A link prediction method, system and storage medium for highly sparse mobile social networks
The graph autoencoder GAE and long short-term memory LSTM module extract features and timing features in strong sparse mobile social networks, solving the problem of low link prediction accuracy, achieving more efficient model learning and more accurate prediction results .
Patent Information
- Application Number
- CN202410620498.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-17
- Publication Date
- 2024-12-13
- Estimated Expiration
- 2044-05-17
AI Technical Summary
In the face of strong sparse mobile social networks, the accuracy of link prediction is affected, making it difficult to effectively reduce model learning costs and eliminate the negative impact of deep neural networks.
The graph autoencoder GAE is used to combine matrix aggregation module and long and short-term memory LSTM module to perform feature extraction and timing feature extraction through graph convolution network GCN to generate a predicted link map, and use multi-layer LSTM to learn timing sequence changes to balance positive and negative Sample proportions to improve prediction accuracy.
It reduces the cost of model learning, eliminates the negative impact of strong sparsity of mobile social networks on deep neural networks, and improves the accuracy of link prediction.
Smart Images
Figure CN118428547B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of link prediction, and in particular, relates to a link prediction method, system and storage medium for a highly sparse mobile social network. Background Art
[0002] With the continuous development of network science, various complex forms of networks have been introduced to describe specific real-world networks, such as the Internet, the Internet of Things, and mobile social networks. In general, real-world networks can be divided into two types: static networks and dynamic networks. Most existing real-world networks are dynamic networks, that is, nodes and links may appear or disappear over time. Predicting future links in dynamic networks is crucial because these links can reflect the potential spatiotemporal relationships between nodes, which can be exploited to implement many applications, such as anomaly detection and recommendation systems.
[0003] For the link prediction problem, how to improve the prediction accuracy remains a major concern. Link prediction methods with higher prediction accuracy can better analyze the evolution of dynamic networks and extract valuable information that is not easily perceived. For example, 80% of the interactions between yeast and proteins in molecular networks are difficult to know. If appropriate link prediction methods are used to predict interactions, the cost of biological experiments on molecular networks can be greatly reduced.
[0004] With the popularity of various mobile devices such as smartphones, laptops, and in-car mobile terminals, mobile social networks (MSNs) have emerged in the past few decades. MSNs are typical dynamic networks, and the relationships between nodes represent the communications between people, organizations, cities, and even countries. Due to the time-varying characteristics attached to these relationships, MSNs are highly dynamic and complex.
[0005] In MSNs, which are mainly composed of humans, link prediction technology can predict the relationships between humans or the communications between handheld devices. Specifically, these relationships reveal the social roles, habits, hobbies, and social tendencies of humans, through which convenient and personalized services can be provided. For example, by analyzing the future population density during peak hours of congested roads (obtained by predicting the relationships between humans), taxi drivers can pick up passengers more easily; on social media, by adapting to people's personalities or hobbies, it is easier to recommend potential friends to people; on online shopping platforms, by exploring customers' browsing history, products can be recommended more accurately. In short, accurate link prediction for MSNs can promote the consumption efficiency of social resources and facilitate people's lives.
[0006] With the development of deep learning methods, it is possible to explore the potential relationships hidden in the data by analyzing a large amount of redundant data, and these relationships can be applied to many practical scenarios, such as some applications of link prediction in mobile social networks. Link prediction refers to the process of predicting the potential relationships between nodes by exploring the evolution of historical network topology. The link prediction results can help to reasonably allocate resources and effectively reduce resource consumption. However, due to the appearance / disappearance of nodes and their links, the topological structure of mobile social networks often changes, and the links between nodes are usually sparse, which may seriously affect the accuracy of link prediction. Summary of the invention
[0007] The main purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and to provide a link prediction method, system and storage medium for highly sparse mobile social networks, which can reduce the cost of model learning, eliminate the negative impact of the strong sparsity of mobile social networks on deep neural networks, and improve the accuracy of link prediction.
[0008] According to one aspect of the present invention, the present invention provides a link prediction method for a strongly sparse mobile social network, the method comprising the following steps:
[0009] The encoder in the graph autoencoder GAE receives the input graph sequence of the mobile social network, performs feature extraction, and obtains a feature matrix;
[0010] The matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix;
[0011] The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE);
[0012] The decoder performs decoding to obtain a predicted link graph.
[0013] Preferably, the GAE uses a graph convolutional network GCN as an encoder, and the encoder performs the following operations to extract features:
[0014]
[0015]
[0016] Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of GCN, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively.
[0017] Preferably, the matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder:
[0018]
[0019] in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Z t represents the encoder output of the t-th snapshot, Represents the feature matrix after aggregation.
[0020] Preferably, the decoding performed by the decoder comprises:
[0021] The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network
[0022]
[0023] Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
[0024] According to another aspect of the present invention, the present invention further provides a link prediction system for a strongly sparse mobile social network, the system comprising a graph autoencoder GAE, a matrix aggregation module and a long short-term memory LSTM module, the graph autoencoder GAE comprising an encoder and a decoder;
[0025] The encoder in the graph autoencoder GAE receives an input graph sequence of a mobile social network, performs feature extraction, and obtains a feature matrix;
[0026] The matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix;
[0027] The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE);
[0028] The decoder performs decoding to obtain a predicted link graph.
[0029] Preferably, the GAE uses a graph convolutional network GCN as an encoder, and the encoder performs the following operations to extract features:
[0030]
[0031]
[0032] Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of GCN, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively.
[0033] Preferably, the matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder:
[0034]
[0035] in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Zt 表 shows the encoder output of the t-th snapshot, Represents the feature matrix after aggregation.
[0036] Preferably, the decoding performed by the decoder comprises:
[0037] The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network
[0038]
[0039] Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
[0040] According to another aspect of the present invention, the present invention also provides a link prediction system for a highly sparse mobile social network, the system comprising: a processor, a memory, the memory storing computer executable instructions, and the computer executable instructions implementing the above method steps when executed by the processor.
[0041] According to another aspect of the present invention, the present invention further provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions implement the above method steps when executed by a processor.
[0042] Beneficial effects: The present invention reduces the cost of model learning by extracting feature matrices through the graph autoencoder GAE; eliminates the negative impact of the strong sparsity of mobile social networks on deep neural networks by fusing the degree matrix and output matrix of the graph convolutional network GCN; and improves the link prediction accuracy by learning the changes in the time series of mobile social networks through a multi-layer long short-term memory LSTM network.
[0043] The features and advantages of the present invention will become clear through reference to the following drawings and detailed description of specific embodiments of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 It is a flow chart of the link prediction method for strongly sparse mobile social networks;
[0045] Figure 2 It is a schematic diagram of the link prediction system for strongly sparse mobile social networks. DETAILED DESCRIPTION
[0046] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the 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 creative work are within the scope of protection of the present invention.
[0047] Example 1
[0048] Figure 1 This is a flow chart of the link prediction method for strongly sparse mobile social networks. Figure 1As shown, this embodiment provides a link prediction method for a strongly sparse mobile social network, and the method includes the following steps:
[0049] S1: The encoder in the graph autoencoder GAE receives the input graph sequence of the mobile social network, performs feature extraction, and obtains a feature matrix;
[0050] S2: A matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix;
[0051] S3: The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE);
[0052] S4: The decoder performs decoding to obtain a predicted link graph.
[0053] Specifically, this method is based on the encounter matrix and the degree matrix, which can effectively handle high-dimensional and nonlinear networks. The real-time system of this method is composed of a graph autoencoder (GAE), a matrix aggregation module, and a multi-layer long short-term memory (LSTM). GAE uses the encounter matrix as the feature matrix of the node, which reduces the cost of model learning and improves the generation possibility of existing links in prediction. The fusion of the degree matrix and the output matrix of the graph convolutional network (GCN) can eliminate the negative impact of the strong sparsity of MSNs on deep neural networks. In addition, the multi-layer LSTM can learn the changes in the time series of MSNs, thereby improving the prediction accuracy.
[0054] First, the adjacency matrix sequence G corresponding to the production graph sequence is used as the input of the graph autoencoder of this method. In addition, the encounter matrix is used as the feature matrix, and the random negative sampling method is used to generate non-existent links (negative samples) to balance the actual existing links (positive samples). This method mainly alleviates the impact of data imbalance in three ways. First, by increasing the number of negative samples to balance the ratio of positive and negative samples, the learning algorithm is prevented from being overly biased towards the majority class; second, the computational efficiency is improved, because it is unrealistic to use all possible negative samples for training in extremely sparse networks; finally, random negative sampling increases the generalization ability of the model by introducing a wider range of negative situations, thereby increasing the possibility of future link generation and reducing training time.
[0055] This method can reduce the cost of model learning, eliminate the negative impact of the strong sparsity of mobile social networks on deep neural networks, and improve the accuracy of link prediction.
[0056] Preferably, the GAE uses a graph convolutional network GCN as an encoder, and the encoder performs the following operations to extract features:
[0057]
[0058]
[0059] Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of GCN, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively.
[0060] Specifically, GAE consists of an encoder and a decoder, which are responsible for extracting the features of the encounter matrix and outputting the adjacency matrix of the prediction results respectively. The LSTM module is located between the encoder and the decoder to extract the time-varying features of the encoder output.
[0061] The main function of the encoder is to extract the features of the encounter matrix and reduce the dimension of the features, thereby reducing the time required for the LSTM module to learn the time series features. However, the encoder cannot balance the number of positive and negative samples well to reduce the impact of strong sparsity on prediction accuracy. Therefore, DLMSS-LP uses the encounter matrix as the input of the encoder to make the corresponding value of the link (which may exist in the future) in the adjacency matrix of the prediction result close to 1, so as to minimize the impact of strong sparsity on prediction accuracy.
[0062] Preferably, the matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder:
[0063]
[0064] in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Z trepresents the encoder output of the t-th snapshot, Represents the feature matrix after aggregation.
[0065] Preferably, the decoding performed by the decoder comprises:
[0066] The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network
[0067]
[0068] Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
[0069] In this embodiment, the LSTM module is a type of RNN, which is used to solve the vanishing gradient problem in ordinary RNN. The LSTM unit consists of a forget gate, an input gate, and an output gate. The forget gate is based on h t-2 (the hidden state of the previous t-2 snapshot sequence) and x t-1 (input of the t-1th snapshot), {x t-N , x t-N+1 , ..., x t-1} means {G t-N , G t-N+1 , ..., G t-1}Snapshot sequence after dimensionality reduction.
[0070] The forget gate determines what information should be discarded from the LSTM cell state. The input gate determines what information should be stored in the LSTM cell state. t-1 Add to LSTM cell state C t-1 In, f t-1 Represents the forget gate output of the t-1th snapshot. The output gate determines which information should be output according to the LSTM unit state, and according to C t-1 and h t-2 Update t-1 .
[0071] Forgotten goalkeeper t-2 With x t-1 Combined and output a vector f t-1 , where f t-1 The value is in the interval [0, 1]. t-1 When the value of an element is equal to 1, C t-2 The elements at the corresponding positions are input into C t-1 On the contrary, when f t-1 If the value of an element is equal to 0, it means that it should be discarded in Ct-2 The elements at the corresponding positions. This process can be expressed as:
[0072] f t-1 =σ(W f ·[h t-2 , x t-1 ]+b f )
[0073] Among them, h t-1 represents the hidden state of the previous t-1 snapshot sequence, W f is the weight of the forget gate, b f is the bias of the forget gate, and σ is the activation function Sigmoid of the forget gate.
[0074] After that, x t-1 and h t-2 is transferred to the input gate. The input gate filters the t-1 and h t-2 The filtered information is used to update C t-1 . This process can be expressed as:
[0075] i t-1 =σ(W i ·[h t-2 , x t-1 ]+b i )
[0076]
[0077] Among them, i t-1 represents the output of the input gate in the t-1th snapshot, and Based on x t-1 and h t-2 When i t-1 When the value of an element is equal to 1, then The elements at the corresponding positions are input into C t-1 In. W i and W c I t-1 and The corresponding weight. Similarly, b i and b c Respectively with i t-1 and The corresponding bias, Represents the LSTM cell state of the previous t-1 snapshot sequence.
[0078] Then, the forget gate and input gate are based on and C t-2 Update cell status C t-1 :
[0079]
[0080] Finally, based on C t-1 and t-1 Calculate the hidden state h t-1 :
[0081] h t-1 =o t-1 tanh(C t-1 )
[0082] Among them t-1 represents the output of the output gate of the t-1th snapshot in , o t-1 =σ(W o ·[h t-2 , x t-1 ]+b o ), where W0 and b0 represent the weight and bias of the output gate. The gated recurrent unit (GRU) simplifies the model structure of LSTM. It has only two gates (update gate and reset gate), no independent cell state, and it merges the forget gate and input gate into a single update gate. Therefore, LSTM can theoretically capture longer sequence dependencies due to its more complex internal structure.
[0083] Finally, the output G of DLMSS-LP is t As the adjacency matrix of the t-th snapshot, the graph of the t-th snapshot is generated.
[0084] This embodiment extracts the feature matrix through the graph autoencoder GAE, thereby reducing the cost of model learning; by fusing the degree matrix and output matrix of the graph convolutional network GCN, the negative impact of the strong sparsity of the mobile social network on the deep neural network is eliminated; and by learning the changes in the time series of the mobile social network through a multi-layer long short-term memory LSTM network, the link prediction accuracy is improved.
[0085] Example 2
[0086] Figure 2 This is a schematic diagram of a link prediction system for highly sparse mobile social networks. Figure 2 As shown, this embodiment provides a link prediction system for a strongly sparse mobile social network, the system comprising a graph autoencoder GAE, a matrix aggregation module and a long short-term memory LSTM module, the graph autoencoder GAE comprising an encoder and a decoder;
[0087] The encoder in the graph autoencoder GAE receives an input graph sequence of a mobile social network, performs feature extraction, and obtains a feature matrix;
[0088] The matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix;
[0089] The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE);
[0090] The decoder performs decoding to obtain a predicted link graph.
[0091] Preferably, the GAE uses a graph convolutional network GCN as an encoder, and the encoder performs the following operations to extract features:
[0092]
[0093]
[0094] Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of GCN, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively.
[0095] Preferably, the matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder:
[0096]
[0097] in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Z t represents the encoder output of the t-th snapshot, Represents the feature matrix after aggregation.
[0098] Preferably, the decoding performed by the decoder comprises:
[0099] The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network
[0100]
[0101] Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
[0102] The specific implementation process of the functions realized by each module in this embodiment 2 is the same as the implementation process of each step in embodiment 1, and will not be repeated here.
[0103] Example 3
[0104] This embodiment provides a link prediction system for a highly sparse mobile social network, the system comprising: a processor and a memory, the memory storing computer executable instructions, the computer executable instructions implementing the method steps in Embodiment 1 when executed by the processor, the specific implementation process can refer to the implementation process of the method steps in Embodiment 1, which will not be repeated here.
[0105] Example 4
[0106] This embodiment provides a computer-readable storage medium, which stores computer-executable instructions. When the computer-executable instructions are executed by a processor, the method steps in Embodiment 1 are implemented. The specific implementation process can refer to the implementation process of the method steps in Embodiment 1, which will not be repeated here.
[0107] It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0108] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1A function specified in one or more boxes.
[0109] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.
[0110] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.
Claims
1. A link prediction method for strongly sparse mobile social networks, characterized in that: The method comprises the following steps: The encoder in the graph autoencoder GAE receives the input graph sequence of the mobile social network, performs feature extraction, and obtains a feature matrix; The matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix; The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE); The decoder performs decoding to obtain a predicted link graph; The GAE uses a graph convolutional network (GCN) as an encoder, which performs the following operations for feature extraction: Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form of express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of the encoder of the t-th snapshot, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively; The matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder: in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Z t represents the output of the encoder for the t-th snapshot, Represents the feature matrix after aggregation.
2. The method according to claim 1, characterized in that The decoding by the decoder comprises: The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
3. A link prediction system for strongly sparse mobile social networks, characterized in that: The system includes a graph autoencoder GAE, a matrix aggregation module and a long short-term memory LSTM module, and the graph autoencoder GAE includes an encoder and a decoder; The encoder in the graph autoencoder GAE receives an input graph sequence of a mobile social network, performs feature extraction, and obtains a feature matrix; The matrix aggregation module aggregates the feature matrix output by the encoder and the degree matrix of the graph sequence to obtain an aggregated feature matrix; The long short-term memory (LSTM) module receives the aggregated feature matrix output by the matrix aggregation module, extracts time series features, and inputs the extracted time series features into the decoder in the graph autoencoder (GAE); The decoder performs decoding to obtain a predicted link graph; The GAE uses a graph convolutional network (GCN) as an encoder, which performs the following operations for feature extraction: Among them, A t represents the adjacency matrix in the t-th snapshot, I N represents the identity matrix of dimension N×N, Indicates A t The transitional form of express The degree matrix of yes The transitional form, W (0) represents the weight of the first layer of GCN, W (1) represents the weight of the second layer of GCN, Z t ReLU represents the output of the encoder of the t-th snapshot, and Softmax is the activation function of the first layer GCN and the second layer GCN respectively; The matrix aggregation module uses a linear layer and a Softmax function to aggregate the feature matrix and degree matrix output by the encoder: in, and Denotes the weights and biases of the linear layer, D t represents the degree matrix of the t-th snapshot, D t -1 Indicates D t The inverse matrix, Z t represents the encoder output of the t-th snapshot, Represents the feature matrix after aggregation.
4. The system according to claim 3, characterized in that The decoding by the decoder comprises: The decoder processes the feature matrix output by the LSTM module to obtain the adjacency matrix of the final prediction network Among them t represents the LSTM module output of the t-th snapshot in , Indicates o t The transpose of .
5. A link prediction system for strongly sparse mobile social networks, characterized in that: The system comprises: a processor and a memory, wherein the memory stores computer executable instructions, and when the computer executable instructions are executed by the processor, the method according to any one of claims 1 to 2 is implemented.
6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, the method according to any one of claims 1 to 2 is implemented.