Dynamic network link prediction method assisted by static network

Abstract

The invention belongs to the technical field of large-scale network data analysis, and particularly relates to a link prediction method by using a static network to assist a dynamic network. Aiming at a static-dynamic double-layer network structure, topological structure information of a static network is fully utilized, node representation of a dynamic network is enhanced, and link prediction accuracy of the dynamic network is improved, and the method specifically comprises the steps that data preprocessing is conducted on the static-dynamic double-layer network, an original network is converted into a double-layer graph sequence by extracting a static layer sub-graph, and the link prediction accuracy of the dynamic network is improved. Initializing node features and edge features; and performing link prediction by using a network fusion edge convolution model (NF-EdgeConv), including capturing and fusing node embedding of a double-layer network, and outputting a probability value of existence of a link through decoding. According to the invention, computing resources can be saved, and the link prediction performance of the dynamic network is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of large-scale network data analysis, and particularly relates to a dynamic network link prediction method. Background Art

[0002] Link prediction, as an important direction in the research of complex networks, aims to predict the possibility of connection between two nodes that have not yet established a connection through known network nodes and network structure information. The content of link prediction mainly includes two categories: one is unknown connections, that is, connections that actually exist in the network but have not been detected; the other is future connections, that is, connections that do not currently exist in the network but may appear or should exist in the future. This prediction not only covers the speculation of unknown connections but also includes the prediction of future connections. Link prediction plays an important guiding role in deeply understanding the structure, function, and dynamic evolution process of complex networks. At the same time, link prediction is the intersection of network science and information science. From the perspective of information science, link prediction mainly solves the problems of supplementing missing data and predicting future trends, providing theoretical support for data processing and analysis in practical applications. Therefore, link prediction is not only of great significance to theoretical research but also shows remarkable value in practical applications.

[0003] Link prediction helps to reveal the evolution law of network structure in theoretical research and promotes the research of network evolution models and the identification of abnormal node behaviors. In practical applications, link prediction is widely used in recommendation systems, criminal investigations, and the biological field, improving information matching efficiency, assisting law enforcement agencies in discovering potential criminal connections, and inferring potential molecular relationships in drug research and development and protein interaction prediction, reducing the cost and cycle of experimental verification.

[0004] Currently, there are many studies on link prediction algorithms in the academic community. Most of the related research methods focus on link prediction under two topological structures: single-layer dynamic networks and multi-layer static networks, and use deep learning models such as graph neural networks to effectively capture the complex non-linear relationships between nodes and the structural features of the network, thereby improving the accuracy and generalization ability of link prediction.

[0005] When the inventor conducts research on link prediction for different network topologies, it is found that the existing dynamic network link prediction methods fail to fully utilize the information of other layers in the multi-layer network structure, resulting in difficulty in comprehensively reflecting the complex dynamic characteristics of the network. At the same time, the existing multi-layer network link prediction methods mainly focus on static intra-layer and inter-layer relationships, fail to effectively capture the dynamic evolution characteristics of the network, and lack the ability to handle dynamic changes. Summary of the Invention

[0006] In view of the above situation, the purpose of the present invention is to provide a dynamic network link prediction method assisted by a static network with high link prediction accuracy and strong generalization ability.

[0007] The dynamic network link prediction method assisted by a static network proposed by the present invention is aimed at a static-dynamic two-layer network structure, makes full use of the topological structure information of the static network, further enhances the node representation of the dynamic layer network, and thus improves the link prediction accuracy of the dynamic network. The specific steps are as follows:

[0008] Step 1: Perform data preprocessing on the static-dynamic two-layer network. By extracting the subgraph of the static layer, the original network is transformed into a two-layer graph sequence, and the node features and edge features are initialized; specifically including:

[0009] Step 1-1: Refer to Figure 2 As shown, according to the node set of the dynamic layer graph snapshot, an independent subgraph extraction operation is performed on the static layer at each time step, so as to construct a two-layer graph sequence;

[0010] Step 1-2: Initialize the node features of each layer of the two-layer network;

[0011] Step 1-3: Perform targeted edge feature initialization on the unweighted network and the weighted network, and normalize the time stamps of the dynamic layer edges within each time slice, so as to endow the edges with different temporal features;

[0012] Step 2: Use the Network Fusion Edge Convolutional network (NF-EdgeConv) model to achieve the fusion of node representations on the static layer and the dynamic layer, and link prediction on the dynamic layer. The overall structure of the NF-EdgeConv model is shown in Figure 3 As shown, it includes the following key components: (1) Static layer encoder: used to perform preliminary mapping on the node and edge features in the static layer subgraph at time step t; (2) Dynamic layer encoder: used to perform preliminary mapping on the node and edge features in the dynamic graph snapshot at time step t; (3) Static layer convolution module: perform convolution processing on the preliminary mapping output by the static layer encoder, specifically including L s convolutional layers, and edge convolution is integrated in each convolutional layer in turn [1] 、Batch Normalization (BN) and PReLU activation function; (4) Dynamic layer convolution module: perform convolution processing on the preliminary mapping output by the dynamic layer encoder, specifically including L dA convolutional layer, in which edge convolution, batch normalization, PReLU activation function, and moving average GRU update module are integrated in sequence, and the update module is used to update the node state in real time; (5) Network fusion module: fuses the node representations of the static layer and the dynamic layer, and is internally composed of two sub-modules; one is the attention mechanism module, including integrated multi-head attention mechanism, batch normalization, and PReLU activation function, and the other is the generalization module, which consists of a fully connected layer, batch normalization, and PReLU activation function; (6) MLP decoder: realizes the final link prediction task through a two-layer MLP. The specific steps are as follows:

[0013] Step 2-1: Encode the initial node features and initial edge features;

[0014] Step 2-2: Learn the node embeddings of each layer in the two-layer network through an edge convolution network with residual connections;

[0015] Step 2-3: At each time step, save the node embeddings after each convolutional layer of the dynamic network when the model performs best on the validation set, and use these embeddings as the hierarchical node state at the current moment; "the model performs best on the validation set" means that during the training process at each time step, the loss on the validation set is the lowest; when the validation loss is less than the historical minimum, the model will update the parameters and save the current model state;

[0016] Step 2-4: Add a moving average gated recurrent unit (GRU) update module after each convolutional layer of the dynamic network to update the node state in real time;

[0017] Step 2-5: Dynamically balance the influence weights of the current node embeddings and historical node states through an adaptive retention rate, and here two adaptive retention rates are used: decay retention rate and Sigmoid retention rate;

[0018] Step 2-6: Through the multi-head attention mechanism, effectively combine the node embeddings of the dynamic layer and the static layer, so as to enhance the node representation of the dynamic layer;

[0019] Step 2-7: Predict the possibility of an edge connection from the source node to the target node through a two-layer multi-layer perceptron (MLP) decoder;

[0020] Step 2-8: Optimize the model performance through the ROLAND evaluation system and training strategy. During the training process, use the binary cross entropy (BCE) loss function to continuously improve the model performance.

[0021] The innovation points of the present invention mainly include:

[0022] The present invention proposes a data preprocessing method for a static-dynamic double-layer network, which makes full use of the static layer information and saves computing resources;

[0023] The present invention proposes an NF-EdgeConv model, which can capture and fuse the node representations of different network layers and achieve link prediction on the dynamic layer;

[0024] The present invention further proposes two adaptive retention rate functions, namely the decay retention rate and the Sigmoid retention rate, to adaptively balance the relationship between the historical node state and the current node embedding, so as to obtain a more effective time series representation and further improve the link prediction performance of the dynamic network. Brief Description of the Drawings

[0025] Figure 1 It is a flowchart of the dynamic network link prediction method assisted by the static network of the present invention.

[0026] Figure 2 It is a flowchart of the data preprocessing method for the static-dynamic double-layer network of the present invention.

[0027] Figure 3 It is a diagram of the structure of the NF-EdgeConv model of the present invention. Detailed Embodiment

[0028] In order to make the above objects and innovative points of the present invention easier to understand, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0029] Step 1: Perform data preprocessing on the static-dynamic double-layer network. By extracting the subgraph of the static layer, the original network is transformed into a double-layer graph sequence, and the node features and edge features are initialized; the specific process is shown in Figure 2 as shown.

[0030] It is known that the static-dynamic double-layer network contains two layers: R = {s, d}, where s represents the static layer and d represents the dynamic layer, and r ∈ R represents any layer in the double-layer network. The static-dynamic double-layer network is represented as a set of a static graph and a series of dynamic graph snapshots The static graph is represented as G s = {V s , E s , X s , F s}, where V s represents the static graph node set, E s represents the static graph edge set, X s represents the node feature matrix of the static layer, and F s represents the edge feature matrix of the static layer. The dynamic graph snapshot sequence is represented as The graph snapshot at time step \(t\) is denoted as where represents the node set of the graph snapshot, represents the edge set of the graph snapshot, represents the node feature matrix of the graph snapshot, represents the edge feature matrix of the graph snapshot. Additionally, the node set \(V\) of the dynamic graph d is defined as the union of the node sets in all graph snapshots The steps of the preprocessing method are as follows:

[0031] Step 1-1: According to the node set of the graph snapshot at time step \(t\) generate the subgraph node set of the static layer and make the generated node set satisfy both and According to the node set extract the corresponding edge set s in the static graph \(G\) and make the extracted edge set satisfy Through the node set and the edge set construct the static layer subgraph corresponding to time step \(t\) Finally, construct the graph sequence of the static layer based on the subgraphs at all time steps

[0032] Step 1-2: Initialize the node features of each layer in the double-layer network: where \(|V\) d | represents the total number of nodes in the dynamic network.

[0033] Step 1-3: Initialize the edge features for the unweighted network or the weighted network. At the same time, not only divide the graph snapshots according to the time stamps, but also use the normalized time stamps to represent the time order of the edges within each time step, so as to generate different initial edge features:

[0034] (1) For the unweighted network, set the edge features of the static layer at the initial moment as: The edge features of the dynamic layer are obtained through normalized time stamps:

[0035]

[0036] where \(t\) d represents the time stamp vector, \(z(\cdot)\) represents the normalization operation, and \(\delta_1\) and \(\delta_2\) represent the lower and upper bounds of the normalization result (the default interval is 0 to 2).

[0037] (2) For the weighted network, set the edge features of the static layer at the initial moment as: Among them, the feature of each edge is equal to the edge weight, denotes the number of subgraph edges in the static layer at time step t. The edge features of the dynamic layer are generated by concatenating the edge weight with the normalized time stamp vector:

[0038]

[0039] where [·|·] is the column concatenation symbol, denotes the number of graph snapshot edges in the dynamic layer at time step t.

[0040] Step 2: Use the NF-EdgeConv model to capture and fuse the node embeddings of the double-layer network, and decode the probability value of the existence of the output link. Specifically:

[0041] Step 2-1: Encode the initial node features: where W x denotes the linear transformation matrix. Then, post-process the encoded node features: where σ1(·) represents the PReLU activation function, which is calculated by formula (1):

[0042] σ1(x) = max(0, x) + αmin(0, x), (1) where α is a learnable parameter. B(·) represents the batch normalization operation, which is calculated by formula (2):

[0043]

[0044] where, and β are trainable parameters, ∈ is a small constant used to avoid division-by-zero errors, μ(·) represents the mean value, and (σ(·)) 2 denotes the variance.

[0045] Encode the edge features at the initial moment: and post-process the encoded edge features: where W f is the linear transformation matrix.

[0046] Step 2-2: Learn the network topology representation from each layer of the network through the EdgeConv network, which specifically includes two links: message passing and aggregation:

[0047] (1) For a single convolutional layer l, the message passing process from node u to node v is shown in formula (3):

[0048]

[0049] where, denotes the message passing from node u to node v in convolutional layer l, represents the feature vector of node v in the previous convolutional layer (l-1). represents the feature vector of edge (u, v). is the weight matrix. represents the bias vector.

[0050] (2) Integrate the information of neighbor nodes through the sum aggregation operation. The message aggregation process is shown in Equation (4):

[0051]

[0052] where represents the set of neighbor nodes of node v. represents the residual representation vector from layer (l-1). represents the weight matrix. represents the bias vector.

[0053] Finally, the node embedding matrix after passing through the l-th convolutional layer is expressed as

[0054] Step 2-3: At each time step, save the node embeddings after each convolutional layer of the dynamic network when the model performs best on the validation set, and use these embeddings as the hierarchical node states at the current moment: where L d represents the number of convolutional layers in the dynamic layer. "The model performs best on the validation set" means that during the training process at each time step, the loss on the validation set is the lowest. When the validation loss is less than the historical minimum, the model updates its parameters and saves the current model state.

[0055] Step 2-4: Add a moving average GRU update module after each convolutional layer of the dynamic network to update the node states in real time. First, the calculation process of the classic GRU is shown in Equations (5)-(8):

[0056]

[0057] where the candidate state is jointly determined by the current input and the weighted previous time step hidden state . controls the influence degree of the previous hidden state on the candidate state . And the final hidden state is controlled by , determines the weighted proportion between the current candidate state and the previous time step hidden state . W z , W r and Wh The weight matrix representing the gate, U z , U r and U h The weight matrices representing the hidden states, b z , b r and b h represent the bias vectors, ⊙ represents the Hadamard product. σ2(·) and σ3(·) represent the Sigmoid activation function and the Tanh activation function respectively, and are calculated using formulas (9) and (10):

[0058]

[0059] The moving average GRU introduces the moving average on the basis of the classical GRU to obtain the final node embedding vector, and is calculated using formula (11):

[0060]

[0061] where, is the retention rate, which is used to balance between the current node embedding and the historical node state.

[0062] Step 2 - 5: Dynamically balance the influence weights of the current node embedding and the historical node state through the adaptive retention rate, where the decaying retention rate and the Sigmoid retention rate are used.

[0063] (1) The decaying retention rate characterizes the forgetting feature in dynamic network learning by applying exponential decay to the historical node state, so as to adaptively adjust its influence, and is calculated using formulas (12) and (13):

[0064]

[0065] where, represents the in - degree of node v at time step t, λ is the decay factor. Δt v represents the time interval between the current time step and the time step when the in - degree of the node was zero last time, and ∈ is a very small constant used to avoid division - by - zero errors.

[0066] (2) The Sigmoid retention rate adaptively adjusts the relationship between the node embedding and the time step using the smoothness of the Sigmoid function, and is calculated using formulas (14) and (15):

[0067]

[0068] Step 2 - 6: Integrate the node embeddings of the dynamic network and the static network through the network integration step:[[]]

[0069] (1) At time step t, represents the complete set of nodes of the dynamic network Vd Remove the current graph snapshot node set from the remaining nodes outside. The corresponding node features are used for the fusion of embeddings, while the corresponding node features are temporarily retained.

[0070] (2) Use the multi-head attention mechanism to balance the information weights of different layers, and calculate using formula (16):

[0071]

[0072] where K represents the number of attention heads, represents the embedding vector of node v at time step t. represents the attention coefficient of layer r in the K-th attention head, and is calculated using formula (17):

[0073]

[0074] where, is the query vector in the k-th attention head of network layer r at time step t.

[0075] Then use the generalization module to perform post-processing to improve the robustness of the fused embedding. The calculation process is shown in formula (18),

[0076]

[0077] (3) Concatenate the transformed node embedding matrix (each row of the matrix corresponds to the transpose of the transformed feature vector of node v ) with the retained embedding to obtain the full node embedding matrix. The specific process is shown in formula (19):

[0078]

[0079] where [·; ·] represents the row concatenation operation of two matrices.

[0080] (4) Finally, use the generalization module to perform post-processing on H t to improve the overall linear and non-linear transformation capabilities of the node embedding matrix. The calculation process is shown in formula (20):

[0081]

[0082] Step 2-7: Predict the possibility of an edge connection from source node u to target node v through a two-layer MLP decoder, and calculate using formulas (21) and (22):

[0083]

[0084] Among them, represents the probability of the existence of the directed edge (u, v), and the superscripts (1) and (2) represent the MLP levels where the weight matrix and the bias vector are located, respectively.

[0085] Step 2 - 8: Optimize the model performance through the ROLAND evaluation system and training strategy [2] Optimize the model performance:

[0086] (1) At each time step t, first collect the current link prediction results and divide them into a training set and a validation set Subsequently, according to fine - tune the model and evaluate the performance on the validation set to determine whether to stop training early. After obtaining the edge labels at time step t + 1, the model is based on the historical node states dynamic graph snapshots and static layer sub - graphs to perform link prediction and report the best performance. Finally, calculate the average value of the evaluation metrics at all time steps as the overall performance.

[0087] (2) During the training process, adopt an incremental learning strategy, only store the current dynamic graph snapshots and historical node states, and regard the link prediction task at each time step as an independent task. On the basis of the original ROLAND training strategy, introduce the static layer sub - graph into the model input, and use the binary cross - entropy loss function to measure the difference between the prediction result and the true label, which is calculated by formula (23):

[0088]

[0089] where, N p is the total number of samples. At time step t, is the true label of the i - th sample, is the predicted probability of the i - th sample.

[0090] Based on four publicly available original datasets, the present invention constructs six static - dynamic double - layer networks as experimental datasets and evaluates them using the proposed algorithm. The datasets used mainly include two categories: one is a multi - layer network that simultaneously contains a static layer and a dynamic layer, such as the Higgs Twitter dataset [3]In this dataset, network nodes represent user IDs and include four types of network relationships. We select the friend relationship layer as the static layer and pair it with three dynamic interaction relationships - Reply, Mention, and Retweet respectively to construct three static-dynamic bilayer networks. Another type is the single-layer network dataset that only contains dynamic evolution relationships, including UCI [4] , PlatformAlpha [5] , and PlatformOTC [6] . Among them, the UCI dataset comes from an online social platform of the University of California, where nodes represent user IDs and edges represent private messages sent between users; PlatformAlpha and PlatformOTC record the trust score relationships between users on two trading platforms respectively. To construct the static-dynamic bilayer network, we merge the first half of the graph snapshots of each dataset into a static graph and then pair it with the second half of the dynamic graph snapshots to form a bilayer network structure. For unweighted graphs, the static layer edge set is the union of edges at all time steps; for weighted graphs, the weights of the same edges at different time steps are averaged as the weights of the static layer edges. The details of the datasets are shown in Table 1 (where S represents the static layer and D represents the dynamic layer):

[0091] Table 1

[0092]

[0093] The present invention uses the AUC metric to measure the effectiveness of the algorithm of the present invention. The calculation formula of the AUC metric is as follows:

[0094]

[0095] where N p and N n are the numbers of positive and negative samples respectively, represents the predicted value of the i-th positive sample, represents the predicted value of the j-th negative sample, and I(·) represents the indicator function.

[0096] In the experiment, the algorithm of the present invention was compared with several advanced link prediction methods. The comparison methods include a baseline method without adding static layer features and a baseline method with static layer features (node in-degree, node out-degree, PageRank score, and clustering coefficient) added. The results are shown in Table 2:

[0097] Table 2

[0098]

[0099]

[0100] In terms of the AUC metric, the method of the present invention has an average improvement of 17.36% compared to the baseline method without introducing static layer features, and also an improvement of 8.44% compared to the baseline method with static features introduced. Although methods such as TGCN, EvolveGCN, and ROLAND perform excellently on some datasets, they highly rely on complex feature engineering, which increases the difficulty of model design and affects the generalization ability. In contrast, the method of the present invention does not require additional feature engineering and can end-to-end fuse static and dynamic features, achieving excellent prediction results.

[0101] References

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[0103] [2] You J, Du T, Leskovec J. ROLAND: graph learning framework for dynamicgraphs[C] / / Proceedings of the 28th ACM SIGKDD conference on knowledgediscovery and data mining. 2022: 2358 - 2366.

[0104] [3] De Domenico M, Lima A, Mougel P, et al. The anatomy of a scientificrumor[J]. Scientific reports, 2013, 3(1): 2980.

[0105] [4] PANZARA S A, OPSAHL T, CARLEY K M. Patterns and dynamics of users’behavior and interaction: Network analysis of an online community[J]. Journalof the American Society for Information Science and Technology, 2009, 60(5): 911 - 932.

[0106] [5] KUMAR S, SPEZZANO F, SUBRAHMANIAN V, et al. Edge weight prediction in weighted signed networks[C] / / Proceedings of the 2016 IEEE 16th International Conference on Data Mining(ICDM). IEEE, 2016: 221 - 230.

[0107] [6] KUMAR S, HOOI B, MAKHIJAD, et al. Rev2: Fraudulent user prediction in rating platforms[C] / / Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining. 2018: 333 - 341.

[0108] [7] SEO Y, DEFFERRARD M, VANDERGHEYNST P, et al. Structured sequence modeling with graph convolutional recurrent networks[C] / / Neural Information Processing: 25th International Conference, ICONIP 2018, Siem Reap, Cambodia, December 13 - 16, 2018, Proceedings, Part I. Springer, 2018: 362 - 373.

[0109] [8] ZHAO L, SONG Y, ZHANG C, et al. T - GCN: A temporal graph convolutional network for traffic prediction[J]. IEEE Transactions on Intelligent Transportation Systems, 2019, 21(9): 3848 - 3858.

[0110] [9]PAREJAA, DOMENICONI G, CHEN J, et al. Evolvegcn: Evolving graph convolutional networks for dynamic graphs[C] / / Proceedings of the AAAI Conference on Artificial Intelligence. 2020:5363-5370。

Claims

1. A method for predicting dynamic network links assisted by a static network, characterized in that, The specific steps are as follows: Step 1: Perform data preprocessing on the static-dynamic bilayer network, specifically including: Step 1-1: According to the node set of the dynamic layer graph snapshots, perform independent subgraph extraction operations on the static layer at each time step, thereby constructing a bilayer graph sequence; Step 1-2: Initialize the node features of each layer of the bilayer network; Step 1-3: Initialize the edge features of the unweighted network and the weighted network in a targeted manner, and normalize the timestamps of the edges in the dynamic layer within each time slice, thereby endowing the edges with different temporal features; Step 2: Use the Network Fusion Edge Convolution (NF-EdgeConv) model for link prediction; the Network Fusion Edge Convolution model includes: (1) Static layer encoder: used to perform preliminary mapping on the node and edge features in the static layer subgraph at time step t; (2) Dynamic layer encoder: used to perform preliminary mapping on the node and edge features in the dynamic graph snapshot at time step t; (3) Static layer convolution module: perform convolution processing on the output of the static layer encoder, specifically including L s convolution layers, and in each convolution layer, edge convolution, batch normalization (BN), and PReLU activation function are integrated in sequence; (4) Dynamic layer convolution module: perform convolution processing on the output of the dynamic layer encoder, specifically including L d convolution layers, and in each convolution layer, edge convolution, batch normalization, PReLU activation function, and moving average GRU update module are integrated in sequence, where the update module is used to update the node state in real time; (5) Network fusion module: fuse the node representations of the static layer and the dynamic layer, and it consists of two sub-modules internally; one is the attention mechanism module, including the integrated multi-head attention mechanism, batch normalization, and PReLU activation function, and the other is the generalization module, which is composed of a fully connected layer, batch normalization, and PReLU activation function; (6) Two-layer multi-layer perceptron (MLP) decoder: achieve the final link prediction task through the two-layer MLP decoder; the specific steps for link prediction are as follows: Step 2-1: Encode the initial node features and initial edge features; Step 2-2: Learn the node embeddings of each layer in the bilayer network through an edge convolutional network with residual connections; Step 2-3: At each time step, save the node embeddings after each convolutional layer of the dynamic network when the model performs best on the validation set, and use these embeddings as the hierarchical node states at the current moment; "the model performs best on the validation set" means that during the training process at each time step, the loss on the validation set is the lowest; when the validation loss is less than the historical minimum, the model will update the parameters and save the current model state; Step 2-4: Add a moving average GRU update module after each convolutional layer of the dynamic network to update the node states in real time; Step 2-5: Dynamically balance the influence weights of the current node embeddings and historical node states through an adaptive retention rate, where two adaptive retention rates are used: the decay retention rate and the Sigmoid retention rate; Step 2-6: Through the multi-head attention mechanism, effectively combine the node embeddings of the dynamic layer and the static layer, thereby enhancing the node representation of the dynamic layer; Step 2-7: Predict the possibility of an edge connection from the source node to the target node through a two-layer multi-layer perceptron (MLP) decoder; Step 2-8: Optimize the model performance through the ROLAND evaluation system and training strategy. During the training process, use the binary cross-entropy (BCE) loss function to continuously improve the model performance.

2. The method for link prediction of the dynamic network according to claim 1, wherein The data preprocessing of the static-dynamic bilayer network described in Step 1 has the following specific process: The known static-dynamic two-layer network contains two layers: R = {s, d}, where s represents the static layer and d represents the dynamic layer, and r ∈ R represents any layer in the two-layer network; the static-dynamic two-layer network is represented as a set of a static graph and a series of dynamic graph snapshots The static graph is represented as G s ={V s , E s , X s , F s}, where V s represents the static graph node set, E s represents the static graph edge set, X s represents the node feature matrix of the static layer, F s represents the edge feature matrix of the static layer; The dynamic graph snapshot sequence is represented as The graph snapshot at time step t is represented as where represents the node set of the graph snapshot, represents the edge set of the graph snapshot, represents the node feature matrix of the graph snapshot, represents the edge feature matrix of the graph snapshot; in addition, the node set V of the dynamic graph d is defined as the union of the node sets in all graph snapshots The steps of preprocessing are as follows: Step 1-1: According to the node set of the snapshot in time step t generate the node set of the subgraph of the static layer and make the generated node set satisfy both and Extract the corresponding edge set in the static graph G According to the node set and make the extracted edge set satisfy s Extract the corresponding edge set and make the extracted edge set satisfy Construct the subgraph of the static layer corresponding to time step t through the node set and the edge set Finally, construct the graph sequence of the static layer according to the subgraphs at all time steps Step 1-2: Initialize the node features of each layer in the double-layer network: |V d | represents the total number of nodes in the dynamic network; Step 1-3: Initialize the edge features of the unweighted network or the weighted network. At the same time, divide the graph snapshots according to the timestamps, and use the normalized timestamps to represent the temporal order of the edges within each time step, thereby generating different initial edge features: (1) For a non-authoritative network, set the edge features of the static layer at the initial moment as follows: The edge features of the dynamic layer are obtained by normalizing the timestamps: where t d represents the timestamp vector, z(·) represents the normalization operation, and δ1 and δ2 represent the lower and upper bounds of the normalization result respectively; (2) For the weighted network, the edge features of the static layer are set at the initial moment as follows: The feature of each edge is equal to the edge weight, and the edge features of the dynamic layer are generated by concatenating the edge weight with the normalized timestamp vector: where [·|·] is the column concatenation symbol, denotes the number of edges in the graph snapshot of the dynamic layer at time step t.

3. The method for link prediction in the dynamic network according to claim 2, wherein The specific process of using the network fusion edge convolution (NF-EdgeConv) model for link prediction described in Step 2 is as follows: Step 2-1: Encode the initial node features: where W x represents the linear transformation matrix; post-process the encoded node features: where σ1(·) represents the PReLU activation function and is calculated using formula (1): σ1(x) = max(0, x) + αmin(0, x), (1) where α is a learnable parameter; B(·) represents the batch normalization operation, which is calculated by formula (2): Among them, and β are trainable parameters, ∈ is a small constant used to avoid division-by-zero errors, μ(·) represents the mean, and (σ(·)) 2 represents the variance; Encode the edge features at the initial moment: And post-process the encoded edge features: Where W f is a linear transformation matrix; Step 2-2: Learn the network topology representation from each layer of the network through the EdgeConv network, specifically including two links: message passing and aggregation: (1) For a single convolutional layer l, the message passing process from node u to node v is shown in formula (3): Among them, represents the message passing from node u to node v in convolutional layer l, represents the feature vector of node v in the previous convolutional layer (l-1), represents the feature vector of edge (u, v), is the weight matrix, represents the bias vector; (2) Integrate the information of neighbor nodes through the summation aggregation operation, and the message aggregation process is shown in formula (4): Among them, represents the set of neighbor nodes of node v, represents the residual representation vector from layer (l - 1), represents the weight matrix, represents the bias vector; Finally, the node embedding matrix after passing through the l-th convolutional layer is represented as Step 2-3: At each time step, save the node embeddings after each convolutional layer of the dynamic network when the model performs best on the validation set, and use these embeddings as the hierarchical node states at the current moment: where L d represents the number of convolutional layers of the dynamic layer; "the model performs best on the validation set" means that during the training process at each time step, the loss on the validation set is the lowest; when the validation loss is less than the historical minimum, the model updates its parameters and saves the current model state; Step 2-4: Add a moving average GRU update module after each convolutional layer of the dynamic network to update the node state in real time; First, the calculation process of the classical GRU is shown in Formulas (5)-(8): Among them, the candidate state is jointly determined by the current input and the weighted hidden state of the previous time step, controlling the influence degree of the previous hidden state on the candidate state; the final hidden state is controlled by and determines the weighted ratio between the current candidate state and the hidden state of the previous time step ; W z , W r and W h represent the weight matrices of the gates, U z , U r and U h represent the weight matrices of the hidden states, b z , b r and b h represent the bias vectors, ⊙ represents the Hadamard product, σ2(·) and σ3(·) represent the Sigmoid activation function and the Tanh activation function respectively, and are calculated using formulas (9) and (10): The moving average GRU introduces a moving average on the basis of the classical GRU to obtain the final node embedding vector, which is calculated by Formula (11): Among them, is the retention rate, which is used to balance between the current node embedding and the historical node state; Step 2-5: Dynamically balance the influence weights of the current node embedding and the historical node state through an adaptive retention rate, where the decay retention rate and the Sigmoid retention rate are used; (1) Decay retention rate, which applies exponential decay to the historical node state to characterize the forgetting characteristics in the learning of the dynamic network, thereby adaptively adjusting its influence, and is calculated by Formulas (12) and (13): Among them, represents the in-degree of node v at time step t, and λ is the decay factor; Δt v represents the time interval between the current time step and the time step when the in-degree of the node was zero last time. ∈ is an extremely small constant used to avoid division-by-zero errors; (2) Sigmoid retention rate, which adaptively adjusts the relationship between the node embedding and the time step by using the smoothness of the Sigmoid function, and is calculated by Formulas (14) and (15): Step 2-6: Fuse the node embeddings of the dynamic network and the static network through a network fusion module: (1) At time step t, represents the complete set of dynamic network nodes V d after removing the current graph snapshot node set from the remaining nodes; The corresponding node features are used for the fusion of embeddings, and the corresponding node features are temporarily retained; (2) Adopt a multi-head attention mechanism to balance the information weights of different layers, and calculate by Formula (16): where K represents the number of attention heads, represents the embedding vector of node v at time step t, represents the attention coefficient of the r-th layer of the K-th attention head, calculated by formula (17): where, is the query vector in the k-th attention head of network layer r at time step t; Then, use the generalization module to perform post-processing to enhance the robustness of the fused embedding. The calculation process is shown in Equation (18). (3) Embed the transformed nodes into a matrix with the retained embeddings to perform row concatenation to obtain the full node embedding matrix. The specific process is shown in Equation (19): Among them, [·;·] represents the row concatenation operation of two matrices; (4)Finally, use the generalization module to process H t for post-processing to enhance the overall linear and non-linear transformation capabilities of the node embedding matrix. The calculation process is shown in Equation (20): Step 2-7: Predict the possibility of an edge connection from the source node u to the target node v through a two-layer MLP decoder, and calculate by Formulas (21) and (22): Among them, represents the probability of the existence of the directed edge (u, v), and the superscripts (1) and (2) are the MLP levels where the weight matrix and the bias vector are located, respectively; Step 2-8: Optimize the model performance through the ROLAND evaluation system and training strategy: (1) At each time step t, first collect the current link prediction results and divide them into a training set and a validation set According to fine-tune the model and evaluate the performance on the validation set to determine whether to stop training early; after obtaining the edge labels at time step t+1, the model is based on the historical node states dynamic graph snapshots and static layer subgraphs for link prediction and report the best performance; finally, calculate the average value of the evaluation metrics at all time steps as the overall performance; (2) During the training process, an incremental learning strategy is adopted, only storing the current dynamic graph snapshot and historical node states, while treating the link prediction task at each time step as an independent task; on the basis of the original ROLAND training strategy, the static layer subgraph is introduced into the model input, and the binary cross-entropy loss function is used to measure the difference between the prediction result and the true label, which is calculated by formula (23): Among them, N p is the total number of samples. At time step t, is the true label of the i-th sample, is the predicted probability of the i-th sample.

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