A multi-view dynamic network link prediction method and system based on temporal neighborhood aggregation

Abstract

The application discloses a multi-view dynamic network link prediction method and system based on a time sequence neighborhood aggregation, which comprises the following steps: taking a time sequence dynamic network as input, capturing a time sequence neighborhood of each node, calculating an attention coefficient and a time decay coefficient between neighbors and nodes in the time sequence neighborhood, constructing a time difference attention mechanism, and aggregating the time sequence neighborhood by using multiplication, summation and splicing operations to generate a local view feature as an initial embedding of the node; calculating a node transition probability by using node interaction time to generate a time sequence biased node random walk path; constructing a target function by using a word vector model to fuse the local feature of the network and the node random walk path to generate a node embedding with a multi-view feature; and predicting a link occurred in a future time sequence dynamic network by using a logistic regression method. The application captures and fuses time sequence dynamic network features from a multi-view angle, and has a good link prediction effect.

Description

Technical Field

[0001] The present invention relates to the technical field of temporal dynamic network link prediction, and in particular to a multi-view dynamic network link prediction method and system based on temporal neighborhood aggregation. Background Art

[0002] Network representation learning is a method for mapping node representations in large-scale network data into a low-dimensional vector space. It is a key step in solving link prediction tasks using machine learning and deep learning techniques. In real life, network data often changes over time, and this change is reflected in the increase in links between nodes. This type of constantly changing network data is called a time-series dynamic network.

[0003] Temporal dynamic networks are ubiquitous in real life. These networks continuously evolve as users and interactions between them continue to grow. During this evolutionary process, interactions between users are not formed simultaneously but rather follow the chronological order of their occurrence. In other words, the neighborhood of a node contains temporal information, which we call a temporal neighborhood.

[0004] The temporal neighborhood of a node contains rich network local features, which reflect the characteristics of the node. The local features of the network can be captured from the process of the node and its interaction with its neighbors. Figure 1 (a) The temporal dynamic network of collaborators shows that node 1 has collaborated on papers with nodes 2 and 3 in the field of physics, with nodes 4 and 5 in the field of artificial intelligence, and with node 6 in the field of communications. This indicates that node 1's research covers the three fields of physics, artificial intelligence, and communications. Furthermore, node 1 collaborated with authors in different fields at different times. Its collaboration with scholars in the field of physics began earlier, in 2002, while its collaboration with authors in the fields of artificial intelligence and communications was later, in 2018 and 2020. This suggests that node 1's research has gradually shifted from physics to artificial intelligence and communications, with its current research focus remaining in these two areas. As the collaborative network expands, node 1 is more likely to collaborate with scholars in the fields of artificial intelligence and communications.

[0005] In addition, in addition to influencing each other with neighboring nodes in the temporal neighborhood, nodes also have an impact on nodes outside the temporal neighborhood. This is also a characteristic of nodes in the global network. Figure 1 (b) In the social temporal dynamic network, it can be seen that the information of node 1 can spread along nodes 1, 2, and 7 to node 8. Each node on the path will be directly or indirectly affected by node 1. This transmission of information is not completely random, but spreads in time order. Figure 1In (b), we can see that after node 2 receives information from node 1, it does not pass it on to node 3, because the interaction between node 2 and node 3 occurs before the interaction with node 1. Therefore, according to the time sequence, node 3 cannot obtain the information from node 1 from node 2, and node 3 is not affected by the information transmitted by node 1.

[0006] The influence of other nodes within and outside the temporal neighborhood of a node reflects local and global network characteristics, respectively. These two features, acquired from different perspectives of the node within the network, are essential for link prediction tasks. However, most models learn local or global network features from a single perspective, resulting in models that are only effective for specific types of data and lack generalizability. Therefore, how to capture and integrate network features from multiple perspectives is a key issue in learning representations for temporal dynamic networks. First, local network features are reflected through the temporal neighborhood of a node. Methods such as GCN, GraphSage, and GAT capture local network features by aggregating neighboring nodes. However, these methods ignore the time between node interactions, and the captured features contain a large amount of stale and redundant information, resulting in the generated node embeddings being out of date and unable to reflect the current local characteristics of the network. HTNE and MMDNE, based on the Hawkes process, use past events to predict the intensity of current events. In other words, the generation of new edges is influenced by the time of old edges and the appearance of old edges. While incorporating time into the acquisition of local network features, this approach is only effective for data that focuses on local characteristics. Secondly, the global characteristics of the network are reflected by the degree of influence of a node on other nodes in the network. The most important method is to use random walks to transmit the influence of nodes to farther locations in the network. Typical representatives include DeepWalk and Node2vec. However, these two methods do not consider the impact of time on the walk path, and many of the generated paths do not occur in reality. To address this problem, methods such as CTDNE and EHNA add time limits to the walk process to ensure the authenticity of the walk process, but the random walk method only works for data that focuses on global characteristics. Summary of the Invention

[0007] Aiming at the problem that existing temporal dynamic network link prediction methods fail to capture and integrate temporal dynamic network features from multiple perspectives, resulting in poor versatility, the present invention proposes a multi-perspective dynamic network link prediction method and system based on temporal neighborhood aggregation.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] In one aspect, the present invention proposes a multi-view dynamic network link prediction method based on temporal neighborhood aggregation, comprising:

[0010] Step 1: Take the temporal dynamic network as input, capture the temporal neighborhood of each node, and calculate the attention coefficient and time decay coefficient between the neighbors and the node in the temporal neighborhood, build a temporal attention mechanism, and use multiplication, summation, and splicing operations to aggregate the temporal neighborhood to generate local field of view features as the initial embedding of the node; the temporal dynamic network includes DBLP, Digg, and Tmall;

[0011] Step 2: Use the node interaction time to calculate the node transfer probability and generate a random walk path of nodes with a heavy time sequence;

[0012] Step 3: Use the word embedding model to build the objective function, fuse the local features of the network and the random walk paths of the nodes, and generate node embeddings with multi-view features;

[0013] Step 4: Use the logistic regression method to predict the links that will occur in the future temporal dynamic network.

[0014] Furthermore, the step 1 includes:

[0015] Step 1.1: Calculate the attention coefficient α between neighbor h and node v in the temporal neighborhood according to the following formula v,h :

[0016]

[0017] Where dis() represents the distance function between neighbor h and node v, H v represents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j;

[0018] Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ):

[0019] κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2)

[0020] where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate;

[0021] Step 1.3: Aggregate the temporal neighborhood according to the following formula:

[0022]

[0023] in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism;

[0024] Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula:

[0025]

[0026] where y v It represents the local visual field feature of the aggregated node v, and σ() is the activation function.

[0027] Furthermore, the step 2 includes:

[0028] Step 2.1: Calculate the node transition probability according to the following formula:

[0029]

[0030] where ω (v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′ represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function;

[0031] Step 2.2: Set the following transfer rules:

[0032]

[0033] Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode.

[0034] Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) :

[0035] π (v,w) =ψ (v,w) ·ω (v,w)

[0036] Step 2.4: Set the longest path length L and the total number of random walk paths k and the transition probability matrix π obtained by combining them (v,w), generating random walk paths of nodes with heavy timing.

[0037] Furthermore, the objective function in step 3 is:

[0038]

[0039] Among them S T Indicates the random walk path of nodes with heavy generation time sequence, C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w}. Represents the path S obtained based on the Skip-Gram model T Midpoint v i The context window, w represents the set window size, y c represents the local visual feature of node c, y v Represents the local visual feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k Represents the number of samples of node v, which obeys the degree distribution of node v.

[0040] Another aspect of the present invention provides a multi-view dynamic network link prediction system based on temporal neighborhood aggregation, comprising:

[0041] The temporal neighborhood aggregation module is used to capture the temporal neighborhood of each node using a temporal dynamic network as input, calculate the attention coefficient and time decay coefficient between the neighbors and the node in the temporal neighborhood, build a temporal attention mechanism, and aggregate the temporal neighborhood using multiplication, summation, and concatenation operations to generate local field of view features as the initial embedding of the node; the temporal dynamic network includes DBLP, Digg, and Tmall;

[0042] The random walk path generation module is used to calculate the node transfer probability using the node interaction time and generate a random walk path of nodes with a heavy time sequence;

[0043] The feature fusion module is used to construct the objective function using the word vector model, fuse the local features of the network and the random walk paths of the nodes, and generate node embeddings with multi-view features;

[0044] The link prediction module is used to predict future network links using logistic regression methods.

[0045] Furthermore, the temporal neighborhood aggregation module is specifically used to:

[0046] Step 1.1: Calculate the attention coefficient α between neighbor h and node v in the temporal neighborhood according to the following formula v,h :

[0047]

[0048] Where dis() represents the distance function between neighbor h and node v, H v represents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j;

[0049] Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ):

[0050] κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2)

[0051] where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate;

[0052] Step 1.3: Aggregate the temporal neighborhood according to the following formula:

[0053]

[0054] in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism;

[0055] Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula:

[0056]

[0057] where y v It represents the local visual field feature of the aggregated node v, and σ() is the activation function.

[0058] Furthermore, the random walk path generation module is specifically used to:

[0059] Step 2.1: Calculate the node transition probability according to the following formula:

[0060]

[0061] where ω(v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′ represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function;

[0062] Step 2.2: Set the following transfer rules:

[0063]

[0064] Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode.

[0065] Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) :

[0066] π (v,w) =ψ (v,w) ·ω (v,w)

[0067] Step 2.4: Set the longest path length L and the total number of random walk paths k and the transition probability matrix π obtained by combining them (v,w) , generating random walk paths of nodes with heavy timing.

[0068] Furthermore, the objective function in the feature fusion module is:

[0069]

[0070] Among them S T Indicates the random walk path of nodes with heavy generation time sequence, C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w}. Represents the path S obtained based on the Skip-Gram model T Midpoint v i The context window, w represents the set window size, y c represents the local visual feature of node c, y v Represents the local visual feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k Represents the number of samples of node v, which obeys the degree distribution of node v.

[0071] Compared with the prior art, the present invention has the following beneficial effects:

[0072] The present invention delimits the scope of the temporal neighborhood, corresponds the local features generated by the node to the temporal neighborhood, and corresponds the global features generated by the node to the outside of the temporal neighborhood, and uses aggregation and random walk methods to capture them respectively, thereby generating node embeddings containing temporal information, and predicting the links that will appear in the future network through the logistic regression method. In the aggregation process, the temporal difference attention mechanism is constructed taking into account the closeness of the relationship between nodes and the time difference, and extracting effective temporal information in the neighborhood. In the random walk process, the present invention adopts a temporal biased random walk method. Under the premise of ensuring that the path conforms to the time sequence, it tries to select a path with farther sampling to find the farthest influence range of the node and extract the global features of the network. In summary, the present invention captures and integrates temporal dynamic network features from multiple perspectives. Through experiments in real networks of different scales, the effect of the present invention in link prediction tasks can reach more than 90%, which has good practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a schematic diagram of a temporal dynamic network;

[0074] Figure 2 This is a flow chart of a multi-view dynamic network link prediction method based on temporal neighborhood aggregation according to an embodiment of the present invention;

[0075] Figure 3 This is a schematic diagram of the architecture of a multi-view dynamic network link prediction system based on temporal neighborhood aggregation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0077] like Figure 2 As shown in FIG, a multi-view dynamic network link prediction method based on temporal neighborhood aggregation (abbreviated as ESNA) includes:

[0078] Step 1: Temporal neighborhood aggregation based on temporal attention mechanism: Take the temporal dynamic network as input and capture the temporal neighborhood N1, N2, ..., N of each node. |V|, and calculate the attention coefficient and time decay coefficient between neighbors and nodes in the temporal neighborhood, build a temporal attention mechanism, and use multiplication, summation, and splicing operations to aggregate the temporal neighborhood to generate local visual features as the initial embedding of the node; the temporal dynamic network includes DBLP, Digg, and Tmall;

[0079] Step 2: Global scope exploration based on time-biased random walk paths: Calculate node transition probabilities using node interaction times, generate time-biased random walk paths for nodes, and explore the scope of a node's impact on the global network.

[0080] Step 3: Fusion of local and global features based on word embedding objective function: The word embedding model is used to construct the objective function, which fuses the local features of the network and the random walk paths of the nodes to generate node embeddings with multi-view features, thereby enhancing the versatility of the model.

[0081] Step 4: Logistic regression training: Use the logistic regression method to predict the links that will occur in the future time series dynamic network.

[0082] Furthermore, the step 1 includes:

[0083] Step 1.1: Calculate the attention coefficient α between neighbor h and node v in the temporal neighborhood according to the following formula v,h :

[0084]

[0085] Where dis() represents the distance function between neighbor h and node v, H v represents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j;

[0086] Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ):

[0087] κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2)

[0088] where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate;

[0089] Step 1.3: Aggregate the temporal neighborhood according to the following formula:

[0090]

[0091] in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism;

[0092] Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula:

[0093]

[0094] where y v It represents the local visual field feature of the aggregated node v, and σ() is the activation function.

[0095] Furthermore, the step 2 includes:

[0096] Step 2.1: Calculate the node transition probability according to the following formula:

[0097]

[0098] where ω (v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′ represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function;

[0099] Step 2.2: Set the following transfer rules:

[0100]

[0101] Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode.

[0102] Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) :

[0103] π (v,w) =ψ (v,w) ·ω (v,w)

[0104] Step 2.4: Set the maximum path length L, the total number of random walk paths k, and the combined transition probability matrix π (v,w) to generate the time-biased node random walk path.

[0105] Further, the objective function in step 3 is:

[0106]

[0107] where S T represents the generation of time-biased node random walk paths, C v = {v i-w ,…,v i-1 ,v i+1 ,…v i+w}. represents the context window of node v T in path S i obtained based on the Skip-Gram model, w represents the set window size, y c represents the local view feature of node c, y v represents the local view feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k represents the number of samples of node v, which is subject to the degree distribution of node v.

[0108] Specifically, the time neighbor aggregation based on the time difference attention mechanism includes:

[0109] In the time dynamic network, the local feature of a node is affected by its neighbors. By aggregating neighbor information, the local feature of the current network can be captured. In the time neighborhood of a node, the aggregation of the node mainly considers two aspects: one is the closeness of the relationship between the node and its neighbors, and the other is the time difference of the interaction between the node and its neighbors.

[0110] The closeness of the relationship between a node and its neighbors can reflect the similarity between them. The attention mechanism is used to depict the closeness of the relationship between the node and different neighbors. The attention mechanism relies on the attention coefficient α∈[0,1], which distinguishes the importance of different neighbor nodes. When the relationship between the neighbor and the node is closer, the nodes are more similar, the degree of mutual influence between the nodes is higher, and the value of α is larger. Conversely, when the relationship between the neighbor and the node is looser, the nodes are more different, the degree of mutual influence between the nodes is lower, and the value of α is smaller.

[0111] For node v and its neighbor h, the attention coefficient α v,hwhere dis() denotes the distance function between nodes, usually calculated by Euclidean distance.

[0112]

[0113] Secondly, the influence of neighbors appearing at different time periods on the current state of a node is different. Generally speaking, the later the neighbor appears, the higher the influence of the neighbor on the current state of the node, and vice versa. Here, the time decay mechanism is used to measure the time of the node appearing. Assuming that the last time of the node v appearing is t v , the time of the node v interacting with its neighbor h is t v,h , then the time difference between them is t v -t v,h , the smaller the time difference, the greater the influence of the neighbor h on the node v, and vice versa. The expression κ() of the time decay mechanism is constructed by using the time difference, as shown in formula (3-2). Where δ represents the time discount rate, which is used to calculate the influence of different lengths of time difference.

[0114] κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2)

[0115] The time difference attention mechanism is constructed by combining the relationship tightness of nodes on the time sequence neighborhood and the time difference between nodes interacting, and the neighbors in the time sequence neighborhood are aggregated, and the calculation formula is as shown in formula (3-3). In addition, in order to ensure that the node itself features are integrated into the network local features, the aggregation result is spliced (||) with the node itself embedding, and then the activation function σ() operation is performed to obtain the aggregated node v embedding representation y v .

[0116]

[0117]

[0118] Specifically, the global range exploration based on the time sequence biased random walk path includes:

[0119] In order to further capture the global features of the network, outside the time sequence neighborhood, the time sequence random walk path S T is constructed by simulating the process of the node propagating information, and the nodes with mutual influence are found. The key factor of the random walk path is the setting of the transition probability matrix π. In the time sequence dynamic network, the transition probability matrix is affected by two factors, one is the inherent transition probability ω of the node, and the other is the transition rule ψ.

[0120] First, the node inherent transfer probability ω is affected by time factors, and nodes tend to transfer to neighbors that appear close to the current time. Assuming that node u transfers to node v, the probability of node v transferring to w is in The ReLU function is used to limit the transfer direction to ensure that the nodes move in time order.

[0121] Secondly, we refer to Node2vec and introduce two parameters p and q to set the node transfer rules. Assuming that node u transfers to node v, the rule for node v to transfer to w is Here, d vw It refers to the shortest distance between node v and node w. From the expression of ψ, we can see that parameter p controls the direction of node v to node u, and parameter q controls whether node v is transferred in depth-first walk or breadth-first walk. Finally, we get the transition probability matrix π of node v (v,w) =ψ (v,w) ·ω (v,w) .

[0122] In addition to the calculation of the transition probability matrix, it is necessary to set the maximum path length L and the number of wandering paths generated by each node k to limit the path length and the number of paths during the sampling process.

[0123] Specifically, the local and global feature fusion based on the word vector objective function includes:

[0124] Drawing on the Skip-Gram in the word vector model Word2vec, according to the generated temporal walk path S T And the set window size w, the path S can be obtained T Midpoint v i The context window is denoted as C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w}. According to node v i features, predict the existence of other nodes in its context window, and transform this problem into formula (3-5).

[0125]

[0126] The local features of the network obtained by aggregation are used as the initial embedding of the nodes and brought into formula (3-5). At the same time, the likelihood logarithm is used to rewrite formula (3-5) and the problem is transformed into formula (3-6), where

[0127]

[0128] To further optimize (3-6), negative sampling technology is used to avoid computing the entire node set and shorten the training time. Generally speaking, according to the degree distribution of the node Sample the nodes that do not appear in the context window and finally optimize formula (3-6) into formula (3-7).

[0129]

[0130] Here, K is the number of negative sampling nodes, which is calculated based on the degree distribution of node v. For the probability function Pr, its calculation method is shown in formula (3-8):

[0131]

[0132] Specifically, logistic regression training includes:

[0133] Link prediction is the process of predicting the edges that may appear during network evolution. It is important for applications such as user recommendations and event prediction. We use logistic regression to learn existing edge features in time-series dynamic networks to predict emerging edges. We use the sklearn library in Python to implement logistic regression. The network representation learning model generates node embeddings. Edge embeddings in the network require further transformation. We use four operations to generate edge embeddings: the average of the node embeddings at both ends of the edge (mean), the Hadamard product (Hadarma), L1 regularization (weighted-L1), and L2 regularization (weighted-L2). The calculation methods are shown in Table 1.

[0134] Table 1 Operations for edge embedding formation

[0135]

[0136] To validate the effectiveness of our method, we conducted experiments on link prediction tasks using three real-world network datasets. We compared this method with existing, well-established methods for learning temporal dynamic network representations to verify its effectiveness. The following details the experimental content and analyzes the experimental results.

[0137] 1. Experimental Setup

[0138] 1. Dataset

[0139] DBLP is a collaborator network in which each node represents a scholar, and edges between nodes represent papers jointly published by scholars. Each scholar has a corresponding research field. Using research fields as labels, we categorize scholars working in unlabeled fields to validate the effectiveness of temporal dynamic network representation learning methods in node classification tasks. Given the numerous academic research fields, we extracted the 10 most popular fields as labels. For scholars with multiple research fields, we used the field with the most published papers as their research field. We also conducted link prediction tasks to explore the network's recovery and prediction capabilities using the feature information contained in node embeddings.

[0140] Digg is a social network that focuses on global features and is a temporal dynamic network. In this network, each node represents a user, and edges between nodes represent friendships between users. The data was collected from 2004 to 2009 and used in link prediction experiments.

[0141] Tmall is an e-commerce network. This data, derived from the Double 11 (Singles' Day) sales data on Tmall.com in 2014, is a temporal dynamic network that focuses on local features. In this network, each node represents a user or an item, and the edges between nodes represent user purchase records. Each item corresponds to a category, and we extracted the five most frequently purchased items from users for node classification experiments. Furthermore, we conducted link prediction experiments on this data to explore user purchasing habits and recommend products to users.

[0142] 2. Comparison method

[0143] The effectiveness of ESNA is verified by comparing it with five classical network representation learning methods with good practical application effects. These five methods are introduced below.

[0144] Node2vec: By combining depth-first traversal (DFS) and breadth-first traversal (BFS), it connects the relationships between neighboring nodes of any order and generates random walk paths for each node. The generated paths are fed into the Skip-Gram model to learn node embeddings, and logistic regression is used to predict future links in the network.

[0145] CTDNE: In the random walk phase, time attributes are added to generate temporal random walk paths based on the order of events. The generated paths are also input into the Skip-Gram model to learn node embeddings, and logistic regression is used to predict future links in the network.

[0146] HTNE: Based on the Hawkes process, it uses historical events to calculate the probability of current events, thereby learning node embeddings and using logistic regression methods to predict links that will appear in the future network.

[0147] MMDNE: This method calculates event probabilities from both micro and macro perspectives to learn node embeddings. At the micro level, it leverages the node's inherent strength and the influence of its bidirectional historical neighbors to construct event probabilities. At the macro level, it uses dynamics principles to constrain the number of historical neighbors, capturing more precise structural and temporal properties. It also uses logistic regression to predict future links in the network.

[0148] EHNA: Node-level aggregation and path-level aggregation are used to aggregate nodes on random walk paths and different random walk paths respectively to obtain node embeddings. Here, the aggregator uses LSTM, and the logistic regression method is used to predict the links that will appear in the future network.

[0149] 3. Parameter settings

[0150] For ESNA, SGD was selected as the optimizer, with the mini-batch size, SGD learning rate, and number of negative samples set to 512, 0.01, and 5, respectively. The number of aggregated historical nodes for DBLP, Digg, and Tmall was set to 3, 2, and 5, respectively. A grid search method was used for p and q, with p,q∈{0.25, 0.5, 1, 2, 4}. The node embedding dimension D, the longest path length L, and the number of walk paths generated per node k were set to 128, 80, and 10, respectively. For CTDNE, uniform sampling was used for initial edges, and a linear approach was used for random walks. Other parameters were the same as for ESNA. For EHNA, two LSTM layers were used, with other parameters the same as for ESNA.

[0151] 2. Experimental Results and Analysis

[0152] The data in Tables 2, 3, and 4 show that ESNA outperforms other baseline methods overall, achieving over 90% performance across all four evaluation metrics. However, the performance of different operations on the link prediction task varies significantly. Different operations represent different edge embedding formation rules and play different roles in different types of dynamic networks. On the DBLP dataset, the Hadamard product performs better than other operations, while on the Digg dataset, the Hadamard product performs far worse than other operations. Therefore, a single operation cannot be used to measure all datasets.

[0153] Table 2 Performance of different methods in link prediction tasks on the DBLP dataset

[0154]

[0155] Table 3 Performance of different methods in link prediction task on Digg dataset

[0156]

[0157]

[0158] Table 4 Performance of different methods in link prediction task on Tmall dataset

[0159]

[0160] In summary, through experiments in real networks of different scales, the effect of ESNA in the link prediction task can reach more than 90%, which has good practical application value.

[0161] On the basis of the above embodiment, as Figure 3 indicated, another aspect of the present application proposes a multi-view dynamic network link prediction system based on time sequence neighborhood aggregation, comprising:

[0162] The time sequence neighborhood aggregation module is used to take the time sequence dynamic network as input, capture the time sequence neighborhood of each node, calculate the attention coefficient and time decay coefficient between the neighbors and the node in the time sequence neighborhood, construct the time difference attention mechanism, and aggregate the time sequence neighborhood by multiplication, summation and splicing operation to generate the local view feature as the initial embedding of the node; the time sequence dynamic network includes DBLP, Digg and Tmall;

[0163] The random walk path generation module is used to calculate the node transition probability by using the node interaction time to generate the time sequence biased node random walk path;

[0164] The feature fusion module is used to construct the target function by using the word vector model, fuse the local features of the network and the node random walk path, and generate the node embedding with multi-view features;

[0165] The link prediction module is used to predict the links occurred in the future network by using the logistic regression method.

[0166] Further, the time sequence neighborhood aggregation module is specifically used for:

[0167] Step 1.1: Calculate the attention coefficient a between neighbor h and node v in the time sequence neighborhood according to the following formula v,h :

[0168]

[0169] Where dis() represents the distance function between neighbor h and node v, H vrepresents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j;

[0170] Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ):

[0171] κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2)

[0172] where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate;

[0173] Step 1.3: Aggregate the temporal neighborhood according to the following formula:

[0174]

[0175] in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism;

[0176] Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula:

[0177]

[0178] where y v It represents the local visual field feature of the aggregated node v, and σ() is the activation function.

[0179] Furthermore, the random walk path generation module is specifically used to:

[0180] Step 2.1: Calculate the node transition probability according to the following formula:

[0181]

[0182] where ω (v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function;

[0183] Step 2.2: Set the following transfer rules:

[0184]

[0185] Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode.

[0186] Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) :

[0187] π (v,w) =ψ (v,w) ·ω (v,w)

[0188] Step 2.4: Set the longest path length L and the total number of random walk paths k and the transition probability matrix π obtained by combining them (v,w) , generating random walk paths of nodes with heavy timing.

[0189] Furthermore, the objective function in the feature fusion module is:

[0190]

[0191] Among them S T Indicates the random walk path of nodes with heavy generation time sequence, C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w}. Represents the path S obtained based on the Skip-Gram model T Midpoint v i The context window, w represents the set window size, y c represents the local visual feature of node c, y v Represents the local visual feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k Represents the number of samples of node v, which obeys the degree distribution of node v.

[0192] In summary, the present invention delimits the scope of the temporal neighborhood, corresponds the local features generated by the nodes to the network within the temporal neighborhood, and corresponds the global features generated by the nodes to the outside of the temporal neighborhood, and uses aggregation and random walk methods to capture them respectively, thereby generating node embeddings containing temporal information, and predicting the links that will appear in the future network through the logistic regression method. In the aggregation process, the temporal difference attention mechanism is constructed taking into account the closeness of the relationship between nodes and the time difference, and extracting effective temporal information in the neighborhood. In the random walk process, the present invention adopts a temporal biased random walk method. Under the premise of ensuring that the path conforms to the time sequence, it tries to select a path with farther sampling to find the farthest influence range of the node and extract the global features of the network. The present invention captures and integrates temporal dynamic network features from multiple perspectives. Through experiments in real networks of different scales, the effect of the present invention in link prediction tasks can reach more than 90%, which has good practical application value.

[0193] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-view dynamic network link prediction method based on temporal neighborhood aggregation, characterized in that: include: Step 1: Take the temporal dynamic network as input, capture the temporal neighborhood of each node, and calculate the attention coefficient and time decay coefficient between the neighbors and the node in the temporal neighborhood, build a temporal attention mechanism, and use multiplication, summation, and splicing operations to aggregate the temporal neighborhood to generate local field of view features as the initial embedding of the node; the temporal dynamic network includes DBLP, Digg, and Tmall; Step 2: Use the node interaction time to calculate the node transfer probability and generate a random walk path of nodes with a heavy time sequence; Step 3: Use the word embedding model to construct the objective function, fuse the local view features of the network and the node random walk path, and generate node embedding with multi-view features; Step 4: Use the logistic regression method to predict the links that will occur in the future temporal dynamic network; The step 1 comprises: Step 1.1: Calculate the attention coefficient α between neighbor h and node v in the temporal neighborhood according to the following formula v,h : Where dis() represents the distance function between neighbor h and node v, H v represents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j; Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ): κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2) where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate; Step 1.3: Aggregate the temporal neighborhood according to the following formula: in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism; Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula: where y v represents the local visual field feature of the aggregated node v, σ() is the activation function, and || represents splicing; The objective function in step 3 is: Among them S T Indicates the random walk path of nodes with heavy generation time sequence, C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w } represents the path S obtained based on the Skip-Gram model T Midpoint v i The context window, w represents the set window size, y c represents the local visual feature of node c, y v Represents the local visual feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k Represents the number of samples of node v, which obeys the degree distribution of node v.

2. The multi-view dynamic network link prediction method based on temporal neighborhood aggregation according to claim 1 is characterized in that: The step 2 includes: Step 2.1: Calculate the node transition probability according to the following formula: where ω (v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′ represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function; Step 2.2: Set the following transfer rules: Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode. Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) : p (v,w) =ψ (v,w) ·oh (v,w) Step 2.4: Set the longest path length L and the total number of random walk paths k and the combined transition probability matrix π (v,w) , generating random walk paths of nodes with heavy timing.

3. A multi-view dynamic network link prediction system based on temporal neighborhood aggregation, characterized by: include: The temporal neighborhood aggregation module is used to capture the temporal neighborhood of each node using a temporal dynamic network as input, calculate the attention coefficient and time decay coefficient between the neighbors and the node in the temporal neighborhood, build a temporal attention mechanism, and aggregate the temporal neighborhood using multiplication, summation, and concatenation operations to generate local field of view features as the initial embedding of the node. The temporal dynamic network includes DBLP, Digg, and Tmall. The random walk path generation module is used to calculate the node transfer probability using the node interaction time and generate a random walk path of nodes with a heavy time sequence; The feature fusion module is used to construct the objective function using the word vector model, fuse the local field of view features of the network and the random walk path of the node, and generate node embeddings with multi-field of view features; Link prediction module, used to predict future network links using logistic regression method; The temporal neighborhood aggregation module is specifically used to: Step 1.1: Calculate the attention coefficient α between neighbor h and node v in the temporal neighborhood according to the following formula v,h : Where dis() represents the distance function between neighbor h and node v, H v represents the set of neighbor nodes of node v, x v The vector representing the node v, x h The vector representing the node h, x j The vector representing node j; Step 1.2: Calculate the time decay coefficient κ(t v ,t v,h ): κ(t v ,t v,h )=exp(-δ(t v -t v,h )) (3-2) where t v Indicates the time when node v last appeared, t v,h represents the time when node v interacts with its neighbor h, and δ represents the time discount rate; Step 1.3: Aggregate the temporal neighborhood according to the following formula: in Represents the temporal neighborhood aggregation result of node v based on the temporal difference attention mechanism; Step 1.4: Generate the local visual field feature of node v as the initial embedding of the node according to the following formula: where y v represents the local visual field feature of the aggregated node v, σ() is the activation function, and || represents splicing; The objective function in the feature fusion module is: Among them S T Indicates the random walk path of nodes with heavy generation time sequence, C v ={v i-w ,…,v i-1 ,v i+1 ,…v i+w } represents the path S obtained based on the Skip-Gram model T Midpoint v i The context window, w represents the set window size, y c represents the local visual feature of node c, y v Represents the local visual feature of node v, y k represents the local view feature of node k, represents the degree distribution of node v, K is the number of negative sampling nodes, Pr() is the probability function, v k Represents the number of samples of node v, which obeys the degree distribution of node v.

4. The multi-view dynamic network link prediction system based on temporal neighborhood aggregation according to claim 3 is characterized in that: The random walk path generation module is specifically used for: Step 2.1: Calculate the node transition probability according to the following formula: where ω (v,w) represents the probability of node v transferring to w, H v represents the set of neighbor nodes of node v, t v,w Indicates the time when nodes v and w interact, t u,v Indicates the time when nodes u and v interact, t v,w′ represents the time when node v interacts with its neighbor w′, ReLU() represents the ReLU function; Step 2.2: Set the following transfer rules: Among them, ψ (v,w) represents the transfer rule from node v to node w, d vw It refers to the shortest distance between node v and node w, p is the control parameter for node v to move toward the information source node u, and q is the control parameter for node v to move in a depth-first walk or breadth-first walk mode. Step 2.3: Calculate the transition probability matrix π from node v to node w according to the following formula (v,w) : p (v,w) =ψ (v,w) ·oh (v,w) Step 2.4: Set the longest path length L and the total number of random walk paths k and the combined transition probability matrix π (v,w) , generating random walk paths of nodes with heavy timing.

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