A method for predicting social network links using incremental strategy

Abstract

This paper discloses a method for predicting social network links using an incremental strategy. The method first processes network data, slices the network, and obtains a sequence of network snapshots. Secondly, the network is layered, and random walks are performed within the slices in the direction of time to obtain a node sequence. Thirdly, a sliding window is moved, and the node sequence is updated according to the incremental strategy. This node sequence is then input into an incremental skip-gram model to update the node embedding vectors of each layer. Finally, a projection matrix is ​​used to project nodes from different layers into the same space. The node embedding vectors of the different layers are fused using an autonomous mechanism, and R dynamically scalable networks are designed as decoders. This method solves the problem that existing technologies, when faced with new data, discard previously trained data, resulting in a significant amount of time spent completely retraining model parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of link prediction, and in particular to a method for predicting social network links using an incremental strategy. Background Art

[0002] Real-world systems are filled with vast amounts of complex information. To extract the information contained in these systems, we can abstract each entity in the system into nodes and the relationships between them into edges. This allows us to abstract the entire system into a complete network, such as a social network, a biological network, or a transportation network.

[0003] A social network is generally a complex network composed of people (nodes) and relationships between them (edges), which can be naturally represented using a graph. Currently, most social networks have multiple relationships between people, resulting in a heterogeneous network. These relationships can be formally categorized into two types: the first type, such as relationships between classmates, friends, or teachers and students in interpersonal communication, are rarely broken once established. The second type, such as interactive relationships between people in forums, occurs instantaneously, representing transient relationships between people. With the widespread adoption of the internet, the number of users of various social apps and forums has skyrocketed, leading to a massive number of network nodes and relationships, and a relatively complex network topology. Uncovering the information contained within these relationships presents a significant challenge for researchers.

[0004] Link prediction, which estimates whether two nodes are likely to connect in the future or predicts unknown connections, is a key research topic in network science. Link prediction methods can also mine semantic information in complex networks and uncover underlying patterns of network evolution, providing a solid foundation for predicting relationships between nodes.

[0005] In real-world networks, new data often contains new objects, such as the constant registration of new users on forums and social networks. Existing link prediction methods discard previously trained data when faced with new data, resulting in a significant amount of time spent completely retraining model parameters. Summary of the Invention

[0006] In response to the above problems, the purpose of the present invention is to propose a method for predicting social network links using an incremental strategy to solve the problem that the existing technology discards previous training data when faced with new data, resulting in a lot of time spent on completely retraining model parameters.

[0007] The technical solution adopted by the present invention is as follows: a method for predicting social network links using an incremental strategy,

[0008] The steps include:

[0009] Step 1: Process the network data and determine the optimal slicing duration by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot. Slice the network according to the optimal slicing duration to obtain a network snapshot.

[0010] Step 2: Divide the network into layers according to different types of edges, perform random walks in the direction of time development, and generate node sequences for each layer;

[0011] Step 3: Update the node sequence according to the incremental strategy and input it into the incremental skip-gram model to update the node embedding vector of each layer;

[0012] Step 4: Use the self-attention mechanism to fuse the embedding vectors of the same node at different layers into the final node representation. Design R dynamically scalable networks as decoders to predict the topology of the network at a preset time in the future, where R is the number of edge types.

[0013] In the above method of predicting social network links using an incremental strategy, in step 1, the network data is processed as follows:

[0014] Map various objects in the original data into nodes, map edge types into integer domain space, convert time information into timestamps, and sort edges in ascending order of timestamps. e represents an edge, which is specifically expressed as:

[0015] e=[vurt] (1)

[0016] Where v and u represent nodes, r represents the type of edge, r = 1, 2, ..., R, and t represents the timestamp;

[0017] In step 1, the optimal slice duration is determined as follows:

[0018] The optimal slice length L is determined by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot T The formula is as follows:

[0019]

[0020] in, is the number of edges generated under snapshot i (i=1,2,…,m), is the number of static edges under snapshot i, and m is the number of slices in the snapshot;

[0021] In step 1, the network is sliced ​​using the optimal slicing duration. When obtaining a network snapshot, a sliding window with a step size of 1 and a size of 5 is set. Four sliding windows are used for random walks to obtain node embedding vectors, and one sliding window is used to build a prediction model.

[0022] In the above method for predicting social network links using an incremental strategy, step 2 specifically includes:

[0023] The network is layered according to different types of edges, so that each layer has only edges of the same type. Each layer randomly walks in the direction of time development. The probability of selecting the next node v in the layer with edge type r is The calculation formula is as follows:

[0024]

[0025] Among them, v, u, u′ are nodes, represents the set of all temporal neighbors of node v in the layer with edge type r, τ r (v,u) represents the timestamps of nodes v and u in the layer to which edge type r belongs;

[0026] The expression is:

[0027]

[0028] Where E is the edge set and t′ is the timestamp;

[0029] τ r The expression of (v,u) is:

[0030] τ r (v,u)={t|(u,v,r,t)∈E} (5)

[0031] Walk according to the above walk strategy to obtain the node sequence;

[0032] In addition, each walk requires an initial node, and the initial node requires an initial timestamp strategy:

[0033]

[0034] in, Indicates that the initial timestamp is the minimum timestamp among the edges connected to the initial node.

[0035] In the above method of predicting social network links using an incremental strategy, in step 3, when the window moves to the next step, the node sequence needs to be updated. 80% of the sequences are updated each time, and historical information can be retained to a certain extent. The probability Pr that the i-th sequence is selected to be updated is i The calculation formula is as follows:

[0036]

[0037] Where k represents the total number of sequences, η i The calculation formula is as follows:

[0038]

[0039] in, represents the end timestamp of the i-th sequence, Indicates the end time of the current window. Indicates the minimum end timestamp of all sequences;

[0040] The selected sequence needs to be updated in the original sequence. The updated sequence meets the following three conditions: ① Completely expired sequences need to discard the previous sequence and re-route in the current time window; ② Sequences that are not completely expired need to delete the expired part and continue to move forward; ③ New nodes need to be used as starting points to generate node sequences. The updated sequence is used as the input of the incremental skip-gram model to update the node embedding vector. The loss function of the incremental skip-gram model is as follows:

[0041]

[0042] Where N represents the number of nodes in all sequences (including repeated nodes), l i represents the node embedding vector (center node) at position i (i=1,2,…,N) in the sequence, l′ i+j represents the node embedding vector (background node) at the i+jth position, j (j = -c, ..., c and j ≠ 0) represents the offset position relative to i (i = 1, 2, ..., N), c represents the range of the offset, Τ represents the vector transpose operation, w represents the negative sample, y is the number of negative samples required each time, σ(x) is the sigmoid function, q(w) represents the noise distribution, and obeys q(w) ∝ f(w) β , f(w) represents the frequency of occurrence of all nodes, β∈(0,1) is a smoothing parameter, according to experience β=3 / 4, E represents the expectation.

[0043] In the above method of predicting social network links using an incremental strategy, in step 4, the nodes of different layers are projected into the same space through the projection matrix. The embedding vector of the projected node v in the layer of edge type r is expressed as The calculation formula is as follows:

[0044]

[0045] Among them, W r Represents the projection matrix of the layer to which edge type r belongs, Represents the node embedding vector of the layer to which edge type r belongs;

[0046] Use the self-attention mechanism to fuse the representations of different nodes at different layers into the final node representation, and calculate the attention factor of node v in the layer to which edge type r belongs. The formula is as follows:

[0047]

[0048] Where T represents the vector transpose operation, q is the weight vector for calculating attention, and the node embedding vectors of node v at different layers are fused by the attention factor to obtain the final embedding vector z of node v. v , the calculation formula is:

[0049]

[0050] R dynamic scalable networks are designed as decoders to predict the topology of the entire network at a preset time in the future. The loss function J is:

[0051]

[0052] in, represents the output of each node embedding vector after passing through the rth (r=1,2,…,R)th decoder in the κth time period, represents the adjacency matrix of the rth (r=1,2,…,R) relationship (edge ​​type) network in the κth time period, represents the L2 regularization of r (r = 1, 2, ..., R) decoder parameters to prevent overfitting of the prediction model, and ρ represents the regularization parameter.

[0053] According to the method for predicting social network links using an incremental strategy provided by the present invention, first, the network data is processed and the network is sliced ​​to obtain a network snapshot sequence; second, the network is layered, and a random walk is performed within the slice in the direction of time development to obtain a node sequence; third, the sliding window moves, and the node sequence is updated according to the incremental strategy, and input into the incremental skip-gram to update the node embedding vector of each layer; finally, the nodes of different layers are projected into the same space using a projection matrix, and the node embedding vectors of different layers are fused using an autonomous mechanism. By designing R (R is the number of edge types) dynamically scalable networks as decoders, it is used to predict the entire network for a period of time in the future. The present invention uses an incremental strategy to update the node sequence, takes into account the different contributions of different layers, uses the self-attention mechanism to fuse the node embedding vectors, and designs an extensible dynamic decoder to achieve incremental network link prediction, so that the model can continuously learn new knowledge without completely retraining the model, so as to achieve faster training time and more accurate network link prediction. The present invention responds to new data by using an incremental strategy, can continuously learn new knowledge from new samples, and can preserve most of the previously learned knowledge for predicting network connectivity in a certain time period in the future. It is not necessary to completely retrain the model, but quickly learn new knowledge, so that the model converges quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of window sliding;

[0055] Figure 2 It is a schematic diagram of network layering;

[0056] Figure 3 It is a schematic diagram of the node embedding model;

[0057] Figure 4 It is a schematic diagram of the prediction model;

[0058] Figure 5 It is a schematic diagram of a dynamically scalable network decoder. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0060] In this embodiment, the forum question-answering social network is defined as G = (V, E), where V is the node set and E is the edge set. After determining the slice length, the network is divided into a series of network snapshots G = {G1, G2, ..., G n-1 ,G n}, where G i Represents the network topology graph of the i-th time period, where the duration of the time period is the slice duration.

[0061] After determining the window size, the present invention uses the first x-1 slices in the sliding window to obtain the node walk sequence and generate the node embedding vector. The xth slice is used to train the prediction model. Similarly, the sliding window moves forward one step, incrementally updates the node walk sequence and embedding vector, and updates the prediction model until it moves to the end of the network. Figure 1 Assuming x is 3, G1 and G2 are used to obtain the node walk sequence and node embedding vectors, and G3 is used to train the pre-model. After the sliding window slides forward one step, G2 and G3 incrementally update the node walk sequence and incrementally update the node embedding vectors. G4 is used to train the pre-model, and so on until the last update of the node embedding vector. The last slice is used to evaluate the performance of the prediction model.

[0062] Based on the above, an embodiment of the present invention provides a method for predicting social network links using an incremental strategy, including the following steps:

[0063] Step 1: Process the network data and determine the optimal slicing duration by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot. Slice the network according to the optimal slicing duration to obtain a network snapshot.

[0064] Step 2: Divide the network into layers according to different types of edges, perform random walks in the direction of time development, and generate node sequences for each layer;

[0065] Step 3: Update the node sequence according to the incremental strategy and input it into the incremental skip-gram model to update the node embedding vector of each layer;

[0066] Step 4: Use the self-attention mechanism to fuse the embedding vectors of the same node at different layers into the final node representation. Design R dynamically scalable networks as decoders to predict the topology of the network at a preset time in the future, where R is the number of edge types.

[0067] The details of step 1 data processing and determining the slicing time are as follows:

[0068] Map various objects in the original data into nodes, map edge types into integer domain space, convert time information into timestamps, and sort edges in ascending order of timestamps. e represents the edge, which can be expressed as:

[0069] e=[vurt] (1)

[0070] Where v and u represent nodes, r (r = 1, 2, ..., R) represents the type of edge, and t represents the timestamp;

[0071] In specific implementation, all times can be converted into timestamps in seconds. For example, 1 day, 2 hours, 10 minutes, and 10 seconds can be converted into the timestamp 4210.

[0072] In step 1, determine the slice duration as follows:

[0073] The optimal (minimum slice edge loss) slice duration L is determined by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot. T The formula is as follows:

[0074]

[0075] Among them, L T Indicates the loss of slice duration when the slice duration is T. is the number of edges generated under snapshot i (i=1,2,…,m), is the number of static edges under snapshot i (i=1,2,…,m), m is the number of slices in the snapshot;

[0076] In step 1, the network is sliced ​​by this duration to obtain a series of network snapshots. A sliding window with a step size of 1 and a size of 5 is set. Four slices are used for random walks to obtain node embedding vectors, and one slice is used to build the prediction model.

[0077] Step 2 specifically includes:

[0078] The network is layered according to different types of edges, so that each layer has only the same type of edges, and each layer randomly walks in the direction of time development, that is, the timestamp of reaching the next node cannot be less than the current timestamp. The smaller the timestamp interval of reaching the next node, the greater the probability of being selected. The probability of selecting the next node v in the layer with edge type r (r = 1, 2, ..., R) is The calculation formula is as follows:

[0079]

[0080] in, represents the set of all temporal neighbors of node v in the layer with edge type r (r = 1, 2, ..., R), which can be expressed as:

[0081]

[0082] Where v and u are nodes, and E is the edge set;

[0083] In step 2, τ r (v,u) represents the timestamps of nodes v and u in the layer with edge type r (r=1,2,…,R), which can be expressed as:

[0084] τ r (v,u)={t|(u,v,r,t)∈E} (5)

[0085] By walking according to the above walking strategy, a walking sequence can be obtained;

[0086] When implementing it specifically, Figure 2 , the network has three types of edges, and the network is divided into three networks by edge type. Each network contains only one edge type. t1~t21 represent timestamps, and are sorted in non-decreasing order according to timestamps. Among them, starting from U1 node as the starting node, the three walk sequences generated in each layer can be {U1, U2, U7}, {U1, U3, U5, U6, U3} and {U2, U1, U3, U5};

[0087] In step 2, each walk requires an initial node. However, only edges have timestamps, so the initial node requires an initial timestamp strategy:

[0088]

[0089] The above formula indicates that the initial timestamp is the minimum timestamp among the edges connected to the initial node.

[0090] Step three specifically includes:

[0091] When the window moves to the next step, the node sequence needs to be updated. 80% of the sequences are updated each time, and historical information can be retained to a certain extent. The probability Pr of the i-th (i=1,2,…,k) sequence being selected to be updated is i The calculation formula is as follows:

[0092]

[0093] Where k represents the total number of sequences, η i The calculation formula is as follows:

[0094]

[0095] in, represents the end timestamp of the i-th (i=1,2,…,k) sequence, Indicates the end time of the current window. Indicates the minimum end timestamp of all sequences;

[0096] In step three, based on the idea of ​​incremental learning, the selected sequence needs to be updated in the original sequence. The following three situations need to be considered when updating the sequence: ① Completely expired sequences need to abandon the previous sequence and re-route in the current time window. ② Sequences that are not completely expired delete the expired part and continue to move forward. ③ New nodes need to be used as starting points to generate a wandering sequence. The updated sequence is used as the input of the incremental skip-gram model to update the node embedding vector. The loss function of the incremental skip-gram model is as follows:

[0097]

[0098] Where N represents the number of nodes in all sequences (including repeated nodes), l i represents the node embedding vector (center node) at position i (i=1,2,…,N) in the sequence, l′ i+j represents the node embedding vector (background node) at the i+jth position, j (j = -c, ..., c and j ≠ 0) represents the offset position relative to i (i = 1, 2, ..., N), c represents the range of the offset, Τ represents the vector transpose operation, w represents the negative sample, y is the number of negative samples required each time, σ(x) is the sigmoid function, q(w) represents the noise distribution, and obeys q(w) ∝ f(w) β , f(w) represents the frequency of occurrence of all nodes, β∈(0,1) is a smoothing parameter, according to experience β=3 / 4, E represents the expectation;

[0099] When implementing it specifically, Figure 3 This is a schematic diagram of the node embedding model. t to t+x means that the sliding window has moved t steps. x represents the size of the sliding window. It will move in these x-1 slices. The xth slice is used to train the prediction model.

[0100] Step 4 specifically includes:

[0101] It is necessary to embed and project nodes of different layers into the same space. The projection matrix is ​​used to project nodes of different layers into the same space. The embedding vector of the projected node v in the layer with edge type r (r = 1, 2, ..., R) is expressed as The calculation formula is as follows:

[0102]

[0103] Among them, W r Represents the projection matrix of the layer to which edge type r (r = 1, 2, ..., R) belongs, Represents the node embedding vector of the layer with edge type r (r=1,2,…,R);

[0104] In step 4, the self-attention mechanism is used to fuse the representations of different nodes at different layers into the final node representation, and the attention factor of node v in the layer with edge type r (r = 1, 2, ..., R) is calculated. The formula is as follows:

[0105]

[0106] Where T represents the vector transpose operation, q is the weight vector for calculating attention, and the node embedding vectors of node v at different layers are fused by the attention factor to obtain the final embedding vector z of node v. v , the calculation formula is:

[0107]

[0108] In step 4, R (R is the number of edge types) dynamically scalable networks are designed as decoders to predict the topology of the entire network in the future. The loss function is:

[0109]

[0110] in, represents the output of each node embedding vector after passing through the rth (r=1,2,…,R)th decoder in the κth time period, represents the adjacency matrix of the rth (r=1,2,…,R) relationship (edge ​​type) network in the κth time period, represents the L2 regularization of r (r = 1, 2, ..., R) decoder parameters to prevent overfitting of the prediction model, and ρ represents the regularization parameter.

[0111] When implementing it specifically, Figure 4 This is a schematic diagram of the prediction model. After the model training is completed, the node embedding vector is input and the entire network situation can be obtained through decoders of different relationships.

[0112] In specific implementation, since new nodes will be added in each time period, the adjacency matrix of the network will also be expanded, so the decoder needs to be dynamically expanded in each time period, such as Figure 5 As shown in the figure, in order to speed up the network training, the decoder weight parameters of the previous time period (solid line part) are used as the initialization of the decoder parameters of the current time period, and the weight parameters of the dynamically expanded new neuron connections (dashed line part) are initialized using random Gaussian distribution.

[0113] According to the above-mentioned method of using incremental strategy to predict social network links, firstly, the network data is processed and the network is sliced ​​to obtain a network snapshot sequence; secondly, the network is layered and randomly walked in the slice in the direction of time development to obtain a node sequence; thirdly, the sliding window moves and the node sequence is updated according to the incremental strategy, and input into the incremental skip-gram to update the node embedding vector of each layer; finally, the projection matrix is ​​used to project the nodes of different layers into the same space, and the autonomous mechanism is used to fuse the node embedding vectors of different layers. By designing R (R is the number of edge types) dynamically scalable networks as decoders, it is used to predict the topology of the entire network in the future. In order to solve the problem of network connection failure, the present invention uses an incremental strategy to update the node sequence, takes into account the different contributions of different layers, uses the self-attention mechanism to fuse the node embedding vectors, and designs an extensible dynamic decoder to realize incremental network link prediction, so that the model can continuously learn new knowledge without completely retraining the model, so as to achieve faster training time and more accurate network link prediction. The present invention responds to new data by using an incremental strategy, can continuously learn new knowledge from new samples, and can preserve most of the previously learned knowledge for predicting network connection status in a certain time period in the future. It is not necessary to completely retrain the model, but quickly learn new knowledge, so that the model converges quickly.

[0114] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0115] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for predicting social network links using an incremental strategy, characterized in that: The steps include: Step 1: Process the network data and determine the optimal slicing duration by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot. Slice the network according to the optimal slicing duration to obtain a network snapshot. Step 2: Divide the network into layers according to different types of edges, perform random walks in the direction of time development, and generate node sequences for each layer; Step 3: Update the node sequence according to the incremental strategy and input it into the incremental skip-gram model to update the node embedding vector of each layer; Step 4: Use the self-attention mechanism to fuse the embedding vectors of the same node at different layers into the final node representation. Design R dynamically scalable networks as decoders to predict the topology of the network at the preset time in the future, where R is the number of edge types. In step 3, when the window moves to the next step, the node sequence needs to be updated. 80% of the sequences are updated each time, and historical information can be retained to a certain extent. The probability Pr that the i-th sequence is selected to be updated is i The calculation formula is as follows: Where k represents the total number of sequences, η i The calculation formula is as follows: in, represents the end timestamp of the i-th sequence, Indicates the end time of the current window. Indicates the minimum end timestamp of all sequences; The selected sequence needs to be updated in the original sequence. The updated sequence meets the following three conditions: ① Completely expired sequences need to discard the previous sequence and re-route in the current time window; ② Sequences that are not completely expired need to delete the expired part and continue to move forward; ③ New nodes need to be used as starting points to generate node sequences. The updated sequence is used as the input of the incremental skip-gram model to update the node embedding vector. The loss function of the incremental skip-gram model is as follows: Among them, N represents the number of nodes in all sequences, l i Represents the node embedding vector of the i-th position in the sequence, l′ i+j represents the node embedding vector at position i+j, j represents the offset position relative to i, j=-c,…,c and j≠0, c represents the range of the offset, Τ represents the vector transpose operation, w represents the negative sample, y is the number of negative samples required each time, σ(x) is the sigmoid function, q(w) represents the noise distribution, and obeys q(w)∝f(w) β , f(w) represents the frequency of occurrence of all nodes, β∈(0,1) is a smoothing parameter, and E represents the expectation.

2. The method for predicting social network links using an incremental strategy according to claim 1, characterized in that: In step 1, network data processing is as follows: Map various objects in the original data into nodes, map edge types into integer domain space, convert time information into timestamps, and sort edges in ascending order of timestamps. e represents an edge, which is specifically expressed as: e=[vurt] (1) Where v and u represent nodes, r represents the type of edge, r = 1, 2, ..., R, and t represents the timestamp; In step 1, the optimal slice duration is determined as follows: The optimal slice length L is determined by calculating the average of the ratio of the number of lost edges to the total number of edges in the time snapshot T The formula is as follows: in, is the number of edges generated under snapshot i, is the number of static edges under snapshot i, and m is the number of slices in the snapshot; In step 1, the network is sliced ​​using the optimal slicing duration. When obtaining a network snapshot, a sliding window with a step size of 1 and a size of 5 is set. Four sliding windows are used for random walks to obtain node embedding vectors, and one sliding window is used to build a prediction model.

3. The method for predicting social network links using an incremental strategy according to claim 1, characterized in that: Step 2 specifically includes: The network is layered according to different types of edges, so that each layer has only edges of the same type. Each layer randomly walks in the direction of time development. The probability of selecting the next node v in the layer with edge type r is The calculation formula is as follows: Among them, v, u, u′ are nodes, represents the set of all temporal neighbors of node v in the layer with edge type r, τ r (v,u) represents the timestamps of nodes v and u in the layer to which edge type r belongs; The expression is: Where E is the edge set and t′ is the timestamp; τ r The expression of (v,u) is: τ r (v,u)={t|(u,v,r,t)∈E} (5) Obtain the node sequence according to the above random walk; In addition, each walk requires an initial node, and the initial node requires an initial timestamp strategy: in, Indicates that the initial timestamp is the minimum timestamp among the edges connected to the initial node.

4. The method for predicting social network links using an incremental strategy according to claim 1, characterized in that: In step 4, the nodes of different layers are projected into the same space through the projection matrix. The embedding vector of the projected node v in the layer of edge type r is expressed as The calculation formula is as follows: Among them, W r Represents the projection matrix of the layer to which edge type r belongs, Represents the node embedding vector of the layer to which edge type r belongs; Use the self-attention mechanism to fuse the representations of different nodes at different layers into the final node representation, and calculate the attention factor of node v in the layer to which edge type r belongs. The formula is as follows: Where T represents the vector transpose operation, q is the weight vector for calculating attention, and the node embedding vectors of node v at different layers are fused by the attention factor to obtain the final embedding vector z of node v. v , the calculation formula is: R dynamic scalable networks are designed as decoders to predict the topology of the entire network at a preset time in the future. The loss function J is: in, represents the output of each node embedding vector after passing through the rth decoder in the κth time period, represents the adjacency matrix of the r-th relationship network in the κ-th time period, represents the L2 regularization of the r decoder parameters, and ρ represents the regularization parameter.

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