interference Node 593 367 Strike Node 536 445 Total number of nodes 1897 1790 Total number of edges 3860 3857

[0097] Network 1 exhibits realistic high-order clustering characteristics. Within the corresponding combat system, certain equipment has a significantly higher probability of participating in specific combat functions. Therefore, these nodes should be the center of high-order functional clusters in Network 1. Table 3 summarizes the combat functions and realistic high-frequency equipment nodes of important combat models in Network 1.

[0098] Table 3. Real high-frequency equipment nodes of important combat models in Network 1

[0099]

[0100]

[0101] In contrast, the status of nodes in Network 2 is relatively balanced, with no equipment clearly standing out in terms of the probability of participating in achieving specific combat functions.

[0102] Experimental setup

[0103] The experiment first tested the computational efficiency of the algorithm, and then conducted two separate experiments based on combat networks 1 and 2 respectively.

[0104] In Experiment 1, the accuracy of the method of the embodiment in discovering high-order functional clusters in combat network 1 was tested. Specifically, the method of the embodiment was tested to see whether it could accurately find functional clusters centered on the real high-frequency equipment nodes in Table 3.

[0105] In Experiment 2, we demonstrated the effectiveness of the method in this embodiment in discovering important functional clusters in Combat Network 2 when prior knowledge of the network's operational patterns is limited. Measuring the importance of different operational patterns and functional clusters is crucial for understanding the high-level structure and functional patterns of a combat system. However, in many practical applications of combat network analysis, relevant prior knowledge is sparse.

[0106] Table 4 shows the parameter settings for Experiments 1 and 2. The cluster size threshold limits the number of nodes in a cluster. Excessively large thresholds can lead to cluster redundancy and cluster nodes with poor collaboration. Too small thresholds can result in excessive cluster granularity, disrupting the existing cluster structure. In the experiments, the threshold was determined through trial and error to ensure clustering performance.

[0107] Table 4. Experimental parameter settings

[0108] parameter Experiment 1 Experiment 2 Cluster size threshold 50 20 Motifs of interest <![CDATA[OM1,OM6,OM7,OM9,OM 10 ]]> <![CDATA[OM1~OM 18 ]]>

[0109] The experiment was implemented in MATLAB and performed on a PC equipped with an AMD Ryzen 75800H CPU (3.2GHz) and 16GB RAM.

[0110] Experimental results

[0111] Experiments show that this method can find high-order functional clusters in simulated combat networks of different scales with high computational efficiency.

[0112] The number of nodes in the simulation network ranges from 500 to 10,000, with an interval of 500. The ratio of decision-making, reconnaissance, jamming and attack nodes in the network is 1:2:1:1. The important combat models in the simulation network include OM1, OM3, OM6, OM7, OM9, OM 10 ,OM 13 and OM 17 The number of instances of each motif is approximately 20% of the total number of network nodes. The feature cluster size threshold T in Algorithm 1 is set to 50.

[0113] Figure 5 The figure shows the average runtime of the proposed method for finding high-order functional clusters for different combat models. It can be seen that the algorithm's computational efficiency remains consistently high, although the runtime slowly increases with network size. When the number of nodes reaches 5,500, the method takes an average of less than 10 seconds to discover high-order functional clusters for different combat models. When the number of nodes reaches 10,000, the runtime is only 47 seconds.

[0114] In actual applications, the scale of a real combat network is usually not as large as that of a simulated combat network. Therefore, the method of the embodiment is sufficiently efficient and can meet the actual application requirements of complex combat network analysis.

[0115] Experiment 1 results

[0116] Figure 6 The figure shows the high-level functional structure of the largest interconnected piece of combat network 1. The figure is divided into three parts from left to right, corresponding to the logical order from the entire network to local details. The left side shows the combat network of functional clusters. Nodes of different grayscales represent functional clusters corresponding to different combat models. It should be noted that some nodes participate in the composition of multiple combat model instances at the same time, but only one node grayscale is shown here. The node in the lower right corner represents equipment that does not participate in the formation of any combat model instance of interest. It can be seen that the network can be mainly divided into 5 high-level functional clusters, corresponding to OM1, OM6, OM7, OM9 and OM 10 The functional cluster of each specific combat model is composed of combat model instances in the network, which can realize the combat functions of the corresponding combat model shown in Table 3.

[0117] The middle section shows functional clusters of different combat modalities of interest. Observe that some nodes at the center of the network participate in functional clusters of multiple combat modalities. These assets can collaborate with other assets in different ways to achieve a variety of combat functions.

[0118] The right side shows the detailed functional subclusters corresponding to OM1. Each subcluster is composed of OM1’s combat model instances. Obviously, OM1’s functional cluster can be further divided into 10 subclusters, among which D 103 、D 111 、D 156 、D 161 、D 172 、D 182 、D 189 、D 237 、D 256 、D 275 This result is consistent with the actual high-frequency equipment node of OM1 in Table 3. This shows that the method of the embodiment accurately discovers the high-order function cluster corresponding to OM1 in Network 1.

[0119] To further verify the accuracy of the embodiment method, we analyzed whether the functional subclusters of other combat models in Network 1 were concentrated on the corresponding real high-frequency equipment nodes. The results are shown in Table 5. This method accurately discovered all the hidden real high-frequency equipment nodes in Table 3. In the results of OM1 and OM6, the high-order functional clusters were accurately divided into 10 subclusters, each of which was concentrated on a real high-frequency equipment node. In OM7, OM9, and OM10 In the results of , there are some subclusters centered around the two real high-frequency equipment nodes due to the close interaction between them. It should be noted that in the results of OM7, this method also found a subclusters centered around D 237 The hidden subcluster centered on is not a real high-frequency equipment node. This subcluster is relatively independent and has no close interaction with other subclusters centered on real high-frequency equipment nodes.

[0120] Table 5. Experimental parameter settings

[0121]

[0122] Note that in the "Subcluster Center" column, each cluster corresponds to a functional subcluster. Elements in this cluster represent the subcluster's central node, whose operational modulus value is significantly higher than that of other nodes. Some subclusters have two cluster centers.

[0123] Experiment 2 Results

[0124] In addition to discovering high-order functional structures in the combat network based on specific combat models of interest, the framework proposed in the embodiment can also analyze the importance of different combat models when the prior knowledge of high-order interaction patterns between equipment in the combat system is unknown, and find functional patterns that have a significant impact on the high-order functional structure of the combat network.

[0125] In Experiment 2, we analyzed the importance of different combat models to Combat Network 2 from two perspectives. The first was the number of nodes and instances corresponding to different combat models. The second was the impact of different combat models on Combat Network 2's high-order function clustering performance.

[0126] By running the algorithm on experimental network 2, functional clusters of different combat models were obtained. Figure 7 The comparison of different combat models in terms of the number of nodes, the number of combat model instances and their ratios is shown. 17 and OM 16 OM17 and OM16 show a significant advantage, followed by OM1, OM3, and OM6. OM17 and OM16 significantly outnumber the other models in terms of the number of operational model instances. This result indicates that the functional clusters corresponding to these operational models play an important role in the high-level functional structure of Combat Network 2. The primary operational functions of the combat system can be summarized and described using these operational models.

[0127] We then further compared the node / instance ratios of different combat models in Experimental Network 2—that is, the ratio of the number of nodes to the number of combat model instances. Since all combat models in the experiment consist of three nodes, the closer the ratio is to 3, the less overlap there is in the combat model instances. When a combat model has many overlapping nodes in its instances, the ratio will be small because the same number of model instances covers fewer nodes. The node / instance ratio also reflects the functional robustness of high-order functional clusters. A high ratio indicates that some nodes are simultaneously involved in the synthesis of multiple combat model instances. When these nodes are damaged, the number of combat model instances in the functional cluster will drop sharply, leading to widespread functional failures in the combat system.

[0128] like Figure 7 As shown, OM 17 and OM 16 has the lowest node / instance ratio. This indicates that there is significant overlap in their combat model instances and the functional robustness of their high-order functional clusters is relatively poor. In contrast, OM7, OM9, and OM 10 The node / instance ratio is the highest, indicating that the instances of these combat models are relatively independent. OM1, OM3, and OM6 also perform well in terms of node / instance ratio, and their functional clusters show high robustness.

[0129] The above analysis leads to the conclusion that: in Combat Network 2, OM1, OM3 and OM6 constitute and maintain the important combat functions of the combat system. 17 and OM 16 It also plays a leading role in achieving the combat functions of the Combat Network 2, but when some central nodes are destroyed, the combat functions of its functional cluster may be greatly reduced. 10 , they play a weaker role in Combat Network 2.

[0130] To further verify the above conclusions, Figure 8 The results show that when the adjacency matrix of the largest connected slice of experimental network 2 is bisected, the conductance of different combat models changes, that is, the scale of S in algorithm 1 and The function graph of the motif is the minimum value of the Conductance score φ best The value of reflects the performance of network high-order function clustering based on different combat models. The results show that OM9 and OM 10 The high-level organizational structure of the combat network is not significantly revealed, as their lowest values of the Conductance score are 0.5 and 0.25 respectively. 13 , its value is close to 0.1. In contrast, OM1, OM3, OM6, OM 16 and OM17 They perform well in the high-order functional clustering of Combat Network 2. The downward-trending peaks in their function graphs indicate that these combat motifs reveal rich high-order functional structures in the combat system.

[0131] In summary, from the perspective of high-level functional structure, it is found that the important operational models for experimental network 2 include OM1, OM3, OM6, OM 16 and OM 17 Table 6 shows their combat functions, which also explains the main combat functions that can be achieved by the combat system corresponding to Network 2.

[0132] Table 6. Important combat motifs found in Network 2

[0133] Combat Model Combat functions OM1 Reporting of strike and damage situations supported by reconnaissance intelligence OM3 Firepower strike under electronic jamming protection OM6 Reconnaissance and situation reporting under electronic jamming protection OM16 Conduct fire strikes using reconnaissance intelligence integrated with decision-making equipment OM17 Collection and fusion of multi-source reconnaissance intelligence by decision-making equipment

[0134] Experimental Conclusion

[0135] High-order network structures describe the interaction patterns between multiple nodes in complex networks, and their research significance has been widely recognized in various fields. As the complexity of interactions and collaborations between equipment in combat systems increases, high-order network structures are becoming increasingly important in combat network analysis. This example introduces the concept of combat motifs to describe the high-order interactions between multiple equipment and proposes a framework for analyzing the high-order functional structures of heterogeneous combat networks based on combat motif spectral clustering. This framework can discover high-order functional clusters in combat networks based on different combat motifs of interest. Three sets of experiments based on combat network datasets demonstrate the effectiveness of this method: 1) High computational efficiency. High-order functional clustering of different combat motifs in large-scale combat networks can be achieved in a short period of time; 2) High accuracy. High-order functional structures centered around real, high-frequency equipment nodes in experimental combat networks were accurately identified; and 3) Important combat motifs can be identified in the absence of prior knowledge. When the high-order interaction patterns in a combat network are unknown, the importance of different combat motifs to the combat network can be analyzed from the perspective of the combat network's high-order organization, thereby identifying key equipment coordination patterns in the combat system. The high-level functional structure analysis method proposed in this embodiment is of great significance to the analysis of large-scale complex combat systems of intelligent equipment.

[0136] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0137] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A system that specifies the functions of a box or boxes.

[0138] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction system that is implemented in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0139] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0140] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0141] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. An analysis method for the high-level structure of heterogeneous combat networks based on combat model spectral clustering, characterized by: It includes the following steps: Step 1: A subgraph pattern consisting of multiple synergistic equipment nodes in the combat network is used as the combat model; Step 2: Convert the combat network into a combat model adjacency matrix based on the different combat models of interest; Step 3: Divide the corresponding combat network into a set of interconnected segments according to the combat model adjacency matrix in step 2; Step 4: For each interconnected patch in the interconnected patch set, perform spectral clustering on its combat model adjacency matrix and gradually divide it into clusters whose node size is no larger than the set threshold; Step 5: Aggregate all clusters of combat models in the interconnected slice to obtain the functional clusters of the combat models. Then aggregate the functional clusters of all combat models of interest to obtain the functional cluster set of different combat models in the complete combat network. Define the adjacency matrix of the combat model as A OM , the combat model of interest is OM, the combat model adjacency matrix A OM Record the number of times each pair of nodes in the combat network appears in the same combat model instance of the combat model OM, indicating the frequency and intensity of each pair of equipment participating in forming a specific functional cluster in the combat system; set the model instance set of the combat model OM in the combat network G to be I G (OM)={I1,I2,…,I p }; then the combat model adjacency matrix A OM The element in is defined as (A OM ) ij : Where 1(C) is the truth function of condition C. If C is true, the function value is 1, otherwise it is 0; V i 、V j For equipment nodes in the combat network, I k ∈I G (OM); Based on the combat model adjacency matrix A OM The high-order Laplace matrix of the combat network and the symmetric and normalized Laplace matrix of the combat model are calculated using the following formulas: L OM =D OM -A OM (2), Among them, L OM is the Laplace matrix of the combat model, D OM is the combat model degree matrix, expressed as: (D OM ) ii =∑ j (A OM ) ij , is the symmetric and normalized Laplace matrix of the combat model, and I is the identity matrix.

2. The method for analyzing high-level structures of heterogeneous combat networks based on combat model spectral clustering according to claim 1, wherein: The spectral clustering process in step 4 includes: Step 41: Calculate the normalized combat model Laplace matrix of the network and perform eigendecomposition on the normalized combat model Laplace matrix to obtain the second smallest eigenvalue λ2 and its eigenvector ω2; Step 42: Connect the slices C according to the elements in the eigenvector ω2 j Node sorting in ; Step 43: Generate a network partitioning strategy for the interconnection slice based on the order of node arrangement, and divide it into two subgraphs S and Find a network partitioning strategy that minimizes the Conductance of the combat model; Step 44: Repeat steps 41 to 43 until the number of nodes in all clusters is no greater than the set threshold.

3. The method for analyzing the high-level structure of a heterogeneous combat network based on combat model spectral clustering according to claim 2, wherein In step 42, all equipment nodes are sorted according to the corresponding values in the eigenvector ω2 of the eigenvalue λ2, with nodes with larger values being placed in front, and then a network partitioning strategy is generated according to the order of the nodes.

4. The method for analyzing the high-level structure of a heterogeneous combat network based on combat model spectral clustering according to claim 3, wherein In step 43, the network partitioning strategy for minimizing the Conductance of the combat model is based on the evaluation index φ OM Determine that the evaluation index is defined as: Among them, S and are two complementary subgraphs of the combat network; is the number of motif instances of the operational motif of interest OM that are destroyed by the partition, i.e., the motif instance has at least one node in S and another node in in;vol OM (S) is the total number of nodes of all motif instances in OM in S; Select the one with the minimum The network partitioning strategy is taken as the optimal network partitioning strategy.

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