A network robustness prediction method based on scale normalization features and dual-view graph representation learning

Abstract

The application belongs to the technical field of network robustness prediction, and relates to a network robustness prediction method based on scale normalization features and double-view graph representation learning, comprising the following steps: collecting different network topologies as training samples, and obtaining real robustness labels of each training sample through node attack simulation; extracting four types of structural features of each node and performing scale normalization processing; arranging the four types of normalized structural features according to node indexes to form a node feature matrix and inputting the node feature matrix into an adaptive feature embedding module to obtain initial node embedding; inputting the initial node embedding into a local view branch and a global view branch to obtain local node representation and global node representation and then fusing the local node representation and the global node representation to form comprehensive graph-level representation; introducing a multilayer perceptron predictor to construct a robustness prediction model, inputting the comprehensive graph-level representation into the multilayer perceptron predictor to output a robustness prediction value, setting an optimization target, updating parameters of the adaptive feature embedding module and the robustness prediction model, and completing model training.

Description

Technical Field

[0001] This invention belongs to the field of network robustness prediction technology, and relates to a network robustness prediction method based on scale-normalized features and dual-view graph representation learning. Background Technology

[0002] Network robustness measures a network's ability to maintain connectivity and basic functionality under conditions of random failures, malicious attacks, or critical node failures. It is a core indicator in complex network analysis, critical infrastructure security assessment, and network topology optimization. Existing robustness calculations typically employ attack simulation methods, which involve continuously removing nodes according to a preset attack strategy and recalculating the network's maximum connectivity component after each round of removal to obtain the network's connectivity maintenance capability throughout the attack. This method is intuitive and accurate, but it requires repeated updates to the network structure and execution of connectivity calculations, and the computational overhead increases rapidly with the number of nodes.

[0003] In large-scale network analysis and iterative topology optimization scenarios, the same batch of candidate topologies often needs to be evaluated hundreds or even thousands of times. Performing a full attack simulation each time would significantly increase the time cost of network design, scheduling, and optimization, making it difficult to meet the needs of online analysis or rapid decision-making. Therefore, using learning models to directly predict robustness values ​​from network topology has become an important technical approach to reduce the cost of robustness evaluation.

[0004] Existing learning-based robustness prediction schemes still suffer from the following problems: First, when converting the adjacency matrix into an image and processing it using a convolutional neural network, it is easily affected by the node arrangement order and matrix sparsity, and it is difficult to directly adapt to different node sizes. Second, traditional graph neural networks are mainly based on local neighborhood message passing, and the receptive field is limited by the number of network layers, making it difficult to explicitly model global structures that have a significant impact on robustness, such as cross-community bridging nodes, long-range paths, and global cut sets. Third, the absolute values ​​of structural features such as node degree, core degree, and PageRank change with network size and density, and the model is prone to learning statistical laws coupled with the training scale, leading to increased prediction errors on networks outside the training scale. Fourth, the contributions of local and global structures to the robustness of different types of networks are not the same, and it is difficult to adapt to topological differences using fixed fusion weights.

[0005] Therefore, a robust prediction method is needed that can mitigate the feature distribution shift caused by changes in network size, extract local neighborhood structure and global node interaction information, and adaptively fuse different structural views based on the input network, so as to balance prediction accuracy, cross-scale generalization ability and computational efficiency. Summary of the Invention

[0006] To address the shortcomings of existing network robustness assessment methods, which rely on full attack simulations and incur high computational costs, as well as the deficiencies of existing learning-based prediction methods in cross-scale feature representation, global structure modeling, and multi-view fusion, this invention proposes a network robustness prediction method based on scale-normalized features and dual-view graph representation learning. This method extracts structural features reflecting local node connectivity, neighborhood redundancy, core hierarchy, and global influence from the topology of the network to be evaluated. Scale normalization mitigates feature distribution shifts caused by variations in the number of network nodes and connection density. The method then learns the network structure in parallel using local and global views. Finally, it adaptively fuses the two types of graph-level representations based on the topological characteristics of the network to be evaluated and outputs the predicted network robustness value.

[0007] This invention provides a robust prediction method for networks based on scale-normalized features and dual-view graph representation learning, comprising:

[0008] Step 1: Collect various network topologies as training samples, and obtain the true robustness labels of each training sample through node attack simulation to form a training dataset;

[0009] Step 2: Extract four types of structural features for each node of the training samples: degree centrality, clustering coefficient, K-Core degree, and PageRank value, and perform scale normalization on the structural features of each node;

[0010] Step 3: Arrange the four normalized structural features of each node in order according to the node index to form a node feature matrix. Input the node feature matrix into the adaptive feature embedding module for adaptive weighted embedding processing to obtain the initial node embedding.

[0011] Step 4: Construct local view branches, embed the initial node into the input local view branch, and aggregate neighbor node information layer by layer along the actual network connection relationship to obtain local node representations;

[0012] Step 5: Construct a global view branch, embed the initial node into the input global view branch, model the long-distance structural interaction relationship between different nodes, and obtain the global node representation;

[0013] Step 6: Perform global average summation on the local node representations and global node representations respectively to obtain local graph-level representations and global graph-level representations; then input the two types of representations into the dynamic gating module to form a comprehensive graph-level representation;

[0014] Step 7: Construct a network robustness prediction model consisting of an adaptive feature embedding module, a local view branch, a global view branch, a dynamic gating module, and a multilayer perceptron predictor; input the comprehensive graph-level representation into the multilayer perceptron predictor, obtain the robustness prediction value of the training samples through nonlinear mapping, use the mean square error between the robustness prediction value and the corresponding true robustness label as the optimization objective, jointly update the parameters of the network robustness prediction model, so that the network robustness prediction model learns the mapping relationship from network topology to robustness index, and completes the model training;

[0015] Step 8: Extract the four types of structural features of the network topology to be evaluated and perform scale normalization to form a node feature matrix; input the node feature matrix into the trained network robustness prediction model, and output the robustness prediction value of the network to be evaluated after one forward calculation.

[0016] The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning of the present invention has the following beneficial effects:

[0017] 1. This invention performs scale normalization on node structural features such as degree centrality, core level, and global importance, making the node representation more focused on its relative structural role in the current network. This can reduce the feature distribution shift caused by changes in network size and improve the stability of cross-scale prediction.

[0018] 2. This invention learns the network structure in parallel using local and global views, and adaptively fuses the two types of graph-level representations using a dynamic gating mechanism. This enables the simultaneous characterization of local redundant connections, bridging nodes, and long-distance structural relationships, thereby improving the accuracy of robust prediction.

[0019] 3. In the actual prediction stage, this invention does not require removing nodes round by round and repeatedly calculating the maximum connected component. It only needs to complete feature extraction and model forward calculation once, which can significantly reduce the computational overhead in large-scale network batch evaluation and topology optimization. Attached Figure Description

[0020] Figure 1 This is a flowchart of a network robust prediction method based on scale-normalized features and dual-view graph representation learning according to the present invention;

[0021] Figure 2 It is the correspondence between network topology and scale-normalized node structure feature matrix. Detailed Implementation

[0022] The network robustness prediction process of the present invention will be described in detail below with reference to the accompanying drawings. This embodiment uses an undirected, unweighted network as an example, where devices, stations, or functional entities in the network are treated as nodes, and the communication, connections, or dependencies between nodes are treated as edges. Specifically, see... Figure 1 As shown, the robust prediction method for networks based on scale-normalized features and dual-view graph representation learning in this embodiment includes:

[0023] Step 1: Collect various network topologies as training samples, and obtain the true robustness labels of each training sample through node attack simulation to form a training dataset, specifically:

[0024] Step 1.1: Collect network topologies with different topology types, node sizes, and connection densities as training samples; given a network topology graph G=(V,E), where V represents the set of nodes and E represents the set of edges.

[0025] In practice, training samples can include scale-free networks, random networks, random regularized networks, small-world networks, and real networks to cover different degree distributions, clustering levels, and overall connectivity patterns.

[0026] Step 1.2: Remove nodes continuously for each training sample according to the preset attack strategy, and record the number of nodes in the largest connected component of the network remaining after each removal.

[0027] Step 1.3: By summarizing the connectivity preservation status throughout the entire attack process, obtain the true robustness label of the training sample:

[0028]

[0029] in, Indicates true robustness labeling. The total number of nodes in the network topology. Indicates cumulative removals The number of nodes in the maximum connected component of the remaining network after each node.

[0030] Formula (1) is used to obtain the true robustness label offline. After the model completes parameter learning and deployment, the online prediction stage no longer performs a full attack simulation on the network to be evaluated, that is, it no longer performs round-by-round node removal and repeated calculation of the maximum connected component. Thus, the high-overhead robustness calculation process is transformed into one feature extraction and one model forward prediction.

[0031] Step 1.4: Based on the training samples and real robustness labels, form a correspondence between the network topology used for supervised learning and the real robustness, thus constructing the training dataset. , This represents the j-th network topology. This represents the true robustness label corresponding to the j-th network topology graph.

[0032] Step 2: Extract four types of structural features for each node in the training samples: degree centrality, clustering coefficient, K-Core degree, and PageRank value. Then, perform scale normalization on the structural features of each node. Specifically:

[0033] Step 2.1: For a training sample containing several nodes and connecting edges, set a unique index for each node and record the connection relationship between nodes using an adjacency matrix A.

[0034] Step 2.2: Extract the degree centrality of each node and perform scale normalization:

[0035]

[0036] in, For nodes The degree; The total number of nodes in the network topology, divided by the theoretical maximum degree. Constrain it to the [0,1] interval to eliminate the influence of network size on local connectivity metrics.

[0037] Step 2.3: Calculate the clustering coefficient for each node. :

[0038]

[0039] in, For nodes The number of connected edges within the neighbor set; this index is naturally located in [0,1] and does not require additional normalization.

[0040] Step 2.4: Calculate the K-Core degree of each node, and iteratively strip away nodes with a degree less than [a certain value]. This decomposition process divides the network into a hierarchical structure from the periphery to the interior, thus representing the core depth of a node within the entire network:

[0041]

[0042] in, Represents a node K-Core core density.

[0043] Since the absolute coreness varies greatly across networks of different densities or sizes, the relative coreness is obtained by normalizing the K-Core coreness by dividing it by the maximum coreness in the network. :

[0044]

[0045] in, This represents the maximum coreness in the network. This processing effectively eliminates the absolute numerical bias caused by network size and global density, enabling the model to stably identify the innermost skeleton nodes across network sizes.

[0046] Step 2.5: Calculate the PageRank value for each node:

[0047]

[0048]

[0049] Where α is the damping coefficient. Pointing to a node The neighborhood group, Pointing to a node neighboring nodes PageRank value, For nodes The out-degree; to prevent the original PageRank value from approaching 0 as the number of nodes increases in a large-scale network, it is compared with the total number of nodes in the current network. Multiply to obtain the normalized PageRank value The expected value of the features is uniformly anchored to 1. This process effectively eliminates the dilution of the global hub feature strength by network size, making the global hub features of networks of different sizes directly comparable.

[0050] Degree centrality reflects the number of direct connections a node has with other nodes, and is a first-order topological feature describing a node's local connectivity. Clustering coefficient reflects the density of connections and local redundant paths within a node's neighborhood, and is a second-order topological feature measuring the local clustering characteristics of the network. K-Core degree reflects whether a node is located on the network periphery or within the structural skeleton. PageRank reflects the accumulated influence of a node through global connectivity. These four features describe the structural role of a node in the network from four aspects: local first-order connectivity, local high-order organization, core hierarchy, and global propagation.

[0051] Since the original structural features in networks of different sizes and densities have different numerical ranges, this invention performs scale normalization on the statistical characteristics of each feature. Node degree is normalized according to the maximum number of connections allowed in the current network, making the direct connection capabilities comparable across different node sizes. Clustering coefficients, being within a uniform range, can be directly retained. Node core degree is normalized according to the maximum core degree in the current network, allowing the model to focus on the relative core level of a node within its own network. PageRank is scale-compensated according to the number of nodes in the current network, reducing the impact of the original PageRank value decreasing overall as the network size increases. After these processing steps, nodes with the same structural role have more similar feature distributions in networks of different sizes, thereby reducing the model's dependence on the size of the training network.

[0052] Step 3: Arrange the four normalized structural features of each node in order according to the node index to form a node feature matrix. Input the node feature matrix into the adaptive feature embedding module for adaptive weighted embedding processing to obtain the initial node embedding, specifically:

[0053] Step 3.1: Construct a node feature matrix. Each row in the node feature matrix corresponds to a node in the network, and each column corresponds to a normalized structural feature. The values ​​in the matrix are all calculated from the actual connection relationships of the corresponding nodes in the original network.

[0054] Figure 2 This demonstrates the correspondence between network topology and scale-normalized node structure feature matrix. The node number clarifies the one-to-one correspondence between the topology nodes on the left and the rows of the feature matrix on the right, avoiding inconsistencies between feature values ​​and node connection relationships.

[0055] Where D, C, K, and P represent the scale normalization results of four structural features: degree centrality, clustering coefficient, K-Core core degree, and PageRank value, respectively.

[0056] Step 3.2: Since the above four types of structural features contribute differently to the robustness of predicting different topologies, a learnable feature bias parameter is introduced. The feature weights are obtained after Softmax normalization:

[0057]

[0058] Node feature matrix Input adaptive feature embedding module and feature weights After element-wise weighting, linear projection, and layer normalization, ReLU activation is performed to obtain the initial node embedding. :

[0059]

[0060] in, and LN(·) represents the weights and biases of the linear projection layer, and LN(·) denotes the layer normalization operation.

[0061] Considering that the contributions of the four types of structural features to the robustness of different network topologies are not fixed, this invention designs an adaptive feature embedding module, sets feature weights, and adaptively adjusts the features for each type. During parameter learning, the model automatically increases the contribution of effective features and suppresses interfering features based on the prediction error. Then, it projects the low-dimensional structural features to a unified hidden space through linear mapping and uses layer normalization to stabilize the feature distribution under different networks and sample batches. After this processing, each node obtains an input representation with a unified dimension, providing a consistent data foundation for subsequent parallel learning of local and global views.

[0062] Step 4: Construct a local view branch, embed the initial node into the input local view branch, and aggregate neighbor node information layer by layer along the actual network connection relationship to obtain the local node representation, specifically:

[0063] GCN was chosen as the backbone encoder for the local view branch. To avoid overly smooth node representations caused by deep GCNs, the GCNs were limited to shallow stacking, and batch normalization was introduced after each layer to stabilize the feature distribution. At the same time, the original input of each layer was directly superimposed on the aggregated result through additive residual connections.

[0064]

[0065] in, As the initial input of the trunk encoder, i.e., the input of the first layer of the trunk encoder; Main encoder number The output of the layer, i.e., the first layer of the backbone encoder. Layer input, Main encoder number The output of the layer, , This refers to the number of layers in the backbone encoder; This represents the symmetric normalized adjacency matrix after introducing self-loops; , and These represent the adjacency matrix and the identity matrix, respectively. It is a matrix The degree matrix; For the first The feature transformation weight matrix of the layer, This indicates batch normalization; it sets the output of the last layer of the trunk encoder to... Local node representations as outputs of local view branches.

[0066] The local view branch uses a graph convolutional network to pass messages along real-world connections within the network. Each node retains its own structural features while aggregating information from neighboring nodes layer by layer, thus obtaining a structural representation within a multi-hop neighborhood. This branch can identify locally dense subgraphs, redundant neighborhood connections, leaf nodes, hub nodes, and local bridging relationships. To avoid the representations of different nodes becoming too similar as the number of graph convolutional layers increases, this invention uses shallower graph convolutional layers and incorporates normalization and residual connections in each layer, allowing the node's initial structural information to be preserved along with the aggregated neighborhood information. Residual connections mitigate the excessive smoothing effect of the neighborhood averaging operator in multi-layer stacking and enable the final local representation to simultaneously integrate the node's initial structural features with the higher-order structural features obtained from multi-hop neighborhood aggregation.

[0067] Step 5: Construct a global view branch, embed the initial node into the input global view branch, model the long-distance structural interaction relationships between different nodes, and obtain the global node representation, specifically:

[0068] Step 5.1: Obtain the query matrix, key matrix, and value matrix from the initial node embeddings through learnable linear projection:

[0069]

[0070]

[0071]

[0072] Step 5.2: Introduce a linear graph attention mechanism based on orthogonal random feature maps to obtain global node representations:

[0073]

[0074] in, For querying the matrix, The key matrix, It is a value matrix; To query the weight parameters of the matrix, The weight parameters of the key matrix are... These are the weight parameters of the value matrix; (·) represents an orthogonal random feature map; This is a normalized matrix; It represents the global node.

[0075] As in the formula As shown, an unbiased approximation of the Softmax attention kernel is achieved using a pair of orthogonal random feature maps. Furthermore, by prioritizing the calculation of key-value products through associative law, the global interaction, which originally relied on the explicit product of Q and K, is rewritten as a linear operation. This reduces the computational complexity of global information encoding to O(Nrd), where N is the number of nodes, r is the dimension of random features, and d is the dimension of hidden layers. This mechanism retains the ability to model global node interactions while exhibiting good scalability to changes in node size.

[0076] The global view is not limited to a node's direct neighbors in the original network, but allows any node to establish information interactions based on its structural characteristics. This is used to identify cross-community bridging nodes, long-distance connections, global cut sets, and long-distance structural relationships that significantly influence the evolution of the maximum connected component. Considering that standard fully connected attention requires constructing an intermediate matrix that is proportional to the square of the number of nodes, this invention employs a Graph Transformer structure with linear complexity. It approximates attention computation through random feature mapping and adjusts the order of operations between queries, keys, and values, making the computational cost of global interactions approximately linear with the number of nodes, thus making it suitable for networks with large node sizes.

[0077] The local view branch and the global view branch employ independent but concurrent coding structures. The local view branch leverages the physical connectivity constraints provided by the network's real edges, exhibiting strong local structure induction capabilities. The global view branch transcends neighborhood limitations, directly establishing long-distance connections between node structural features. These two types of views respectively undertake the tasks of extracting micro-neighborhood structures and macro-level overall connectivity patterns, enabling the model to focus on both the supporting role of local redundant connections in fault recovery and the impact of bridging nodes and long-range paths on the network splitting process, thus forming a complementary network structure description.

[0078] Step 6: Perform global averaging and summarization of the local node representations and global node representations respectively to obtain local graph-level representations and global graph-level representations; then input both types of representations into the dynamic gating module to form a comprehensive graph-level representation, specifically:

[0079] Step 6.1: Perform global averaging and summarizing of local node representations to transform networks with different node sizes into fixed-dimensional local graph-level representations. :

[0080]

[0081] Local graph-level representations mainly summarize neighborhood connectivity strength, local clustering degree, and redundant path distribution.

[0082] Step 6.2: Perform global averaging and summarizing of global node representations to transform networks with different node sizes into fixed-dimensional global graph-level representations. :

[0083]

[0084] Global graph-level representations primarily summarize the overall connectivity patterns, bridging structures, and long-range dependencies of a network. Fixed-dimensional graph-level representations enable the same predictor to handle networks of varying sizes.

[0085] Step 6.3: The two types of representations are then input into the dynamic gating module to generate gating fusion coefficients between 0 and 1:

[0086]

[0087] in, The gating fusion coefficients are automatically learned during the training process, enabling the model to adjust the relative contributions of local and global information based on the current network's structural characteristics, without requiring manual setting of a fixed fusion ratio. This indicates that the local graph-level representation and the global graph-level representation are combined. Represents a multilayer perceptron; This represents the activation function.

[0088] To avoid applying a fixed dual-view fusion ratio to all networks, this invention incorporates a dynamic gating module. This module takes both local and global graph-level representations as input, analyzes the overall structure of the network to be evaluated, generates gating fusion coefficients within a preset range, and then fuses the two types of graph-level representations according to these coefficients. When the network has a high degree of local clustering and abundant redundant connections, the dynamic gating module can increase the contribution of the local view; when the network is sparse, has obvious bridging nodes, or has many long-distance connections, it can increase the contribution of the global view. Thus, networks of different topologies and sizes can obtain comprehensive graph-level representations adapted to their robustness formation mechanisms.

[0089] A comprehensive graph-level representation is formed based on gating fusion coefficients:

[0090]

[0091] in, This is a comprehensive graph-level representation.

[0092] Step 7: Construct a network robustness prediction model consisting of an adaptive feature embedding module, a local view branch, a global view branch, a dynamic gating module, and a multilayer perceptron predictor; input the comprehensive graph-level representation into the multilayer perceptron predictor, obtain the robustness prediction values ​​of the training samples through nonlinear mapping, and use the mean squared error between the robustness prediction values ​​and the corresponding true robustness labels as the optimization objective to jointly update the parameters of the network robustness prediction model, enabling the network robustness prediction model to learn the mapping relationship from network topology to robustness indicators, thus completing the model training. Specifically:

[0093] Step 7.1: Integrated Graph-Level Representation After Fusion The data is fed into a multilayer perceptron predictor, and the network outputs robust predictions through a nonlinear mapping:

[0094]

[0095] in, This represents a multilayer perceptron predictor. This represents the robustness prediction value.

[0096] Step 7.2: Set the optimization objective to minimize the mean squared error between the predicted value and the true robustness label:

[0097]

[0098] in, This represents the number of samples in the training dataset.

[0099] Step 7.3: Update the parameters of the adaptive feature embedding module, local view branch, global view branch, dynamic gating module, and multilayer perceptron predictor to enable the model to learn the mapping relationship from network structure to robustness index, and complete the model training.

[0100] Step 8: Extract the four types of structural features of the network topology to be evaluated and perform scale normalization to form a node feature matrix; input the node feature matrix into the trained network robustness prediction model, and output the robustness prediction value of the network to be evaluated after one forward calculation.

[0101] This invention aims to provide a robust network prediction method based on scale-normalized features and dual-view graph representation learning. This method reduces the input distribution bias between different node sizes by constructing node structural features that are weakly correlated with network size; it extracts local neighborhood information along the edges of the real topology through graph convolutional network branches, and models the global interactions between nodes through linear complexity Graph Transformer branches; through a graph-level dynamic gating mechanism, it adaptively determines the contribution ratio of the local view and the global view based on the structural characteristics of the network to be predicted, thereby quickly outputting network robustness predictions without performing full attack simulations and improving the prediction stability of the model on networks of different sizes and topologies.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A robust prediction method for networks based on scale-normalized features and dual-view graph representation learning, characterized in that, include: Step 1: Collect various network topologies as training samples, and obtain the true robustness labels of each training sample through node attack simulation to form a training dataset; Step 2: Extract four types of structural features for each node of the training samples: degree centrality, clustering coefficient, K-Core degree, and PageRank value, and perform scale normalization on the structural features of each node; Step 3: Arrange the four normalized structural features of each node in order according to the node index to form a node feature matrix. Input the node feature matrix into the adaptive feature embedding module for adaptive weighted embedding processing to obtain the initial node embedding. Step 4: Construct local view branches, embed the initial node into the input local view branch, and aggregate neighbor node information layer by layer along the actual network connection relationship to obtain local node representations; Step 5: Construct a global view branch, embed the initial node into the input global view branch, model the long-distance structural interaction relationship between different nodes, and obtain the global node representation; Step 6: Perform global average summation on the local node representations and global node representations respectively to obtain local graph-level representations and global graph-level representations; then input the two types of representations into the dynamic gating module to form a comprehensive graph-level representation; Step 7: Construct a network robustness prediction model consisting of an adaptive feature embedding module, a local view branch, a global view branch, a dynamic gating module, and a multilayer perceptron predictor; input the comprehensive graph-level representation into the multilayer perceptron predictor, obtain the robustness prediction value of the training samples through nonlinear mapping, use the mean square error between the robustness prediction value and the corresponding true robustness label as the optimization objective, jointly update the parameters of the network robustness prediction model, so that the network robustness prediction model learns the mapping relationship from network topology to robustness index, and completes the model training; Step 8: Extract the four types of structural features of the network topology to be evaluated and perform scale normalization to form a node feature matrix; input the node feature matrix into the trained network robustness prediction model, and output the robustness prediction value of the network to be evaluated after one forward calculation.

2. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 1, characterized in that, Step 1 specifically involves: Step 1.1: Collect network topologies with different topology types, node sizes, and connection densities as training samples; given a network topology graph G=(V,E), where V represents the set of nodes and E represents the set of edges; Step 1.2: For each training sample, remove nodes continuously according to the preset attack strategy, and record the number of nodes in the largest connected component of the network remaining after each removal; Step 1.3: By summarizing the connectivity preservation status throughout the entire attack process, obtain the true robustness label of the training sample: in, Indicates true robustness labeling. The total number of nodes in the network topology. Indicates cumulative removals The number of nodes in the maximum connected component of the remaining network after each node; Step 1.4: Based on the training samples and real robustness labels, form a correspondence between the network topology used for supervised learning and the real robustness, thus constructing the training dataset. , This represents the j-th network topology. This represents the true robustness label corresponding to the j-th network topology graph.

3. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 1, characterized in that, Step 2 specifically involves: Step 2.1: For a training sample containing several nodes and connecting edges, set a unique index for each node and record the connection relationship between nodes using an adjacency matrix A; Step 2.2: Extract the degree centrality of each node and perform scale normalization: in, For nodes The degree; The total number of nodes in the network topology, divided by the theoretical maximum degree. Constrain it to the [0,1] interval to eliminate the influence of network size on local connectivity measurement; Step 2.3: Calculate the clustering coefficient for each node. : in, For nodes The number of edges connected within the neighbor set; this index is naturally located in [0,1] and does not require additional normalization. Step 2.4: Calculate the K-Core degree of each node, and iteratively strip away nodes with a degree less than [a certain value]. This decomposition process divides the network into a hierarchical structure from the periphery to the interior, thus representing the core depth of a node within the entire network: in, Represents a node K-Core core density; Since the absolute coreness varies greatly across networks of different densities or sizes, the relative coreness is obtained by normalizing the K-Core coreness by dividing it by the maximum coreness in the network. : in, This represents the maximum core degree in the network; Step 2.5: Calculate the PageRank value for each node: Where α is the damping coefficient. Pointing to a node The neighborhood group, Pointing to a node neighboring nodes PageRank value, For nodes The out-degree; to prevent the original PageRank value from approaching 0 as the number of nodes increases in a large-scale network, it is compared with the total number of nodes in the current network. Multiply to obtain the normalized PageRank value The expected value of the features is uniformly anchored to 1.

4. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Construct a node feature matrix. Each row in the node feature matrix corresponds to a node in the network, and each column corresponds to a normalized structural feature. The values ​​in the matrix are all calculated from the actual connection relationships of the corresponding nodes in the original network. Step 3.2: Since the above four types of structural features contribute differently to the robustness of predicting different topologies, a learnable feature bias parameter is introduced. The feature weights are obtained after Softmax normalization: Node feature matrix Input adaptive feature embedding module and feature weights After element-wise weighting, linear projection, and layer normalization, ReLU activation is performed to obtain the initial node embedding. : in, and LN(·) represents the weights and biases of the linear projection layer, and LN(·) denotes the layer normalization operation.

5. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 4, characterized in that, Step 4 specifically involves: GCN was chosen as the backbone encoder for the local view branch. To avoid overly smooth node representations caused by deep GCNs, the GCNs were limited to shallow stacking, and batch normalization was introduced after each layer to stabilize the feature distribution. At the same time, the original input of each layer was directly superimposed on the aggregated result through additive residual connections. in, As the initial input of the trunk encoder, i.e., the input of the first layer of the trunk encoder; Main encoder number The output of the layer, i.e., the first layer of the backbone encoder. Layer input, Main encoder number The output of the layer, , This refers to the number of layers in the backbone encoder; This represents the symmetric normalized adjacency matrix after introducing self-loops; , and These represent the adjacency matrix and the identity matrix, respectively. It is a matrix The degree matrix; For the first The feature transformation weight matrix of the layer, This indicates batch normalization; it sets the output of the last layer of the trunk encoder to... Local node representations as outputs of local view branches.

6. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 5, characterized in that, Step 5 specifically involves: Step 5.1: Obtain the query matrix, key matrix, and value matrix from the initial node embeddings through learnable linear projection: Step 5.2: Introduce a linear graph attention mechanism based on orthogonal random feature maps to obtain global node representations: in, For querying the matrix, The key matrix, It is a value matrix; To query the weight parameters of the matrix, The weight parameters of the key matrix are... These are the weight parameters of the value matrix; (·) represents an orthogonal random feature map; This is a normalized matrix; It represents the global node.

7. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 6, characterized in that, Step 6 specifically involves: Step 6.1: Perform global averaging and summarizing of local node representations to transform networks with different node sizes into fixed-dimensional local graph-level representations. : Step 6.2: Perform global averaging and summarizing of global node representations to transform networks with different node sizes into fixed-dimensional global graph-level representations. : Step 6.3: The two types of representations are then input into the dynamic gating module to generate gating fusion coefficients between 0 and 1: in, The gating fusion coefficients are automatically learned during the training process; This indicates that the local graph-level representation and the global graph-level representation are combined. This represents a multilayer perceptron; Indicates the activation function; A comprehensive graph-level representation is formed based on gating fusion coefficients: in, This is a comprehensive graph-level representation.

8. The robust prediction method for networks based on scale-normalized features and dual-view graph representation learning according to claim 7, characterized in that, Step 7 specifically involves: Step 7.1: Integrated Graph-Level Representation After Fusion The data is fed into a multilayer perceptron predictor, and the network outputs robust predictions through a nonlinear mapping: in, This represents a multilayer perceptron predictor. Indicates robust prediction values; Step 7.2: Set the optimization objective to minimize the mean squared error between the predicted value and the true robustness label: in, The number of samples in the training dataset; Step 7.3: Update the parameters of the adaptive feature embedding module, local view branch, global view branch, dynamic gating module, and multilayer perceptron predictor to enable the model to learn the mapping relationship from network structure to robustness index, and complete the model training.

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