A Method for Learning Representations of Dynamic Social Networks

Abstract

The present invention discloses a method for learning representation of a dynamic social network, which relates to the field of network representation learning and solves the technical problem that the current method cannot retain the low-dimensional feature vectors of the evolution pattern and community structure of a real social network during learning, including the analysis of the triadic closure pattern and the community structure. After analyzing the triadic closure pattern, the present invention jointly models the evolution process of nodes and edges in the social network by combining important factors of the social network such as the influence of nodes, the similarity of nodes, and the community structure. This method can retain both the network structure of nodes and the dynamic features to learn the low-dimensional representation of nodes, and by capturing the evolution patterns of different nodes in the social network, the learned low-dimensional representation is more discriminative. Community is one of the most important features of a real social network, and the learned network representation can well reflect the structure of the community, which can help users obtain more useful information and better optimize the triadic closure process.

Description

Technical Field

[0001] The present invention relates to the field of network representation learning, and particularly to a method for dynamic social network representation learning. Background Art

[0002] The advent of the Internet era has given birth to many kinds of social network service platforms, greatly improving people's living standards. Such platforms are also called Online Social Networks (OSNs), such as Weibo, Douban, Tieba in China, and Facebook, Twitter, Instagram abroad. Studying and analyzing the widespread social networks has high commercial and academic value, attracting a large number of domestic and foreign scholars to conduct research. For example, the research on the information diffusion problem in social networks can be applied to scenarios such as rumor detection, public opinion guidance, and influence maximization. However, the continuously accumulating massive and rich data in today's online social networks has brought new opportunities and challenges to social network analysis.

[0003] Network Representation Learning (NRL), also known as "Network Embedding (NE)", is a fundamental and key issue in social network analysis tasks, aiming to map a social network into a low-dimensional vector space while maximizing the retention of the attribute features of nodes in the network. The performance of machine learning algorithms depends to a large extent on the choice of the data representation form or features used. And network representation learning can improve the performance of algorithms by converting the input data into effective feature representations. Therefore, combining deep learning techniques with network representation learning to solve practical problems has achieved remarkable results. With the development of deep learning techniques, the research work on the representation learning of social networks is currently still in a period of rapid development, and various methods emerge in an endless stream, becoming a hot topic of current research.

[0004] Early social network representation learning mainly focused on static social networks. The solution was to embed the high-dimensional structure of the static network into a low-dimensional representation space through some dimensionality reduction methods (such as matrix factorization, deep autoencoders, deep learning, etc.). Its main idea was that similar nodes in the network should be closer in the embedded representation space. These methods have the following two significant drawbacks:

[0005] 1. It is difficult to reflect the dynamic characteristics of social networks evolving over time. The social networks in the real world are not static but evolving continuously with time. For example, in online social platforms, new users are constantly joining, and new friendship relationships are continuously emerging among users, which will lead to the emergence of new nodes and edges in the network. Therefore, traditional methods only study the fixed nodes and edges in static networks without considering the update of network information, and the learned feature representations are difficult to maintain the dynamic characteristics of the real network. Moreover, although a small number of studies on the representation learning of dynamic social networks have been proposed recently, it is difficult to capture the differences in the evolution patterns of different nodes in social networks. During the evolution of social networks, nodes with similar network structures may adopt different evolution patterns, such as whether to establish new connections with others in the future. This reflects implicit information such as the personality characteristics and social strategies of different users, and this important information cannot be directly obtained through the network structure. Therefore, traditional methods cannot measure various influencing factors in the network and construct an accurate evolution model based on the basic mechanism of the evolution of dynamic social networks, and thus it is difficult to accurately depict the different evolution trends of nodes in the network.

[0006] 2. It is difficult to reflect the important network property of social networks - community structure. Most of the existing network embedding methods focus on maintaining the local proximity between nodes, that is, according to homophily, highly connected nodes should be closely embedded in the latent representation space. However, the community structure, as one of the most important features of social networks, which can reveal the hidden features of complex networks, has been largely ignored. For example, in the social network at the current moment, two nodes are not directly connected. If only based on the connection relationship of the node pair, the similarity between the two will tend to be very small. However, communities in dynamic networks are clusters composed of nodes with similar functions and intensive communication. Therefore, even if they are not directly connected, if these two nodes belong to the same community, their similarity should be different from when they do not belong to the same community. Summary of the Invention

[0007] The purpose of the present invention is: to solve the above technical problems, the present invention provides a method for representing and learning dynamic social networks, which can learn and retain a low-dimensional feature vector that simultaneously preserves the evolution pattern and community structure of real social networks.

[0008] The technical solution adopted by the present invention is as follows:

[0009] A method for representing and learning dynamic social networks includes the following steps:

[0010] Step 1: Construct a dynamic network sequence. Based on a given set of time steps {1, 2, …, T}, for the social network data at a certain time step (a certain moment), construct a subgraph G {a} =(V, E {a} , W {a}), a ∈ {1, 2, …, T};

[0011] Among them, V is the set of nodes, representing users in the network; E {a} is the set of edges at the current time step, representing the relationships between users (such as friends, follow / follower, etc.); W {a} is the set of weights, representing the connection strength between users; The dynamic network is a sequence of subgraphs at all time steps G = {G (1) , G (2) , …, G (T)};

[0012] Step 2: Community division. According to the structure of the network, mark the community where each node is located; Since the dynamic network evolves over time, it is necessary to perform community division on the network at each time step

[0013] Step 3: Retain the network evolution characteristics based on the triadic closure process; For G {a} , where three users satisfying the following relationship form an open triad (v i , v j , v k ): Users v i and v j do not know each other, but they have a common friend v k ; The common friend v k will decide whether to introduce v i and v j to know each other in the next time step to make the open triad closed; The three main factors affecting his decision in this process are: user influence, user similarity, and community structure;

[0014] Step 4: Retain the network structure characteristics based on homophily and community structure. Nodes pairs connected according to social homophily will be more closely embedded in the potential representation space; Network representation learning methods that only consider this property ignore another significant feature of the dynamic network, that is, the community structure. Even if nodes are not directly connected in the original network, the representations of nodes belonging to the same community should be more closely embedded in the potential representation space than those in different communities.

[0015] Step 5: Temporal smoothness. In real-world networks, it is natural to assume that nodes do not completely reconstruct at each time step, but evolve smoothly over time. To maintain the smooth evolution of the dynamic network at time step a, construct a temporal smoothness loss function as follows.

[0016]

[0017] Step 6: Combine the network evolution features and structural features for embedding to obtain the feature representation of each node; To learn the low-dimensional embedding representation of nodes in a dynamic social network while preserving both the evolution features and structural features of the nodes, we need to optimize three loss functions and ; We set the weight parameter of the global structure loss function to 1 and use two hyperparameters β0 and β1 to control the triadic closure process and temporal smoothness respectively; Therefore, for a given initial time step T, the overall optimization problem is

[0018]

[0019] where and are normalization terms, and the regularization objective is omitted when processed by normalization techniques during training. Finally, the classical optimization algorithm Stochastic Gradient Descent (SGD) combined with the Adagrad method is used to solve this minimization problem. Set the latent space dimension to d, and finally obtain the node embedding representation U = {U (1) , U (2) , …, U (T)} of the social network;

[0020] It can be applied to various specific social network analysis tasks.

[0021] Furthermore, community information is obtained through the classical community discovery algorithm semi-synchronized LPA.

[0022] Furthermore, in the said Step 3,

[0023] User influence: If v k is a user with greater influence in the social network, then the probability that he introduces v i and v j to know and establish connections in the next time step is relatively small; For example, the influence of opinion leaders is much higher than that of ordinary users, so the probability that they introduce two users connected to themselves to know each other is obviously different, with the former being lower than the latter;

[0024] User similarity: When v k is similar to v i and v j , it is more inclined to introduce v i and v j to know and establish connections in the next time step, so the probability of open triadic closure increases;

[0025] Community structure: Compared with the situation where v i and v j belong to the same community, v kThe effort required to introduce these two friends belonging to different communities is obviously greater, and the probability of closing an open triple is relatively small.

[0026] Furthermore, v k Making a decision can be quantified as follows:

[0027]

[0028] where, represents the weights of v i and v k at time step a, represents the degree of v k ; is the embedding vector of user v k , defined as indicating the influence of the community structure, meaning that when v i and v j belong to the same community, that is, the edge that may be generated in the future to be predicted does not cross different communities, otherwise,

[0029] then the probability that a new edge is generated between v i and v j under the influence of their common friend v k at the next time step is

[0030]

[0031] where θ is the set vector parameter, representing the social strategy information of the node;

[0032] Since v i and v j may have multiple common friends in the network, by further assuming that the influence of each common friend on the potential link between v i and v j is independent, the probability that a new link e ij is created at the next moment is

[0033]

[0034] where, represents the set of common neighbors of v i and v j at time step a. If a link is generated due to the role of common friends at the next time step, then has a value of 1;

[0035] Correspondingly, v k will not introduce a new link e ijThe probability of being created in the next time step is:

[0036]

[0037] Define the set where represents user v i and v j successfully generated a link at time step a + 1, and the set represents user v i and v j did not generate a link at time step a + 1.

[0038] Furthermore, in step 4, the network structure features are retained, the network evolution features are retained, and the loss function in the embedding training process is:

[0039]

[0040] Furthermore, in step 4, the network structure features are retained, and the loss function in the embedding training process is:

[0041]

[0042] where represents all node pairs in G (a) , represents the Euclidean distance between nodes v i and v j in the latent space. For any real number, [x]+ = max(0, x); γ ∈ R + is the margin value, and define g (a) (i, j) indicates the connection relationship of the node pair at time step a, which means that when v i and v j are connected by an edge, g (a) (i, j) = 1; otherwise, g (a) (i, j) = -1.

[0043] Furthermore, in step 4, for any set of node pairs in the network: According to the link relationship and community structure, it can be divided into the following four sets:

[0044] S1 = {(v i , v j ) | e ij ∈ E (a) ∩ p = q}: Vertex pairs that belong to the same community and have links;

[0045] S2 = {(v i , v j ) | e ij ∈ E (a)∩p≠q}: vertex pairs that belong to different communities and have links;

[0046] Vertex pairs that belong to the same community and have no links;

[0047] S4 = {(v i , v j ) | e ij ∈E (a) ∩p≠q}: vertex pairs that belong to different communities and have no links.

[0048] The beneficial effects of the present invention are as follows:

[0049] 1. The present invention discloses a method for jointly modeling the evolution process of nodes and edges in a social network by analyzing the triadic closure pattern and combining important factors such as the influence of nodes, the similarity of nodes, and the community structure. This method can simultaneously retain the network structure and dynamic characteristics of nodes to learn the low-dimensional representation of nodes, and by capturing different node evolution patterns in the social network, the learned low-dimensional representation is more discriminative.

[0050] 2. Community is one of the most important features of a real social network. The learned network representation can well reflect the structure of the community, which can help users obtain more useful information and better optimize the triadic closure process. And better predicting the evolution of the network in turn acts on finding a clearer community structure. This is our motivation. In the process of retaining the network structure, the present invention uses the community structure at different time steps to supplement the connection information of local node pairs in the network, so as to obtain richer network information. Description of the Drawings

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. It should be understood that the proportional relationship of each component in the drawings of this specification does not represent the proportional relationship in actual material selection and design. It is only a schematic diagram of the structure or position, where:

[0052] Figure 1 is the flowchart of the present invention;

[0053] Figure 2 is the comparison chart of F1-score values applied to link reconstruction in the four networks of fb-messages, ia-facebook, ia-contacts, and ia-retweet of the present invention;

[0054] Figure 3It is a comparison chart of F1-score values applied to link prediction in four networks of the present invention, namely fb-messages, ia-facebook, ia-contacts, and ia-retweet. Detailed implementation manners

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0056] The following combines Figure 1 , Figure 2 and Figure 3 , to describe the present invention in detail.

[0057] Embodiment 1

[0058] A dynamic social network representation learning method is implemented based on triadic closure pattern analysis and community structure; it includes the following steps:

[0059] Step 1: Construct a dynamic network sequence. Based on a given set of time steps {1, 2, …, T}, for the social network data at a certain time step, construct a subgraph G {a} =(V, E {a} , W {a} ), a ∈ {1, 2, …, T};

[0060] Among them, V is the node set, representing the users in the network; E {a} is the edge set at the current time step, representing the relationships between users; W {a} is the weight set, representing the connection strength between users; the dynamic network is a sequence G = {G (1) , G (2) , …, G (T)} composed of subgraphs at all time steps;

[0061] Step 2: Community partitioning. According to the structure of the network, mark the community to which each node belongs; since the dynamic network evolves over time, it is necessary to perform community partitioning on the network at each time step {1, 2, …, T};

[0062] Step 3: Retain the network evolution characteristics based on the triadic closure process; for G {a} , three users satisfying the following relationship form an open triple (v i , v j , v k ): Users v i and vj They don't know each other, but they have a common friend v k ; The common friend v k will decide whether to introduce v at the next time step i and v j getting to know each other makes the open triple closed; The three main factors influencing his decision in this process are: user influence, user similarity, and community structure;

[0063] Step 4: Based on homophily and community structure, retain the network structure features. Nodes pairs connected according to social homophily will be more tightly embedded in the latent representation space;

[0064] Step 5: Temporal smoothness. To maintain the smooth evolution of the dynamic network at time step a, construct a temporal smoothness loss function as follows:

[0065]

[0066] Step 6: Combine the network evolution features and structure features for embedding to obtain the feature representation of each node; To learn the low-dimensional embedding representation of the nodes in the dynamic social network while retaining the evolution features and structure features of the nodes, we need to optimize three loss functions and ; Set the weight parameter of the global structure loss function to 1, and use two hyperparameters β0 and β1 to control the triadic closure process and temporal smoothness respectively; Therefore, for a given initial time step T, the overall optimization problem is:

[0067]

[0068] where and are normalization terms, set the latent space dimension to d, and finally obtain the node embedding representation U = {U (1) , U (2) , …, U (T)};

[0069] It can be applied to various specific analysis tasks of social networks.

[0070] The working principle / process of the present invention is as follows: The problem of dynamic network representation learning has been widely studied in the academic community, and a large number of relevant papers are available for reference. The following six related inventions are retrieved from the Chinese invention patent database:

[0071] (1) CN112925953A

[0072] A method and system for dynamic network representation

[0073] (2)CN111126437A

[0074] Anomaly group detection method based on weighted dynamic network representation learning

[0075] (3)CN111460275A

[0076] A dynamic network representation learning method and system for social networks

[0077] (4)CN108540327A

[0078] A method and system for detecting abnormal link behavior in dynamic networks

[0079] (5)CN110020379A

[0080] A link prediction method based on a deep dynamic network embedding representation model

[0081] (6)CN112446489A

[0082] A variational autoencoder-based dynamic network embedding link prediction method

[0083] However, this solution is completely different from the above 6 technologies. This solution can learn and retain low-dimensional feature vectors that simultaneously preserve the evolution pattern and community structure of real social networks, mainly including two components: First, based on the principle of triadic closure in social networks, as the basic dynamic mechanism of social network evolution, and combined with factors such as node influence, node similarity, and community structure to strengthen this process, an accurate social network evolution model is constructed. This method can more effectively predict changes in network structure and capture differences in the evolution patterns of different nodes in social networks, so that the embeddings of nodes capture relevant dynamic information. Second, as the node connection relationship changes based on triadic closure, the community structure may also change accordingly. On the basis of retaining the network evolution pattern and node local proximity, using the community structure as the high-order proximity of nodes, using the community structure to obtain richer information about the network, and learning more discriminative low-dimensional representations of nodes. By improving the quality of node embeddings, the accuracy of various social network analysis tasks using this as input is improved.

[0084] Example 2

[0085] This example is four real social network datasets, including fb-messages, ia-facebook, ia-contacts, and ia-retweet, and their specific information is shown in Table 1.

[0086] Table 1 Weibo-Douban network data statistics table

[0087]

[0088] Step 1: For each dataset, we first construct the corresponding dynamic network sequence G = {G (1) , G (2) , …, G (T)}, and then learn the low-dimensional vectors U = {U (1) , U (2) , …, U (T)} of each node at different time steps through the present invention.

[0089] Step 2: To verify the performance of the proposed method, five classic network representation learning methods are selected for comparison in this example, including: DeepWalk, LINE, Node2vec, DynamicTriad, and TNE, where DeepWalk, LINE, and Node2vec are static network representation learning models, while DynamicTriad and TNE are dynamic network representation learning models. After weighing the computational complexity and computational performance, we use the dimension d = 48 for performance comparison.

[0090] Step 3: In this example, all methods are used to obtain the embedding vectors of the nodes, and the learned embedding vectors of the nodes are used to construct the feature representation of the edges in the network. For each edge, e ij = |u i - u j |, where the absolute value symbol is defined to perform the absolute value operation on each component of the subtracted vector. Then, the obtained feature representation of the edge is used as the input and applied to four specific social network tasks: link reconstruction, link prediction, changed link reconstruction, and changed link prediction. Then, all positive and negative samples are collected from different time steps, and the logistic regression model is used as the classifier. Finally, 5-fold cross-validation is repeated 10 times on the collected sample set, and the average performance is compared. After weighing the computational complexity and performance, for all models, the dimension of the network node representation vector is set to 48 dimensions.

[0091] Step 4: In this example, the F1-score metric is used to evaluate the performance of the proposed method. For each link, the experimental results are divided into four categories, as shown in the confusion matrix of Table 2:

[0092] Table 2 Confusion Matrix

[0093]

[0094]

[0095] The calculation formula of the F1-score metric is:

[0096]

[0097]

[0098]

[0099] Step 5: In the experiment, we conducted 5 random repeated experiments for each method and took the average value as the final result. Figure 2 and Figure 3 respectively show the comparison results of the F1-score values applied to link reconstruction and link prediction in the four networks of fb-messages, ia-facebook, ia-contacts, and ia-retweet of the present invention. The experimental results show that the present invention has significant superiority compared with the classical algorithms.

[0100] By observing and comparing the example results, the following conclusions can be drawn:

[0101] (1) The present invention is based on dynamic network for representation learning, and its performance is significantly better than the other three static network representation learning methods: DeepWalk, LINE, and Node2vec. It shows that the learned low-dimensional representation can better reflect the evolution of the social network over time and is more in line with the characteristics of the real network, and the network evolution pattern provides richer information.

[0102] (2) Compared with the dynamic network representation learning method TNE, the present invention has better performance, indicating that by modeling and analyzing the triadic closure as the network evolution mechanism, the differences in the evolution patterns of different nodes in the social network can be captured, and the learned low-dimensional representation is more discriminative.

[0103] (3) Compared with the dynamic network representation learning method DynamicTriad, the present invention uses three important factors of the social network to enhance the triadic closure process, and combines the community structure in the network node representation to provide effective and rich information to supplement the local structure, so the performance is also improved.

[0104] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for learning dynamic social network representation, characterized in that, It includes the following steps: Step 1: Construct a dynamic network sequence. Based on a given set of time steps {1, 2, …, T}, for the social network data at a certain time step, construct a subgraph , ; Among them, is a set of nodes, representing users in the network; is a set of edges at the current time step, representing the relationships between users; is a set of weights, representing the connection strength between users; A dynamic network is a sequence composed of subgraphs at all time steps ; Step 2: Community division. According to the structure of the network, mark the community to which each node belongs. Since the dynamic network evolves over time, it is necessary to perform community division on the network at each time step. , ; Step 3: Preserve the network evolution characteristics based on the triadic closure process; for , where three users satisfying the following relationship form an open triple : User and do not know each other, but they have a common friend ; the common friend will decide whether to introduce and to know each other to make the open triple closed; the three main factors influencing his decision in this process are: user influence, user similarity, and community structure; Step 4: Retain the network structure features based on homogeneity and community structure. Nodes pairs connected according to homogeneity will be more closely embedded into the potential representation space; Step 5: Temporal smoothness. To maintain the smooth evolution of the dynamic network at each time step, a temporal smoothness loss function is constructed as follows: Among them, represents the node at the embedding vector at the time step, represents the Euclidean distance between the embedding vectors of the same node at adjacent time steps and ; Step 6: Combine the network evolution features and structural features for embedding to obtain the feature representation of each node; optimize the three loss functions and ; set the weight parameter of the global structure loss function to 1, and adopt two hyperparameters and to control the triadic closure process and temporal smoothness respectively; thus, for a given initial time step T, the overall optimization problem is as follows: Among them, and are normalization terms, set the latent space dimension to , and finally obtain the node embedding representation of the social network and the social strategy parameter ; represents the loss function that preserves homophily and community structure, represents the loss function of the triadic closure process, represents the loss function of temporal smoothness; two hyperparameters and are used to control the triadic closure process and temporal smoothness respectively, and T is the given total number of time steps; In step 3, user influence: If is a user with a relatively high influence in the social network, then the probability that he introduces and to know and establish connections at the next time step is relatively small; User similarity: When is similar to and it is more inclined to introduce and to recognize and establish a connection at the next time step, thus increasing the probability of open triple closure; Community structure: Compared with and being in the same community, it is obviously more effortful to introduce these two friends who belong to different communities, so the probability of closing an open triple is relatively small.

2. The dynamic social network representation learning method according to claim 1, wherein In the said Step 2, community information is obtained through the classic community discovery algorithm semi-synchronized LPA.

3. A method for learning the representation of a dynamic social network according to claim 1, characterized in that Making a decision can be quantified as follows: Among them, represents and at the weight of the time step, represents the degree of, is the embedding vector of the user ; and respectively represent the embedding vectors of nodes and at the time step; represents the influence of the indicated community structure. When and belong to the same community, that is, when the edge that may be generated in the future to be predicted does not cross different communities, ; otherwise, ; Then and under the influence of common friends the probability of generating a new edge at the next time step is: Among them is the set vector parameter, representing the social strategy information of the node; Since and may have multiple mutual friends in the network, by further assuming that the influence of each mutual friend on the potential link between and is independent, the probability that a new link is created at the next moment is Among them, , represents and in the set of common neighbors at the time step. If a link is generated due to the influence of common friends in the next time step, then the value of Accordingly, the probability of introducing a new link created at the next time step is: Define the set where represents the user and at time step successfully generated a link, the set represents the user and at time step did not generate a link.

4. A method for learning dynamic social network representation according to claim 3, characterized in that In the said Step 4, retain the network structure features, retain the network evolution features, and the loss function in the embedding training process is: Among them, represents the loss function of the triadic closure process, the probability that a new link will be created at the next moment, while represents the probability that the new link will not be created at the next moment; Set represents the user and at a link was successfully generated at the time step, the set represents the user and at a link was not generated at the time step.

5. A method for learning dynamic social network representation according to claim 1, characterized in that In the said Step 4, retain the network structure features, and the loss function in the embedding training process is: Among them, denotes all node pairs in denotes node and in the Euclidean distance in the latent space; for any real number, ; is the marginal value, defined as indicates the connection relationship of the node pair at the time step, indicating that when and are connected by an edge, ; Otherwise, .

6. A method for learning dynamic social network representation according to claim 1 or 5, characterized in that, In step 4, for any pair of nodes in the network: , it can be divided into the following four sets according to the link relationship and community structure: : vertex pairs that belong to the same community and are linked; : vertex pairs that belong to different communities and are linked; : vertex pairs that belong to the same community and have no links; : Vertex pairs that belong to different communities and have no links.

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