Heterogeneous cluster key node identification method and related equipment

Abstract

The invention discloses a heterogeneous cluster key node identification method and related equipment. The method comprises the following steps: constructing a heterogeneous cluster based on a meta path to obtain a function dependent network; calculating node importance of the function-dependent network under an uncertain condition to obtain a robust importance index; quantifying the irreplaceable degree of the node function of the function dependent network to obtain a function uniqueness factor; and performing key node identification processing on the function dependent network based on the robust importance index and the function uniqueness factor to obtain a target key node. The key node identification accuracy in the cluster can be improved, and the method can be widely applied to the technical field of key node identification.

Description

Technical Field

[0001] This application relates to the field of critical node identification technology, and in particular to a method and related equipment for identifying critical nodes in heterogeneous clusters. Background Technology

[0002] In modern multi-agent interaction applications, cluster targets are typically composed of multiple heterogeneous platforms working together. These platforms form close functional dependencies through information sharing, behavioral coordination, and resource allocation. Related technologies primarily rely on network topology for key node identification, using metrics such as degree centrality, betweenness centrality, and proximity centrality to quantify the structural importance of nodes. However, practical applications have shown that these methods assume a node's importance is entirely determined by its network connectivity, neglecting the dynamic functional coupling relationships between nodes. This can lead to subsequent erroneous decisions.

[0003] In summary, the technical problems existing in the relevant technologies need to be improved. Summary of the Invention

[0004] The main objective of this application is to propose a method and related equipment for identifying key nodes in heterogeneous clusters, which can improve the accuracy of key node identification.

[0005] To achieve the above objectives, one aspect of this application proposes a method for identifying key nodes in a heterogeneous cluster, the method comprising: Functionally dependent networks are constructed from heterogeneous clusters based on meta-paths; The importance of nodes in the functionally dependent network under uncertainty conditions is calculated to obtain a robust importance index; The irreplaceability of the node functions in the aforementioned function-dependent network is quantified to obtain the function uniqueness factor; Based on the robust importance index and the functional uniqueness factor, the functionally dependent network is subjected to key node identification processing to obtain the target key node.

[0006] In some embodiments, calculating the node importance of the functionally dependent network under uncertainty conditions to obtain the importance distribution characteristics includes the following steps: Under uncertainty conditions, the uncertainty of the network parameters of the functionally dependent network is mathematically characterized to obtain an uncertainty characterization; Monte Carlo simulation was performed on the node importance evaluation process of the functionally dependent network based on the aforementioned uncertainty characterization to obtain an importance sample set; Analyze and statistically analyze the aforementioned important sample set to obtain the expected importance and standard deviation; The robust importance index is calculated based on the expected importance and the standard deviation.

[0007] In some embodiments, the step of mathematically characterizing the uncertainty of the network parameters of the function-dependent network under uncertainty conditions to obtain an uncertainty characterization includes the following steps: Under the aforementioned uncertainty conditions, obtain the network parameters of the function-dependent network; The network parameters are characterized using a truncated normal distribution to obtain the uncertain characterization.

[0008] In some embodiments, the process of evaluating the node importance of the functionally dependent network based on the uncertain characterization, using Monte Carlo simulation to obtain an importance sample set, includes the following steps: Random sampling is performed on the uncertain characterization to obtain sampling parameters; The baseline operability level of all nodes in the function-dependent network is calculated based on the sampling parameters. Based on the baseline operability level, the current simulated operability level of all nodes in the function-dependent network is calculated through the cascading propagation effect after performance degradation. The dependency chain importance index is calculated for the target node in the current simulation based on the current simulation operability level. Returning to the previous step, random sampling is performed on the uncertain representation. After multiple independent simulations, all the obtained dependency chain importance indices are added to the importance sample set.

[0009] In some embodiments, calculating the dependency chain importance index for the target node in the current simulation based on the current simulation operability level includes the following steps: The number of nodes in the dependency chain of the target node and the total number of dependency chains passing through the target node are statistically obtained. The dependency chain importance index is obtained by calculating the current simulation operability level, the number of nodes, and the total number of dependency chains based on the dependency chain importance index calculation formula.

[0010] In some embodiments, quantifying the non-substitutability of node functions in the function-dependent network to obtain a function uniqueness factor includes the following steps: Each node in the functionally dependent network is vectorized to obtain a node function vector. The functional similarity of nodes is calculated based on the node function vectors to obtain the node functional similarity. The functional similarity of the nodes is calculated based on the formula for calculating functional uniqueness, and the functional uniqueness factor is obtained.

[0011] In some embodiments, the process of identifying key nodes in the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain target key nodes includes the following steps: The robust importance index and the functional uniqueness factor are calculated based on the comprehensive importance index calculation formula to obtain the comprehensive importance index; Based on the comprehensive importance index, the nodes of the functionally dependent network are sorted and filtered to obtain the target key nodes.

[0012] To achieve the above objectives, another aspect of this application proposes a heterogeneous cluster key node identification device, the device comprising: The network building module is used to build functionally dependent networks from heterogeneous clusters based on meta-paths. An importance calculation module is used to calculate the importance of nodes in the functionally dependent network under uncertainty conditions, and obtain a robust importance index. The function uniqueness calculation module is used to quantify the irreplaceability of the node functions of the function-dependent network to obtain the function uniqueness factor. The node identification module is used to perform key node identification processing on the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain the target key node.

[0013] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0014] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method.

[0015] The embodiments of this application include at least the following beneficial effects: This application provides a method and related equipment for identifying key nodes in heterogeneous clusters. This scheme constructs a function-dependent network for heterogeneous clusters based on meta-paths; it calculates the importance of nodes in the function-dependent network under uncertainty conditions to obtain a robust importance index, which can comprehensively consider the expected level and fluctuation risk, effectively addressing the inherent randomness of parameter estimation in the application environment; furthermore, this scheme quantifies the irreplaceability of node functions in the function-dependent network to obtain a functional uniqueness factor, which can effectively distinguish nodes with similar topological locations but different functional substitutability; in addition, this scheme performs key node identification processing on the function-dependent network based on the robust importance index and the functional uniqueness factor to obtain target key nodes, which can integrate the topological importance and functional uniqueness of the function-dependent network for comprehensive measurement, improving the accuracy of key node identification. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of an implementation environment provided in the embodiments of this application; Figure 2 This is a flowchart of a method for identifying key nodes in a heterogeneous cluster, provided in an embodiment of this application. Figure 3 This is a schematic diagram of the relationship between nodes and edges within a network, provided in an embodiment of this application. Figure 4 This is a schematic diagram of a spatial deployment of an unmanned vessel fleet provided in an embodiment of this application; Figure 5 This is a schematic diagram of a multi-level functional dependency network provided in an embodiment of this application; Figure 6 This is a schematic diagram of the result distribution of a Monte Carlo simulation provided in an embodiment of this application; Figure 7 This is a schematic diagram of a box plot overlaid with scatter points provided in an embodiment of this application; Figure 8 This is a schematic diagram of the structure of a heterogeneous cluster key node identification device provided in an embodiment of this application; Figure 9 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0018] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0019] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0021] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0022] 1) Heterogeneous clusters refer to clusters containing unmanned systems with different structures, parameters, and functions. Based on the degree of heterogeneity, heterogeneous clusters can be categorized into structural heterogeneity, parametric heterogeneity, and functional heterogeneity. Structural heterogeneity refers to a cluster containing two completely different types of unmanned systems, such as a quadcopter-fixed-wing hybrid or a drone-unmanned vehicle hybrid. The different types of unmanned systems in the cluster have completely different dynamic models and use entirely different control methods. Parametric heterogeneity refers to unmanned systems in a heterogeneous cluster having the same dynamic model, but differing dynamic parameters such as mass and aerodynamic shape, such as different types of quadcopter drones, unmanned vehicles, and helicopters. Functional heterogeneity is the simplest type of heterogeneity, where the dynamic models of the unmanned systems in the cluster are completely identical, but differences in the unmanned systems' functions arise due to factors such as different payloads.

[0023] 2) Graph Neural Network (GNN) is an algorithmic framework based on deep learning for processing graph-structured data. It performs tasks such as classification, prediction, and generation by extracting features from nodes, edges, and the graph as a whole. This framework can transform non-Euclidean graph data into a normalized representation and can be applied to multiple fields such as social networks, transportation networks, and molecular structures.

[0024] In modern multi-agent interaction applications, cluster objectives are typically composed of multiple heterogeneous platforms working together. These platforms form close functional dependencies through information sharing, behavioral coordination, and resource allocation. This systematic action organization makes the overall efficiency of the cluster far exceed the simple sum of the capabilities of each platform, but it also means that there are several key nodes within it that have a dominant influence on the system's functionality.

[0025] In related technologies, key node identification methods are mainly based on network topology, using indicators such as degree centrality, betweenness centrality, and proximity centrality to quantify the structural importance of nodes. These methods assume that a node's importance is entirely determined by its connection pattern within the network, neglecting the dynamic functional coupling relationships between nodes. In recent years, network science research has gradually recognized that node importance is reflected not only in its static topological role but also in the dynamic processes of resource flow and function transfer. However, related functional modeling methods typically rely on pairwise interaction assumptions or linear dependency models, making it difficult to characterize the inherent nonlinear and multi-level dependency characteristics of heterogeneous cluster systems. Furthermore, the aforementioned methods often evaluate nodes as isolated individuals, failing to reveal the synergistic effects between nodes and the cascading propagation effects of functional degradation.

[0026] In view of this, this application provides a method and related equipment for identifying key nodes in heterogeneous clusters. This solution analyzes the contribution of nodes to the overall system performance from the perspective of functional effectiveness. By comprehensively considering the functional dependencies between nodes and their cascading propagation characteristics, and addressing the randomness of parameter estimation in the application environment, it can provide theoretical support and methodological reference for identifying key nodes in cluster systems, and provide decision-making basis for action planning and strategy optimization in actual cluster objectives.

[0027] This application provides a method for identifying key nodes in a heterogeneous cluster, relating to the field of key node identification technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, vehicle terminal, drone, unmanned boat, etc., but is not limited thereto; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application implementing a method for identifying key nodes in a heterogeneous cluster, but is not limited to the above forms.

[0028] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0029] Figure 1 This is a schematic diagram illustrating the implementation environment of a method provided in an embodiment of this application. (Refer to...) Figure 1The main hardware and software components of this implementation environment include a terminal 101 and a server 102, which are communicatively connected. The method can be executed based on the interaction between the terminal 101 and the server 102. Furthermore, the terminal 101 and the server 102 can be nodes in a blockchain; this embodiment does not specifically limit this.

[0030] Figure 2 This is an optional flowchart of a method for identifying key nodes in a heterogeneous cluster provided in an embodiment of this application. Figure 2 The method may include, but is not limited to, steps S201 to S204.

[0031] Step S201: Construct a functional dependency network for the heterogeneous cluster based on the meta-path; Step S202: Calculate the node importance of the functionally dependent network under uncertainty conditions to obtain a robust importance index; Step S203: Quantify the irreplaceability of the node functions of the function-dependent network to obtain the function uniqueness factor; Step S204: Based on the robust importance index and the functional uniqueness factor, perform key node identification processing on the functionally dependent network to obtain the target key node.

[0032] Steps S201 to S204, as shown in the embodiments of this application, are used to accurately characterize the diverse functional relationships between nodes. This application employs a meta-path method to model heterogeneous networks. By connecting the functional layers within and between layers in the heterogeneous cluster through relationships defined by meta-paths, a multi-layered functional dependency network is formed. Meta-paths define specific types of connection patterns between nodes, enabling the explicit expression of complex multi-hop dependency semantics. A functional dependency network is a directed network. The model includes basic concepts such as nodes, edges, dependencies, operability levels, and autonomy, forming a logical topology that represents the propagation of effectiveness among network nodes. The functional dependency network analysis method models and measures the dependencies between system components using two key parameters: dependency strength and dependency criticality.

[0033] However, in real-world complex system operating environments, various parameters of function-dependent networks are often difficult to obtain accurately, resulting in inherent uncertainties. Therefore, this application's embodiments calculate the node importance of function-dependent networks under uncertain conditions, obtaining a robust importance index. This index can capture the complete probability distribution characteristics of the node importance index, thus providing decision-makers with a more robust basis for ranking node importance. In actual action systems, the importance of a node is also closely related to the substitutability of its function. If a node performs a highly unique function, meaning there are no other nodes in the system that can replace its function, then the failure of that node will cause an irreparable functional loss. Conversely, if there are multiple nodes with similar functions, the failure of a single node can be compensated to some extent through functional redundancy. To this end, this application's embodiments introduce a functional uniqueness factor to quantify the irreplaceability of node functions, thereby calculating the functional uniqueness factor. Finally, by comprehensively considering the robust importance index and the functional uniqueness factor, the importance of each node in the function-dependent network is calculated, and the results are ranked to identify key nodes in heterogeneous clusters.

[0034] One of the above technical solutions has the following advantages or beneficial effects: This application establishes a formal description mechanism for functional coupling relationships, characterizing the functional dependencies between nodes through two parameters: dependency strength and dependency criticality. Based on the constrained average weakest chain rule, a cascading propagation model is constructed, overcoming the limitation of relying solely on topology and achieving accurate quantification of the impact of node failure on system performance. Furthermore, this application proposes a comprehensive measurement method that integrates the topological importance and functional uniqueness of functionally dependent networks. The dependency chain concept captures the system contribution of nodes from the perspective of functional effectiveness, while the functional uniqueness factor effectively distinguishes nodes with similar topological locations but different functional substitutability. The combination of these two methods achieves a comprehensive characterization of key nodes in the system. In addition, this application constructs a robust evaluation framework under uncertainty conditions. The probability distribution characteristics of node importance are obtained through Monte Carlo simulation. Based on the robust importance index, the expected level and fluctuation risk are comprehensively considered, effectively addressing the inherent randomness of parameter estimation in the application environment and improving the identification efficiency of key nodes.

[0035] In some embodiments, a functionally dependent network is constructed from the heterogeneous clusters based on meta-paths; In this embodiment, a node function representation framework for heterogeneous clusters is established based on OODA ring theory. Then, the meta-path method is used to characterize the functional dependency semantics between nodes. Finally, a multi-layered network architecture from detection to decision-making is constructed to accurately describe the complex relationships within the system. The OODA ring describes a closed-loop decision-making process of "Observe-Orient-Decide-Act." In a heterogeneous cluster scenario, the functional roles of nodes can be mapped to different stages of the OODA ring: the observation stage corresponds to information acquisition, the orientation stage to situational understanding and information fusion, the decision stage to task planning and solution generation, and the action stage to specific execution. Through this functional abstraction, heterogeneous nodes can be uniformly represented under the OODA framework, providing a unified semantic foundation for subsequent functional dependency modeling.

[0036] To accurately characterize the diverse functional relationships between nodes, this application employs the meta-path method to model heterogeneous networks. Meta-paths define specific types of connection patterns between nodes, explicitly expressing complex multi-hop dependency semantics. Based on the functional attributes of nodes in the combat system, they are categorized into four types: reconnaissance (D), command and control (S), attack (A), and target (T), corresponding to observation, judgment and decision-making, action, and action object in the OODA loop, respectively. Based on this classification, a series of meta-path patterns can be constructed to characterize different functional mechanisms. For example, the meta-path "D→S" represents information flow from the reconnaissance node to the command and control node, "S→A" represents control flow from the command and control node to the execution node, and "D→S→A→T" describes the complete functional link from information acquisition, situational understanding, decision-making to mission execution. Furthermore, meta-paths can also characterize more complex collaborative patterns, such as "D→S→D" representing multi-node information sharing, and "S→A→A→T" representing a collaborative execution mechanism. This application provides a set of metapaths covering typical OODA loops, including typical OODA loops, OODA loops involving cooperative actions, OODA loops involving cooperative detection, OODA loops containing detection information feedback, OODA loops containing information sharing and feedback, and OODA loops involving cooperative detection and cooperative actions. These metapath patterns constitute the basic association patterns of heterogeneous cluster function-dependent networks.

[0037] This application constructs a multi-layered functional network architecture based on an OODA ring: node functions are divided into three sub-layers according to the OODA ring: a detection layer, a decision layer, and an action layer, corresponding to information acquisition, situational understanding and decision-making, and task execution, respectively. Nodes in heterogeneous clusters often possess multiple functions simultaneously; a single node may simultaneously assume multiple functional roles such as detection, decision-making, and action. Therefore, a node can belong to multiple functional layers and participate in different functional interactions within each layer. Each functional layer is connected internally and between layers through relationships defined by meta-paths, forming a multi-layered functional dependency network. This multi-layered architecture explicitly characterizes the functional dependencies, providing a more refined network representation for identifying key nodes based on functional importance.

[0038] This application's embodiments construct a functional dependency network from a heterogeneous cluster. The functional dependency network analysis method is based on graph theory concepts, providing a visual representation of the interdependencies between component systems. The functional dependency network is a directed network, and the model includes basic concepts such as nodes, edges, dependencies, operability levels, and autonomous effectiveness, forming a logical topology that represents the propagation of effectiveness within network nodes. The functional dependency network analysis method models and measures the dependencies between various component elements of the system using two key parameters: dependency strength and dependency criticality. Dependency strength... This indicates the degree to which the operability level of the receiving node depends on the supplying node, reflecting the supplying node's contribution to the receiving node. The strength of this dependence is expressed as... express, To provide node numbers, The node number to be accepted has a value range of [0,1]. A larger value indicates a stronger dependence of the receiving node on the supplying node, and a greater contribution of the supplying node to the receiving node. Based on the parameters described above, embodiments of this application use the following equation to determine the nodes... level of operability Modeling the autonomous effectiveness of nodes This refers to the performance of a node itself without considering any dependencies; the operability level of the root node is equal to that of its nodes. : At the initial stage of system operation, the default settings are generally as follows: .

[0039] The operability function for function-dependent network analysis based on the constrained average weakest chain rule is shown below: ; ; ; ; ; in, This indicates the level of operability of the receiving node. This indicates the operability level of the supply node, and , If accepting node have Each supply node, then .

[0040] In some embodiments, calculating the node importance of the functionally dependent network under uncertainty conditions to obtain the importance distribution characteristics includes the following steps: Under uncertainty conditions, the uncertainty of the network parameters of the functionally dependent network is mathematically characterized to obtain an uncertainty characterization; Monte Carlo simulation was performed on the node importance evaluation process of the functionally dependent network based on the aforementioned uncertainty characterization to obtain an importance sample set; Analyze and statistically analyze the aforementioned important sample set to obtain the expected importance and standard deviation; The robust importance index is calculated based on the expected importance and the standard deviation.

[0041] In real-world complex system environments, various parameters of function-dependent networks are often difficult to obtain precisely, exhibiting inherent uncertainty. While deterministic assessment methods can provide point estimates of node importance, they cannot characterize the impact of parameter fluctuations on the assessment results. Therefore, this application embodiment uses Monte Carlo simulation to assess node uncertainty, obtaining the complete probability distribution characteristics of node importance indicators to provide decision-makers with a more robust basis for ranking node importance. This application embodiment mathematically represents the uncertainty of network parameters in function-dependent networks, where network parameters refer to dependency strength, dependency criticality, node autonomy, etc. Then, it constructs an importance assessment algorithm based on Monte Carlo simulation. This algorithm, through extensive random sampling and statistical analysis, can obtain the complete probability distribution characteristics of node importance indicators. Based on the importance distribution characteristics obtained from the Monte Carlo simulation, this application embodiment further constructs a comprehensive importance index system under uncertainty conditions. Furthermore, by introducing a functional uniqueness factor to quantify the irreplaceability of node functions, the comprehensive importance index calculation under uncertainty conditions can simultaneously capture information in three dimensions: the structural importance of nodes in the function-dependent network topology, the risk factors brought about by parameter uncertainty, and the irreplaceability at the functional level.

[0042] In some embodiments, the step of mathematically characterizing the uncertainty of the network parameters of the function-dependent network under uncertainty conditions to obtain an uncertainty characterization includes the following steps: Under the aforementioned uncertainty conditions, obtain the network parameters of the function-dependent network; The network parameters are characterized using a truncated normal distribution to obtain the uncertain characterization.

[0043] In the embodiments of this application, the uncertainty of function-dependent network parameters in heterogeneous cluster systems mainly comes from the following three aspects.

[0044] First, there are inherent errors in the parameter estimation process. Dependency strength The true value is not a fixed constant, but rather is affected by factors such as dynamic changes in the communication environment, limitations in sensor measurement accuracy, and expert evaluation bias, exhibiting random fluctuations within a certain range. Similarly, depending on criticality... It also suffers from measurement errors and time-varying characteristics. Especially in dynamic adversarial scenarios, the strength of the dependencies between nodes may change as the task progresses.

[0045] Secondly, node autonomy performance exhibits variability. The parameter represents the inherent performance level of a node without considering external dependencies. However, due to factors such as equipment aging, environmental interference, and maintenance status, this parameter is not a constant value, but rather exhibits a certain degree of random fluctuation around the nominal value.

[0046] Finally, external interference is unpredictable. When a node suffers an external attack or malfunctions, the degree of performance degradation is inherently random. For example, an interference that causes a 20% performance degradation to a node may result in an actual degradation that fluctuates between 15% and 25%, depending on the precision of the interference method and the node's own resilience.

[0047] Based on the above analysis, this application embodiment uses a truncated normal distribution to mathematically characterize the uncertainty of network parameters. Let the set of network parameters be... The parameters follow the following distribution: ; ; ; in, The mean is variance is The range of values ​​is limited to A truncated normal distribution within the interval. The advantage of using a truncated normal distribution is that it can characterize the random fluctuations of parameters around their nominal values ​​while ensuring that the sampled values ​​always fall within the physically permissible effective range. The degree of node performance degradation is also modeled using a truncated normal distribution: ,in For the expected downgrade rate, This reflects the uncertainty of the degree of downgrade.

[0048] In some embodiments, the process of evaluating the node importance of the functionally dependent network based on the uncertain characterization, using Monte Carlo simulation to obtain an importance sample set, includes the following steps: Random sampling is performed on the uncertain characterization to obtain sampling parameters; The baseline operability level of all nodes in the function-dependent network is calculated based on the sampling parameters. Based on the baseline operability level, the current simulated operability level of all nodes in the function-dependent network is calculated through the cascading propagation effect after performance degradation. The dependency chain importance index is calculated for the target node in the current simulation based on the current simulation operability level. Returning to the previous step, random sampling is performed on the uncertain representation. After multiple independent simulations, all the obtained dependency chain importance indices are added to the importance sample set.

[0049] In this embodiment, the importance assessment algorithm based on Monte Carlo simulation, through extensive random sampling and statistical analysis, can obtain the complete probability distribution characteristics of node importance indicators. By inputting a specified number of simulations, the algorithm incorporates the function-dependent network, the target node, and parameters sampled from a truncated normal distribution, including parameter distribution and degradation distribution. The algorithm characterizes the impact of parameter uncertainty on node importance through large-scale random sampling. Each simulation iteration comprises three stages: first, calculating the baseline operability level of all nodes based on the sampled parameters; then, simulating the performance degradation of the target node and its cascading propagation effect to downstream nodes through functional dependencies. Indicates dependency on nodes The set of all downstream nodes is obtained; finally, the node importance index for this simulation is calculated according to the functional dependency formula. After multiple independent simulations, an importance sample set is obtained. By statistically analyzing the importance sample set, the expected importance can be obtained. This is used to quantify the average degree of impact of node degradation on system performance, as well as its standard deviation. This is used to characterize the fluctuation characteristics of importance under parameter uncertainty. Based on the importance distribution characteristics obtained from the Monte Carlo simulation, this application further constructs a comprehensive importance index system under uncertainty conditions. To comprehensively consider the expected level and fluctuation risk of node importance, the calculation formula for the robust importance index is defined as follows: ; In the formula, This is the risk aversion coefficient, reflecting the decision-maker's sensitivity to uncertainty; This is a robustness importance indicator.

[0050] In some embodiments, calculating the dependency chain importance index for the target node in the current simulation based on the current simulation operability level includes the following steps: The number of nodes in the dependency chain of the target node and the total number of dependency chains passing through the target node are statistically obtained. The dependency chain importance index is obtained by calculating the current simulation operability level, the number of nodes, and the total number of dependency chains based on the dependency chain importance index calculation formula.

[0051] In this embodiment, the importance index of the target node's dependency chain is derived by calculating the degree of influence of each node on other nodes and then summing these influences. The greater the influence on other nodes, the higher the node's importance index. Assuming the initial operability level of a node is 100, the importance index of the target node's dependency chain can be defined as the ratio of the total change in the operational level of the information dependency chain in which the node is located to its initial operability level. The importance index is calculated based on the dependency chain importance index calculation formula, obtained by statistically analyzing the number of nodes in the dependency chain and the total number of dependency chains passing through the target node. The expression for the dependency chain importance index calculation formula is as follows: ; In the formula, after passing through the node In the runtime dependency chain, Indicates the first The first link The operational level of each node Indicates the first The number of nodes contained in a dependency chain. For the nodes The total number of dependency chains. Under certain external disturbances, the dependency chain importance index... The larger the value, the greater the impact of the node's performance loss on the overall system performance, and the more important the node. Conversely, the smaller the value, the less important the node, and the smaller the impact of its performance degradation on the system. The above dependency chain importance index... The influence of nodes is mainly characterized from the perspective of network topology formed by function-dependent transmission.

[0052] Specifically, this application embodiment uses "effectiveness" to measure the impact on overall performance of the cluster target system after a single node is removed or damaged. Figure 3 Taking a simple multi-node functional dependency network as an example, dependency chains exist. ,in The changes only affect those that depend on it. ,but The changes will affect , , and All of these factors have an impact. This is related to the number of dependency chains passing through this node. Therefore, due to the existence of dependencies in the system, when measuring the importance of a node, or the impact on the overall functional system after a node's operability decreases due to external interference, it is related to the number of dependency chains passing through it and the changes in the nodes contained in those dependency chains.

[0053] In some embodiments, quantifying the non-substitutability of node functions in the function-dependent network to obtain a function uniqueness factor includes the following steps: Each node in the functionally dependent network is vectorized to obtain a node function vector. The functional similarity of nodes is calculated based on the node function vectors to obtain the node functional similarity. The functional similarity of the nodes is calculated based on the formula for calculating functional uniqueness, and the functional uniqueness factor is obtained.

[0054] In this embodiment of the application, each node in the function-dependent network is vectorized to obtain a node function vector, wherein the node function vector is represented as: ,in Represents a node In the Capability values ​​in terms of class functionality This represents the total number of functional types. Cosine similarity is used to calculate node similarity. and nodes The functional similarity is calculated using the following formula: ; In the formula, It is a node and nodes Functional similarity, the similarity value ranges from 1 to 10. The larger the value, the more similar the functions of the two nodes are, and the higher the possibility of substitution.

[0055] Then, the functional uniqueness factor is calculated based on the functional uniqueness calculation formula, which is shown below: ; In the formula, Indicates the functional uniqueness factor, It is a node The weighting factor, defined based on its operability level, is The purpose of introducing weighting factors is to ensure that only nodes currently in normal operating condition have the ability to substitute, and nodes with higher operating levels have stronger substitution capabilities. Therefore, the calculation of functional uniqueness comprehensively considers the degree of functional matching between similar nodes and their actual availability.

[0056] As can be seen from the formula structure, when the node... The larger the sum of weighted functional similarities with other nodes, the larger the denominator. The smaller the value, the easier it is for the node to be replaced; conversely, if the node... Its function differs significantly from other nodes, therefore A value close to 1 indicates that the node is highly unique.

[0057] To ensure that the functional uniqueness factor has a uniform dimension and comparability, it is normalized: ; in, and These represent the maximum and minimum values ​​of the functional uniqueness of all nodes, respectively. This normalization method will... Mapped to The interval ensures that functional uniqueness, when used as a moderating factor, does not excessively diminish the fundamental contribution of function-dependent network topology importance.

[0058] In some embodiments, the process of identifying key nodes in the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain target key nodes includes the following steps: The robust importance index and the functional uniqueness factor are calculated based on the comprehensive importance index calculation formula to obtain the comprehensive importance index; Based on the comprehensive importance index, the nodes of the functionally dependent network are sorted and filtered to obtain the target key nodes.

[0059] In this embodiment, the functional uniqueness factor is further combined with the comprehensive importance index calculation formula under the condition of calculation uncertainty. The expression of the comprehensive importance index calculation formula is as follows: ; In the formula, As a normalized functional uniqueness factor, and For the weighting coefficients, satisfying This comprehensive indicator captures information from three dimensions: the structural importance of nodes in a function-dependent network topology, the risk factors arising from parameter uncertainty, and the irreplaceability of nodes at the functional level.

[0060] The solutions of this application embodiment will be described in detail and explained below with reference to specific application examples: This application involves a heterogeneous cluster application scenario, selecting an unmanned surface vessel (USV) cluster as the target cluster. Specifically, a USV formation (S1-S10) consisting of 10 USVs is deployed in a certain sea area. The formation needs to conduct coordinated reconnaissance and action missions against four potential threat targets (T1-T4). Based on the operational mechanism of the formation action system, the functional hierarchy is divided into three levels: reconnaissance (R), decision-making (D), and action (A). Each USV can assume the functional node role at one or more levels based on its equipment characteristics. To quantify the multi-dimensional operational capabilities of the USVs, a functional capability vector is defined. , representing the unmanned surface vessel's capabilities in the three dimensions of reconnaissance, decision-making, and action, respectively, with values ​​ranging from . A higher value indicates a stronger capability in the corresponding dimension.

[0061] Based on the formation's functional configurations (detection, communication, command, and action) and the inter-node dependencies, a functional dependency network model is constructed. The spatial deployment and physical connections of the formation are as follows: Figure 4 As shown, the set of functional layer nodes can be represented as: the set of reconnaissance layer nodes. Decision-making level node set Action layer node set Target node set Based on this, a multi-layered function-dependent network topology is constructed as follows: Figure 5 As shown. Figure 5 The hierarchical logical structure of the formation function-dependent network is depicted. The network is divided into four layers from top to bottom: the target layer (T1-T4) represents the target to be processed; the reconnaissance layer (R1-R6) is responsible for detecting and sensing the target, and transmitting the acquired situational information to the decision layer; the decision layer (D1-D4) integrates multi-source reconnaissance information for threat assessment and mission planning, generating action commands and issuing them to the action layer; and the action layer (A1-A6) executes the action tasks. The directed edges in the vertical direction represent the information flow and command transmission relationships between layers, while the bidirectional edges between nodes at the same layer represent horizontal coordination and information sharing relationships. The overall network forms a complete closed-loop action sequence: "Target → Reconnaissance → Decision → Action → Target".

[0062] The set of directed edges in a function-dependent network is determined based on the functional interactions between nodes. To characterize the strength and criticality of these dependencies, the edge weights are set to binary tuples. The parameter values ​​for various connections are set according to the unmanned vessel type, functional attributes, and collaborative mode. Based on the functional dependency network of the heterogeneous cluster of surface unmanned vessel formations, this application embodiment verifies and analyzes the proposed method for identifying key nodes in the system. In the initial state, all nodes in the unmanned vessel formation cluster system are in normal operation, that is, the initial operability level of all nodes is 100. To verify the cascading propagation mechanism of the functional dependency network, it is assumed that node S4 in the cluster suffers external action or interference, and the operability levels of its controlled nodes R2 and D4 decrease by 20%. Based on the established restricted average weakest chain rule, the operability level of each node after performance degradation is calculated, and the results are shown in Table 1:

[0063] Table 1. Impact of a 20% performance reduction on node operability. As shown in Table 1, after the operability levels of nodes R2 and D4 are directly downgraded to 80, their impact propagates downstream along the functional dependency chain. Nodes A6, D2, and R3 are most affected, with their operability levels dropping to 81.80, 86.68, and 87.00, respectively. This is due to the strong functional dependency between these three nodes and the S4 control node. As the propagation path lengthens, the impact gradually diminishes, but 13 nodes are still affected to varying degrees, verifying that the functional dependency network can effectively characterize the cascading effect between nodes. Based on the above cascading propagation mechanism, a 20% performance degradation is applied to each unmanned surface vessel in the formation, and its impact on the entire system is calculated. Using a node importance measurement model based on the operational dependency chain, combined with the functional uniqueness factor, the comprehensive importance assessment results of each unmanned surface vessel under deterministic conditions are obtained, as shown in Table 2.

[0064] Table 2 Results of Determining Importance Measurement Based on Dependency Chains Table 2 shows the key roles of multi-level nodes: (1) Unmanned vessels that serve as nodes at multiple functional levels (such as S4 controlling R2 and D4, and S8 controlling R6 and A4) rank highly in importance within the entire system. This is because performance degradation across different levels can simultaneously affect multiple operational dependency chains, resulting in a greater cascading impact on the overall system functionality.

[0065] (2) Correlation between the number of dependency chains and importance: The number of operational dependency chains passing through the unmanned ship node shows a strong positive correlation with the importance of the node system. S4 passes through 23 dependency chains and S8 passes through 16 dependency chains, indicating that the more dependency chains a node is on the critical path, the greater its importance to the realization of system functions.

[0066] (3) The differentiating effect of functional uniqueness: The functional uniqueness factor plays an effective differentiating role among unmanned vessel nodes with similar topological positions in the dependency chain. Taking S1 and S9 as examples, they have similar topological positions in the dependency chain and both control only a single node. However, S1 has a functional uniqueness of 1.000, indicating that its function is completely irreplaceable, while S9 has a value of 0.754, resulting in a significant difference in the overall ranking. This shows that introducing functional uniqueness can more comprehensively identify the importance of nodes within the system.

[0067] Considering factors such as sensor measurement errors, communication delay fluctuations, and environmental interference in real-world operational environments, both functionally dependent parameters and degradation effects exhibit a degree of randomness. Therefore, a Monte Carlo simulation method is employed to model the parameter uncertainties, with a set number of simulations. The downgrade rate follows a truncated normal distribution. That is, a random disturbance with a mean of 20% and a standard deviation of 5%. Figure 6 The distribution of Monte Carlo simulation results is shown, displaying the unmanned vessels arranged in descending order of expected performance loss. S1 exhibits the highest mean loss (approximately 13.0%), followed by S4 (approximately 12.9%) and S8 (approximately 11.2%). The width of the violin plot represents the probability density at each performance level. The core centroid nodes (S1, S4) not only have higher means but also exhibit larger distribution widths, reflecting their amplified sensitivity to system disturbances. Figure 7 As shown, the distribution characteristics are illustrated by overlaying scatter plots with box plots, with 50 points randomly sampled for each unmanned surface vessel (USV). Analysis indicates that despite random variations in the degradation rate, the relative ranking remains highly stable. S1 consistently dominates across all simulations, with its lower quartile exceeding the upper quartiles of most other USVs, demonstrating that S1 maintains the highest system importance even under the most unfavorable parameter perturbations. Based on the Monte Carlo simulation results, the expected importance of each USV is calculated. Standard deviation The importance of robustness and overall importance The results are shown in Table 3:

[0068] Table 3. Results of Identification of Key Nodes in the System under Uncertainty Conditions As shown in Table 3, compared with the deterministic assessment results in Table 2, the top three rankings, S1, S4, and S8, remained unchanged after the uncertainty assessment, verifying the robustness of the proposed method. S2 rose from fourth place under deterministic conditions to fourth place under uncertainty conditions (its overall score increased from 7.13 to 11.29), while S5 remained stable at fifth place. This is because the Monte Carlo simulation considers the cumulative effect of parameter fluctuations, revealing the potential importance of these unmanned vessels under adverse conditions. The standard deviation of S4 (3.06) is slightly higher than that of S1 (3.04), indicating that S4 is more sensitive to parameter disturbances. This characteristic is valuable for formulating action strategies: if a stable action effect is desired, S1 should be preferred; if a greater benefit is expected under favorable conditions, S4 can be considered.

[0069] Please see Figure 8 This application also provides a heterogeneous cluster key node identification device, which can implement the above-mentioned heterogeneous cluster key node identification method. The device includes: Network building module 801 is used to build a functionally dependent network for heterogeneous clusters based on meta-paths; Importance calculation module 802 is used to calculate the importance of nodes in the functionally dependent network under uncertainty conditions to obtain a robust importance index; The functional uniqueness calculation module 803 is used to quantify the irreplaceability of the node functions of the functionally dependent network to obtain the functional uniqueness factor. The node identification module 804 is used to perform key node identification processing on the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain the target key node.

[0070] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0071] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0072] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0073] Please see Figure 9 , Figure 9The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 901 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 902 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 902 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 902 and is called and executed by the processor 901. The input / output interface 903 is used to implement information input and output; The communication interface 904 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 905 transmits information between various components of the device (e.g., processor 901, memory 902, input / output interface 903, and communication interface 904); The processor 901, memory 902, input / output interface 903, and communication interface 904 are connected to each other within the device via bus 905.

[0074] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0075] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0076] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0077] This application provides a method and related device for identifying key nodes in heterogeneous clusters. It constructs a node-aware multi-level attention mechanism for the heterogeneous graph of a functionally dependent network in the heterogeneous cluster, introducing a two-layer architecture combining node-level attention and meta-path preferences to learn representations of nodes in the associated network. Then, a deep attention network is used to complete the missing edges. This application can capture the importance of local neighbors and learn the importance of global semantic paths. This allows each node to form its own unique meta-path preferences, suitable for network completion tasks in heterogeneous graphs. Furthermore, through the dual-path architecture and centralized control strategy, it achieves accurate identification and quantification of functional dependencies in heterogeneous clusters.

[0078] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0079] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0080] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0081] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or appropriate combinations thereof.

[0082] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0083] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0084] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0085] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0086] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0087] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0088] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for identifying key nodes in a heterogeneous cluster, characterized in that, The method includes the following steps: Functionally dependent networks are constructed from heterogeneous clusters based on meta-paths; The importance of nodes in the functionally dependent network under uncertainty conditions is calculated to obtain a robust importance index; The irreplaceability of the node functions in the aforementioned function-dependent network is quantified to obtain the function uniqueness factor; Based on the robust importance index and the functional uniqueness factor, the functionally dependent network is subjected to key node identification processing to obtain the target key node.

2. The method according to claim 1, characterized in that, The calculation of node importance in the functionally dependent network under uncertainty conditions to obtain importance distribution characteristics includes the following steps: Under uncertainty conditions, the uncertainty of the network parameters of the functionally dependent network is mathematically characterized to obtain an uncertainty characterization; Monte Carlo simulation was performed on the node importance evaluation process of the functionally dependent network based on the aforementioned uncertainty characterization to obtain an importance sample set; The expected importance and standard deviation are obtained by analyzing and statistically analyzing the aforementioned important sample set. The robust importance index is calculated based on the expected importance and the standard deviation.

3. The method according to claim 2, characterized in that, The process of mathematically characterizing the uncertainty of network parameters in the function-dependent network under uncertainty conditions to obtain an uncertainty characterization includes the following steps: Under the aforementioned uncertainty conditions, obtain the network parameters of the function-dependent network; The network parameters are characterized using a truncated normal distribution to obtain the uncertain characterization.

4. The method according to claim 2, characterized in that, The process of evaluating the node importance of the functionally dependent network based on the uncertain characterization, using Monte Carlo simulation to obtain an importance sample set, includes the following steps: Random sampling is performed on the uncertain characterization to obtain sampling parameters; The baseline operability level of all nodes in the function-dependent network is calculated based on the sampling parameters. Based on the baseline operability level, the current simulated operability level of all nodes in the function-dependent network is calculated through the cascading propagation effect after performance degradation. The dependency chain importance index is calculated for the target node in the current simulation based on the current simulation operability level. Returning to the previous step of randomly sampling the uncertain representation, after multiple independent simulations, all the obtained dependency chain importance indices are added to the importance sample set.

5. The method according to claim 4, characterized in that, The process of calculating the dependency chain importance index for the target node in the current simulation based on the current simulation operability level includes the following steps: The number of nodes in the dependency chain of the target node and the total number of dependency chains passing through the target node are statistically obtained. The dependency chain importance index is obtained by calculating the current simulation operability level, the number of nodes, and the total number of dependency chains based on the dependency chain importance index calculation formula.

6. The method according to claim 1, characterized in that, The process of quantifying the irreplaceability of node functions in the functionally dependent network to obtain a functional uniqueness factor includes the following steps: Each node in the functionally dependent network is vectorized to obtain a node function vector. The functional similarity of nodes is calculated based on the node function vectors to obtain the node functional similarity. The functional similarity of the nodes is calculated based on the formula for calculating functional uniqueness, and the functional uniqueness factor is obtained.

7. The method according to any one of claims 1 to 6, characterized in that, The process of identifying key nodes in the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain target key nodes includes the following steps: The robust importance index and the functional uniqueness factor are calculated based on the comprehensive importance index calculation formula to obtain the comprehensive importance index; Based on the comprehensive importance index, the nodes of the functionally dependent network are sorted and filtered to obtain the target key nodes.

8. A device for identifying key nodes in a heterogeneous cluster, characterized in that, The device includes: The network building module is used to build functionally dependent networks from heterogeneous clusters based on meta-paths. The importance calculation module is used to calculate the importance of nodes in the functionally dependent network under uncertainty conditions, and obtain a robust importance index. The function uniqueness calculation module is used to quantify the irreplaceability of the node functions of the function-dependent network to obtain the function uniqueness factor. The node identification module is used to perform key node identification processing on the functionally dependent network based on the robust importance index and the functional uniqueness factor to obtain the target key node.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

Images