Network Topology Inference Method, System, Device and Medium

Abstract

The present invention discloses a network topology inference method, system, device and medium. The inference method includes obtaining dynamic network data; sorting all links in the dynamic network data by time, and dividing all the time-sorted links by using a window to generate continuous snapshots; constructing a sample data set with continuous Q snapshots as a sample; constructing a network topology inference model; wherein, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module and an output layer; training and testing the network topology inference model by using the sample data set to obtain a target network topology inference model; and performing network topology inference by using the target network topology inference model. The present invention improves the accuracy and efficiency of network topology inference.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication network topology perception, and in particular relates to an end-to-end network topology reasoning method, system, device and medium for realizing the inference of topology structure in a dynamic communication network. Background Art

[0002] The research on topology inference in communication networks has attracted significant attention and achieved remarkable success. For example, topology inference can be used to infer the topology of the physical layer of the network, thereby optimizing resource allocation, improving traffic prediction and fault detection capabilities, and identifying key nodes. However, topology inference in dynamic communication networks still faces two key challenges:

[0003] (1) Frequent topology shifts caused by node mobility: Network topology is not static. The mobility of network nodes causes the network topology to change over time, which may affect the accuracy of traditional topology reasoning methods.

[0004] (2) Traditional statistical methods depend on manual calibration: Most topological inference methods are based on statistical analysis and require manual intervention, making them unsuitable for practical applications. These dynamic changes increase computational overhead and labor costs, because frequent manual adjustments not only place high demands on human expertise, but also increase the burden on hardware resources.

[0005] Therefore, the change of network topology over time not only affects the inference accuracy, but also leads to excessive consumption of human and computing resources.

[0006] Topological reasoning refers to the process of inferring the topological relationship between nodes through data analysis based on the collected observation data. Existing topological reasoning methods are mainly based on time series analysis techniques of statistical tools, such as transfer entropy, Granger causality, and Hawkes processes. However, these methods are too dependent on the collected data and are therefore not suitable for topological reasoning in dynamic communication networks.

[0007] With the rapid development of dynamic network link prediction, it has shown great potential in the topological reasoning problem in dynamic communication networks. Dynamic network link prediction involves analyzing and modeling historical interaction data between network nodes to predict potential future links or relationships. By capturing the temporal dependencies between network nodes, it can more accurately reflect the evolution of node connection relationships over time, thus providing strong help in solving the topological reasoning challenges in dynamic networks. Summary of the invention

[0008] The object of the present invention is to provide a network topology inference method, system, device and medium, so as to solve the problems that the topology inference accuracy is poor due to the change of network nodes over time, the calculation overhead and cost are increased, and the real-time and effectiveness requirements of dynamic network topology inference cannot be met.

[0009] The present invention solves the above technical problems through the following technical solutions: A network topology inference method, comprising:

[0010] Obtain dynamic network data;

[0011] Sort all the links in the dynamic network data according to time, and divide all the time-sorted links by using a window to generate continuous snapshots; wherein, the link refers to the edge between two nodes;

[0012] Construct a sample data set with continuous Q snapshots as a sample; wherein, the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label;

[0013] Construct a network topology inference model; wherein, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module and an output layer; the node feature extraction module is used to extract node features from each input snapshot to obtain the node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of continuous Q - 1 snapshots to obtain a fusion feature matrix; the temporal information extraction module is used to extract temporal information from the fusion feature matrix to obtain an intermediate feature matrix; the output layer is used to predict the intermediate feature matrix to obtain a predicted adjacency matrix;

[0014] Train and test the network topology inference model by using the sample data set to obtain a target network topology inference model;

[0015] Perform network topology inference by using the target network topology inference model.

[0016] Furthermore, the node feature extraction module is used to extract node features from each input snapshot, specifically including:

[0017] Use the Node2Vec algorithm to extract node features from each input snapshot, and the specific formula is:

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] Among them, represents the random walk probability between the i-th node and the j-th node in the snapshot; represents the number of links experienced between the i-th node and the j-th node in the snapshot; p and q represent parameters for controlling the exploration steps; represents that the number of nodes is and the number of links is of the snapshot; RandomWalk represents the random walk algorithm; represents the walk sequence starting from the node ; Word2vec represents the word embedding algorithm; represents the word embedding vector; Concat represents concatenating the word embedding vectors row by row; C represents the node feature matrix of the snapshot.

[0023] Furthermore, the spatial evolution information extraction module includes a plurality of multi-head graph attention networks connected in sequence and an ordinary differential equation module provided at the output end of the plurality of multi-head graph attention networks;

[0024] Each multi-head graph attention network is used to extract features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot to obtain the discrete spatial feature matrix of this multi-head graph attention network; among them, the first multi-head graph attention network is used to extract features from the node feature matrix and the adjacency matrix of each snapshot to obtain the discrete spatial feature matrix of the first multi-head graph attention network;

[0025] The ordinary differential equation module is used to perform continuous spatial feature extraction on the discrete spatial feature matrices output by the plurality of multi-head graph attention networks to obtain a spatial evolution feature sequence.

[0026] Furthermore, each multi-head graph attention network is used to extract features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot, and the specific formula is:

[0027] , ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] Among them, represents the matrix obtained by performing a linear transformation on the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; C represents the node feature matrix of the snapshot; represents the trainable weight parameter; represents the attention coefficient of the k-th attention head; LeakyReLU represents the leaky rectified linear unit; represents the adjacency matrix of the snapshot; the superscript T represents the matrix transpose; represents the matrix the feature vector of the i-th node in; represents the matrix the feature vector of the j-th node in; represents the concatenation symbol; represents the normalized attention coefficient of the k-th attention head; N i represents the matrix the set of neighbor nodes of the i-th node in; represents the feature matrix updated by the k-th attention head; ELU represents the exponential linear unit; represents the discrete spatial feature matrix output by the m-th multi-head graph attention network; K represents the number of attention heads in each multi-head graph attention network.

[0033] Furthermore, the ordinary differential equation module is used to extract continuous spatial features from the discrete spatial feature matrices output by multiple multi-head graph attention networks. The specific formula is:

[0034] ;

[0035] ;

[0036] ;

[0037] Among them, represents the attention calculation function of the m-th multi-head graph attention network; K represents the number of attention heads in the m-th multi-head graph attention network; N i represents the matrix the set of neighbor nodes of the i-th node in; represents the matrix obtained by performing a linear transformation on the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; represents the normalized attention coefficient of the k-th attention head in the m-th multi-head graph attention network; represents the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; Represents a trainable parameter tensor; Represents the discrete spatial feature matrix output by the m-th multi-head graph attention network; Represents an ordinary differential equation; M represents the number of multi-head graph attention networks; Represents a composite operator; Represents a non-linear activation function; Represents the sequence of spatial evolution features of the snapshot; Represents the initial feature vector; Represents the granularity of solving the ordinary differential equation; Represents the granularity variable; Represents the -th discrete spatial feature matrix output by the multi-head graph attention network.

[0038] Furthermore, the temporal information extraction module includes multiple LSTM units. Each LSTM unit is used to extract features from the normalization result of the current moment hidden state output by the previous LSTM unit to obtain the current moment hidden state of this LSTM unit; the first LSTM unit is used to extract features from the fused feature matrix to obtain the current moment hidden state of the first LSTM unit; the current moment hidden state output by the last LSTM unit is the intermediate feature matrix;

[0039] Among them, the specific calculation formula for the normalization result of the current moment hidden state output by each LSTM unit is:

[0040] ;

[0041] Among them, Represents the current moment hidden state output by the LSTM unit; Represents the normalization result of the current moment hidden state output by the LSTM unit; And Respectively represent the scaling factor and the offset factor; And Respectively represent the mean and variance of the current moment hidden state ; Represents a constant used to prevent division by zero errors.

[0042] Furthermore, training the network topology inference model using the sample data set specifically includes:

[0043] Input the first Q - 1 snapshots of each sample and their adjacency matrices into the network topology inference model to obtain the predicted adjacency matrix of the network topology inference model;

[0044] Calculate the loss error between the predicted adjacency matrix and the expected label of the sample. The specific calculation formula is:

[0045] ;

[0046] wherein, represents the loss error; N e represents the number of links of the predicted adjacency matrix or the expected label, including existing and non-existing links; V represents the set of nodes of the predicted adjacency matrix or the expected label; represents the probability that there is a link between the i-th node and the j-th node in the expected label; represents the probability that there is a link between the i-th node and the j-th node in the predicted adjacency matrix;

[0047] Adjust the parameters of the network topology inference model according to the loss error to implement the training of the network topology inference model;

[0048] Iteratively train until the training termination condition is reached.

[0049] Based on the same concept, the present invention also provides a network topology inference system, including:

[0050] An acquisition unit configured to acquire dynamic network data;

[0051] A snapshot generation unit configured to sort all the links in the dynamic network data by time, and divide all the time-sorted links by a window to generate continuous snapshots; wherein, the link refers to an edge between two nodes;

[0052] A dataset construction unit configured to construct a sample dataset with continuous Q snapshots as a sample; wherein, the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label;

[0053] A model construction unit configured to construct a network topology inference model; wherein, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module, and an output layer; the node feature extraction module is used to extract node features from each input snapshot to obtain a node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and the adjacency matrix of each snapshot to obtain a spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of continuous Q - 1 snapshots to obtain a fused feature matrix; the temporal information extraction module is used to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer is used to predict the predicted adjacency matrix from the intermediate feature matrix;

[0054] A training unit, configured to train and test the network topology inference model by using the sample data set to obtain a target network topology inference model;

[0055] An inference unit, configured to perform network topology inference by using the target network topology inference model.

[0056] Based on the same concept, the present invention further provides an electronic device, including a memory, a processor, and a computer program / instruction stored on the memory, and the processor executes the computer program / instruction to implement the network topology inference method as described above.

[0057] Based on the same concept, the present invention further provides a computer-readable storage medium, on which a computer program / instruction is stored, and when the computer program / instruction is executed by a processor, the network topology inference method as described above is implemented.

[0058] Compared with the prior art, the advantages of the present invention are as follows:

[0059] The present invention first captures the structural semantics of the network topology by extracting node features from snapshots, then uses a spatial evolution information extraction module to capture fine-grained spatial evolution features, and finally uses a temporal information extraction module to learn the long-term dependencies between network topologies, enabling topology inference in a dynamic communication network and improving the accuracy of topology inference; the present invention does not require manual intervention, reduces labor costs, and improves the real-time performance of topology inference;

[0060] Compared with traditional statistical analysis methods, the present invention uses a deep learning method for topology inference, and the required amount of data and hardware resources are relatively small; at the same time, the present invention uses a graph embedding algorithm to convert high-dimensional graph structure data into low-dimensional embedding vectors and fully utilizes a normalization layer in the temporal information extraction module to further reduce the computational complexity and reduce the computing resources. Description of the Drawings

[0061] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present invention, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0062] Figure 1 is a flowchart of the network topology inference method in an embodiment of the present invention;

[0063] Figure 2 is a schematic diagram of generating continuous snapshots in an embodiment of the present invention;

[0064] Figure 3It is the overall architecture diagram of the network topology inference model in the embodiments of the present invention;

[0065] Figure 4 It is the ER performance fluctuation curve of the inference results of different models on the Contact dataset in the embodiments of the present invention;

[0066] Figure 5 It is the ER performance fluctuation curve of the inference results of different models on the Hypertext09 dataset in the embodiments of the present invention;

[0067] Figure 6 It is the ER performance fluctuation curve of the inference results of different models on the Radoslaw dataset in the embodiments of the present invention;

[0068] Figure 7 It is the ER performance fluctuation curve of the inference results of different models on the Fbforum dataset in the embodiments of the present invention. Detailed implementation manners

[0069] Next, with reference to the accompanying drawings in the embodiments of the present invention, the technical solutions in the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention.

[0070] Next, the technical solutions of the present application will be described in detail with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0071] Embodiment 1

[0072] In a complex network topology, network nodes may have mobility, resulting in the network topology changing over time. Most topology inference methods are mainly based on statistical analysis, involving multiple threshold decisions that require manual intervention (such as F-test thresholds, adjacency matrices, and Neyman-Pearson criteria). However, due to the time variability of the network topology, manual threshold adjustment becomes tricky in a dynamic network, affecting not only the accuracy of network topology inference but also the inference efficiency. Based on the above technical problems, the present invention provides a network topology inference method, which realizes the inference of the network topology through node feature extraction, spatial evolution feature extraction, and temporal information extraction, improving the inference accuracy and inference efficiency.

[0073] Figure 1 Illustrates the flowchart of the network topology inference method provided by the present invention. As Figure 1 shown, the network topology inference method of the present invention includes the following steps:

[0074] Step S1: Obtain dynamic network data.

[0075] Use publicly available datasets as the dynamic network data in the embodiments of the present invention. The datasets in this embodiment include Contact, Hypertext09, Radoslaw, and Fbforum. These datasets communicate in different ways, such as mobile phones, emails, etc. The detailed information of each dataset is shown in Table 1.

[0076] In Table 1, represents the number of nodes, V represents the node set, represents the number of links, E represents the link set, represents the average degree of nodes, represents the maximum degree of nodes. Among them, a link refers to an edge between two nodes.

[0077] Step S2: Sort all the links in the dynamic network data by time, and divide all the time-sorted links using a window to generate consecutive snapshots.

[0078] For each dataset, arrange all the links in the dataset in chronological order, and divide all the chronologically arranged links using a time window to generate a series of consecutive snapshots, as Figure 2 shown.

[0079] Step S3: Construct a sample dataset with consecutive Q snapshots as one sample.

[0080] To obtain sufficient samples, the present invention takes consecutive Q snapshots as one sample. Among them, the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label. The adjacency matrix of a snapshot is a matrix representing the adjacent relationship between nodes in the snapshot. When there is a link between two nodes, the corresponding element in the adjacency matrix takes 1; when there is no link between two nodes, the corresponding element in the adjacency matrix takes 0. In this embodiment, Q is set to 11, that is, the first 10 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the 11th snapshot in each sample is used as the expected label.

[0081] The sample dataset is divided into a training set and a test set in a ratio of 3:1. The training set is used to train the network topology inference model, and the test set is used to test the trained network topology inference model.

[0082] Step S4: Construct a network topology inference model.

[0083] As Figure 3As shown in the figure, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module, and an output layer. The node feature extraction module is used to extract node features from each input snapshot to obtain the node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and the adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of consecutive Q-1 snapshots to obtain a fused feature matrix; the temporal information extraction module is used to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer is used to predict the intermediate feature matrix to obtain a predicted adjacency matrix. Figure 3 In, G1, G2, …, G Q-1 represents the first Q-1 snapshots of each sample, A1, A2, …, A Q-1 represents the adjacency matrix of the first Q-1 snapshots of each sample, y1, y2, …, y Q-1 represents the spatial evolution feature sequence of the first Q-1 snapshots of each sample, represents the predicted adjacency matrix, represents the predicted snapshot.

[0084] To effectively extract spatial evolution information from each snapshot, the node feature extraction module is first used to extract node features from each snapshot, that is, the embedding expression of the node. In a specific embodiment of the present invention, the Node2Vec algorithm is used to perform the embedding expression of the node for each snapshot. The Node2Vec algorithm is a graph embedding technology that fully combines the random walk algorithm (RandomWalk) and the word embedding algorithm (Word2vec), and can effectively express the semantic structure inside the network topology. In particular, the random walk algorithm in the Node2Vec algorithm also introduces breadth-first sampling (Broad-first Sampling) and depth-first sampling (Depth-first Dampling) to achieve a more flexible walking strategy. For a snapshot with the number of nodes being and the number of links being for a pair of nodes i and j, the specific calculation process of feature extraction is as follows:

[0085] (1)

[0086] (2)

[0087] (3)

[0088] (4)

[0089] wherein, represents the random walk probability between the i-th node and the j-th node in the snapshot; represents the number of links experienced between the i-th node and the j-th node in the snapshot; p and q represent parameters for controlling the exploration steps; represents a random walk sequence starting from the node ; Word2vec represents a word embedding algorithm; ; represents the word embedding vector; Concat represents concatenating the word embedding vectors row by row; C represents the node feature matrix of the snapshot; represents the number of nodes in the snapshot. Each node in the snapshot can be used as a starting node, so the number of random walk sequences is equal to the number of nodes in the snapshot, and the number of word embedding vectors is equal to the number of nodes in the snapshot. The parameters p and q are determined according to the network scale. Exemplarily, for a small-scale network (e.g., the number of nodes is less than or equal to 1000), p is set to 0.5 and q is set to 2; for a large-scale network (e.g., the number of nodes is greater than 1000), p is set to 1 and q is set to 1.5.

[0090] In order to further learn the local and global dependencies between nodes, the spatial evolution information extraction module extracts spatial evolution information from the node feature matrix and the adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot. In the specific implementation manner of the present invention, the spatial evolution information extraction module includes a plurality of multi-head graph attention networks (Graph Attention Networks, GAT) connected in sequence and an ordinary differential equation module (Ordinary Differential Equations, ODE) provided at the output end of the plurality of multi-head graph attention networks. By attentively weighting and aggregating neighbor information, the node features are gradually optimized, and at the same time, the ODE is introduced to improve the GAT so that it can capture fine-grained spatial evolution features.

[0091] Each multi-head graph attention network extracts features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot to obtain the discrete spatial feature matrix of this multi-head graph attention network; the first multi-head graph attention network extracts features from the node feature matrix and the adjacency matrix of each snapshot to obtain the discrete spatial feature matrix of the first multi-head graph attention network; the ordinary differential equation module performs continuous spatial feature extraction on the discrete spatial feature matrices output by the plurality of multi-head graph attention networks to obtain the spatial evolution feature sequence.

[0092]

[0093] ​In each multi - head graph attention network, the discrete spatial feature matrix (or node feature matrix) first undergoes a linear transformation, and then the attention mechanism is applied to calculate the attention coefficients between each pair of nodes and normalize them to ensure that the model can selectively focus on the important information between nodes. Finally, the coefficients obtained from the multi - head attention mechanism are non - linearly activated and averaged to obtain the final discrete spatial feature matrix. The specific calculation process is as follows:

[0094] , (5)

[0095] (6)

[0096] (7)

[0097] (8)

[0098] (9)

[0099] where, represents the matrix obtained by linearly transforming the discrete spatial feature matrix output by the (m - 1) - th multi - head graph attention network; represents the trainable weight parameter; represents the attention coefficient of the k - th attention head; LeakyReLU represents the leaky rectified linear unit; represents the adjacency matrix of the snapshot; the superscript T represents the matrix transpose; represents the matrix the feature vector of the i - th node in (i.e., the i - th row in the matrix ); represents the matrix the feature vector of the j - th node in; represents the concatenation symbol; represents the normalized attention coefficient of the k - th attention head; N i represents the set of neighbor nodes of the i - th node in the matrix ; represents the feature matrix updated by the k - th attention head; ELU represents the exponential linear unit; represents the discrete spatial feature matrix output by the m - th multi - head graph attention network; K represents the number of attention heads in each multi - head graph attention network.

[0100] Similar to traditional neural network architectures, graph attention networks propagate hidden layer states through discrete computational steps. This discrete propagation method essentially limits the extraction of continuous space features and makes it difficult to capture the continuous evolution process of node interactions in dynamic networks. Therefore, the present invention also introduces ordinary differential equations and utilizes their continuous characteristics to improve graph attention networks, enabling them to track the dynamic evolution process and capture fine-grained spatial evolution features in snapshots. Through the ordinary differential equation module, spatial evolution feature representations can be obtained at any granularity, thereby ensuring the continuity of node hidden layer states.

[0101] The ordinary differential equation module performs continuous space feature extraction on the discrete space feature matrices output by multiple multi-head graph attention networks. The specific formula is:

[0102] (10)

[0103] (11)

[0104] (12)

[0105] Among them, represents the attention calculation function of the m-th multi-head graph attention network; represents the discrete space feature matrix output by the (m - 1)-th multi-head graph attention network; represents the trainable parameter tensor; represents the discrete space feature matrix output by the m-th multi-head graph attention network; represents the ordinary differential equation; M represents the number of multi-head graph attention networks; represents the composition operator; represents the non-linear activation function; represents the spatial evolution feature sequence of the snapshot; represents the initial feature vector; represents the granularity of the ordinary differential equation solution; represents the granularity variable; represents the th discrete space feature matrix output by the multi-head graph attention network.

[0106] To fuse the evolution information from different snapshots, the fusion module performs element-wise addition on the spatial evolution feature sequences of the first Q - 1 snapshots of each sample. The specific formula is:

[0107] (13)

[0108] Among them, represents the fused feature matrix, represents the spatial evolution feature sequence of the k-th snapshot.

[0109] Considering the time dependence between network topologies, the present invention uses a temporal information extraction module to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix. In a specific embodiment of the present invention, the temporal information extraction module employs stacked Long Short-Term Memory (LSTM) modules, specifically including a plurality of LSTM cells. Each LSTM cell extracts features from the normalized result of the hidden state at the current moment output by the previous LSTM cell to obtain the hidden state of the current moment of this LSTM cell; the first LSTM cell extracts features from the fused feature matrix to obtain the hidden state of the current moment of the first LSTM cell; the hidden state of the current moment output by the last LSTM cell is the intermediate feature matrix.

[0110] As a variant of RNN, LSTM is specifically designed to capture long-term dependencies across snapshots, thus enabling effective modeling of time-varying features. Each LSTM cell mainly consists of a forget gate, an input gate, and an output gate. The specific calculation process of the first LSTM cell includes:

[0111] (14)

[0112] (15)

[0113] (16)

[0114] (17)

[0115] (18)

[0116] (19)

[0117] Among them, and represent learnable weight parameters, and represent biases; and represent the forget gate, the input gate, and the output gate respectively, and represent the hidden state at the previous moment and the hidden state at the current moment respectively, represents the candidate cell state, and represent the cell state at the previous moment and the cell state at the current moment respectively, and represent the Sigmoid and hyperbolic tangent activation functions respectively.

[0118] To prevent overfitting during training and improve the convergence speed of the model, the hidden state at the current moment output by each LSTM cell is normalized and then input into the next LSTM cell. The specific formula for the normalization process is:

[0119] (20)

[0120] where, represents the normalization result of the hidden state at the current moment output by the LSTM cell; and represent the scaling factor and the offset factor respectively; and represent the mean and variance of the hidden state at the current moment respectively; represents a constant used to prevent division-by-zero errors. For the 2nd to the last LSTM cell, its specific calculation process is similar to that of the 1st LSTM cell, only replacing the fused feature matrix with the normalization result of the hidden state at the current moment output by the previous LSTM cell.

[0121] In the specific embodiment of the present invention, the output layer adopts two layers of MLP (Multilayer Perceptron). The first layer uses the ReLU activation function to accelerate the model convergence, and the second layer uses the Sigmoid activation function to deduce the network connection state matrix of the next snapshot, that is, to predict the adjacency matrix.

[0122] The specific calculation formula of the output layer is:

[0123] (21)

[0124] (22)

[0125] where, represents the normalization result of the hidden state at the current moment output by the last LSTM cell; and represent the weight parameters; and represent the biases; represents the hidden state at the next moment; represents the predicted adjacency matrix.

[0126] Step S5: Use the sample data set to train and test the network topology inference model to obtain the target network topology inference model.

[0127] In a specific embodiment of the present invention, the network topology inference model is trained using a sample data set, which specifically includes:

[0128] Step S5.1: Input the first Q - 1 snapshots of each sample and their adjacency matrices into the network topology inference model to obtain the predicted adjacency matrix of the network topology inference model.

[0129] Specifically, the node feature extraction module extracts node features from each of the first Q - 1 snapshots to obtain the node feature matrix of each snapshot; the spatial evolution information extraction module extracts spatial evolution information from the node feature matrix and adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot; the fusion module fuses the spatial evolution feature sequences of the first Q - 1 snapshots to obtain a fused feature matrix; the temporal information extraction module extracts temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer makes a prediction on the intermediate feature matrix to obtain the predicted adjacency matrix.

[0130] Step S5.2: Calculate the loss error between the predicted adjacency matrix and the expected label of the sample. The specific calculation formula is:

[0131] (23)

[0132] where represents the loss error; N e represents the number of links in the predicted adjacency matrix or the expected label, including existing and non - existing links (or edges); V represents the set of nodes in the predicted adjacency matrix or the expected label; represents the probability that there is a link between the i - th node and the j - th node in the expected label. When there is a link between the i - th node and the j - th node in the expected label, takes the value of 1, otherwise 0; represents the probability that there is a link between the i - th node and the j - th node in the predicted adjacency matrix.

[0133] Step S5.3: Adjust the parameters (i.e., weight parameters, parameter tensors, biases, etc.) of the network topology inference model according to the loss error to achieve the training of the network topology inference model.

[0134] Step S5.4: Determine whether the training termination condition is reached. If so, stop the training; otherwise, repeat steps S5.1 to S5.4.

[0135] In this embodiment, the training termination condition is that the number of iterations reaches the set maximum number of iterations.

[0136] Input the samples in the test set into the trained network topology inference model for network topology inference, output the inference results, and then analyze each evaluation metric in the inference results by comparing with the baseline method.

[0137] The evaluation metrics in this embodiment include AUC (Area Under the Curve), GMAUC, and Error Rate (ER). The Error Rate (ER) can intuitively reflect the accuracy of topology inference. For AUC and GMAUC, higher values indicate better performance, while for ER, lower values indicate better performance.

[0138] GMAUC combines PRAUC (Precision-Recall AUC) and AUC and is calculated in the form of a geometric mean. The specific calculation formula is:

[0139] (24)

[0140] where L A and L R represent the number of newly added links and the number of removed links respectively; represents the PRAUC value calculated for the newly added links, represents the AUC value of the observed links.

[0141] ER fully combines the network scale and SHD to measure the inference accuracy of different network topologies. SHD represents the Hamming distance, which is a commonly used evaluation metric in causal models. The specific calculation formula is:

[0142] (25)

[0143] where N e represents the number of links in the network topology, represents the true positive, represents the false positive. Considering the interactivity between nodes in the communication network, when calculating SHD, the expected label and the predicted adjacency matrix are first symmetrized. Therefore, the calculation formula of ER is:

[0144] (26)

[0145] where represents the number of nodes in the network topology.

[0146] To verify the superiority of the target network topology inference model of the present invention (i.e., the GAE-LSTMs model), it is compared with a series of advanced dynamic link prediction methods, including methods based on matrix factorization and deep learning methods. Specifically, there are mainly the following five baseline methods.

[0147] (1) GrNMF is a temporal link prediction algorithm that combines graph structure with non - negative matrix factorization to achieve link prediction;

[0148] (2) GCN - GAN combines the generative adversarial network (GAN) with the graph convolutional network (GCN). It uses the generative ability of GAN to generate new graph structures, while GCN is used to extract effective representations from the graph structure;

[0149] (3) Dyngraph2vec adopts a fully - connected encoder before the LSTM network to obtain low - dimensional hidden representations, thereby reducing model parameters and achieving more efficient temporal link learning;

[0150] (4) STGSN is designed specifically for dynamic graphs, combining the graph convolutional network with the time network to effectively process spatio - temporal information;

[0151] (5) T - SIRGN is a deep - learning model for time - link prediction, which combines time modeling to capture the characteristics of the changing graph structure over time.

[0152] To ensure fair comparison, the data processing and training methods involved in all baseline methods are consistent with the GAE - LSTMs model. Since the evolution pattern of the dynamic network may change over time, the present invention divides the test set into the first 25% of the samples and the entire 100% of the samples to verify the short - term (timeliness) and long - term (scalability) inference performance of the model respectively, and reports the average results separately. All baseline methods select the recommended parameter settings. Specifically, for GrNMF, the hidden space sizes corresponding to the Contact, Fbforum, Hypertext09, and Radoslaw datasets are set to 128, 256, 128, and 128 respectively. For GAE - LSTMs, a rolling test procedure is adopted during the experiment, which means that training and testing are carried out alternately. In addition, GAE - LSTMs uses a grid - search algorithm to automatically select parameters. The detailed parameter settings are shown in Table 2, where, represents the hidden - layer setting in GAT, represents the hidden - layer setting in LSTMs, represents the output - layer size setting.

[0153] GrNMF is implemented in Python. Other methods are implemented using PyTorch. All experiments are carried out on a workstation equipped with an Intel Xeon Gold - 6326@2.90GHz CPU, 512GB of memory, and an NVIDIA A100 GPU (with 80G of memory).

[0154] On the first 25% and the entire 100% of the test set, the present invention takes the average result of 10 random runs as the final experimental result, as shown in Tables 3, 4 and 5. It can be observed from Tables 3 to 5 that the present invention performs best on most datasets and achieves the second-best results on the remaining datasets.

[0155] The GAE-LSTMs model performs best on most evaluation metrics of the four datasets. Except for the GAE-LSTMs model, according to the AUC score, Dyngraph2vec achieves the second-best results on most datasets, especially significantly outperforming the other four baseline methods on the Contact dataset and slightly exceeding the method of the present invention. This indicates that using a fully connected encoder can effectively capture the structural information of the graph. At the same time, T-SIRGN shows competitiveness in terms of the GMAUC score and ER, which may be because T-SIRGN focuses more on capturing the temporal information between graphs. However, the present invention achieves the best results on most metrics, which indicates that from the perspective of spatial evolution, the present invention can effectively learn dynamic changes during the structure learning process and capture sufficient potential evolution information.

[0156] Compared with other methods, the GAE-LSTMs model demonstrates strong stability and generalization ability. By comparing the performance of the first 25% data and the entire 100% data in the test set, it can be found that the performance of the GAE-LSTMs model fluctuates less and all achieve good results, which indicates that the present invention has excellent and stable inference ability. In addition, it can also be found that the performance of short-term inference is slightly higher than that of long-term inference. In contrast, the results of other methods do not follow the same trend. For example, compared with its performance on the first 25% test set, the AUC score of Dyngraph2vec on the entire Fbforum test set drops by 5.01%, indicating that the model performs well in short-term prediction but has weak generalization ability due to overfitting problems. On the contrary, the AUC score of STGSN on the entire Hypertext09 test set is 3.13% higher than that on the first 25% test set, which may be due to underfitting problems during the training process. Therefore, the GAE-LSTMs model has both high accuracy and low bias, further demonstrating its stability.

[0157] The number of nodes in the network topology affects the difficulty of extracting potential features from link information. For example, the AUC score of Dyngraph2vec on the Contact dataset (containing 274 nodes) is 97.83%, but it drops to 82.59% on the Fbforum dataset (containing 899 nodes). This indicates that as the network scale grows, it becomes increasingly difficult to extract potential features and maintain satisfactory performance. However, the present invention always exhibits stable performance, with an AUC score of no less than 94% on most datasets, and even reaching 94.09% on the Fbforum dataset. This further proves the superiority of the present invention.

[0158] To study the impact of network change frequency on the model prediction performance, the present invention divides four datasets into snapshots according to different time windows to simulate different network change frequencies, and selects T-SIRGN and STGSN as comparison methods. To ensure the reliability of the experimental results, the present invention conducts 10 independent runs for each time window and takes the average as the final result. At the same time, the performance fluctuation curves of ER corresponding to each dataset are plotted in Figures 4 to 7 The results show that the GAE-LSTMs model outperforms the baseline methods and has more stable performance on the four datasets, which also verifies the robustness of the GAE-LSTMs model of the present invention. Specifically, on the Contact dataset, the ER fluctuation range of the GAE-LSTMs model is from 2% to 3%, while its performance on other datasets is still excellent, with a fluctuation range between 4% and 6%. In contrast, among the four datasets, especially on the Fbforum dataset, the fluctuation ranges of T-SIRGN and STGSN are relatively large, reaching 11% to 16%. The fundamental reason for this phenomenon may be that the size of the time window affects the amount of information in each snapshot. However, GAE-LSTMs can still capture more subtle features, thus effectively reducing the impact of the time window on the model performance.

[0159] Step S6: Perform network topology inference using the target network topology inference model.

[0160] Embodiment 2

[0161] The network topology inference system provided by the embodiment of the present invention includes an acquisition unit, a snapshot generation unit, a dataset construction unit, a model construction unit, a training unit, and an inference unit.

[0162] The acquisition unit is configured to acquire dynamic network data.

[0163] A snapshot generation unit, configured to sort all the links in the dynamic network data according to time, and divide all the time-sorted links by a window to generate consecutive snapshots; wherein, the link refers to an edge between two nodes.

[0164] A dataset construction unit, configured to construct a sample dataset with consecutive Q snapshots as a sample; wherein, the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label.

[0165] A model construction unit, configured to construct a network topology inference model; wherein, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module, and an output layer; the node feature extraction module is used to extract node features from each input snapshot to obtain a node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and the adjacency matrix of each snapshot to obtain a spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of consecutive Q - 1 snapshots to obtain a fused feature matrix; the temporal information extraction module is used to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer is used to make a prediction on the intermediate feature matrix to obtain a predicted adjacency matrix.

[0166] A training unit, configured to train and test the network topology inference model using the sample dataset to obtain a target network topology inference model.

[0167] An inference unit, configured to perform network topology inference using the target network topology inference model.

[0168] In some embodiments, the network topology inference system may incorporate the features of the network topology inference method in Embodiment 1 of the present application, and vice versa, which will not be elaborated here.

[0169] Embodiment 3

[0170] The embodiment of the present invention further provides an electronic device, which includes: a memory, a processor, and a computer program / instructions stored on the memory, and the processor executes the computer program / instructions to implement the network topology inference method in the embodiments of the present application.

[0171] Although not shown, the electronic device includes a processor that can perform various appropriate operations and processes according to programs and / or data stored in a read-only memory (ROM) or programs and / or data loaded from a storage section into a random access memory (RAM). The processor can be a multi-core processor or can include multiple processors. In some embodiments, the processor can include a general-purpose main processor and one or more special coprocessors, such as, for example, a central processing unit, a graphics processing unit (GPU), a neural network processing unit (NPU), a digital signal processing unit (DSP), and so on. In the RAM, various programs and data required for device operation are also stored. The processor, the ROM, and the RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0172] The above-mentioned processor and memory are jointly used to execute the programs / instructions stored in the memory, and when the programs / instructions are executed by a computer, they can implement the methods, steps, or functions described in the above embodiments.

[0173] Although not shown, an embodiment of the present invention also provides a computer-readable storage medium on which computer programs / instructions are stored, and when the computer programs / instructions are executed by a processor, the network topology inference method in the embodiments of the present application is implemented.

[0174] The readable storage medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), or other optical storage, magnetic cassette tapes, disk storage, or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media do not include transitory computer-readable media, such as modulated data signals and carrier waves.

[0175] The specific embodiments disclosed above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or variations within the technical scope disclosed by the present invention, and all of them should be covered by the protection scope of the present invention.

Claims

1. A network topology inference method, characterized in that, The inference method includes: Obtaining dynamic network data; Sorting all the links in the dynamic network data by time, and dividing all the time-sorted links using a window to generate consecutive snapshots; wherein, the link refers to the edge between two nodes; Constructing a sample data set with consecutive Q snapshots as one sample; wherein, the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label; Constructing a network topology inference model; wherein, the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module, and an output layer; the node feature extraction module is used to extract node features for each input snapshot to obtain the node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and the adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of consecutive Q - 1 snapshots to obtain a fused feature matrix; the temporal information extraction module is used to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer is used to predict the intermediate feature matrix to obtain a predicted adjacency matrix; Training and testing the network topology inference model using the sample data set to obtain a target network topology inference model; Performing network topology inference using the target network topology inference model; Wherein, the spatial evolution information extraction module includes a plurality of multi-head graph attention networks connected in sequence and an ordinary differential equation module provided at the output end of the plurality of multi-head graph attention networks; Each multi-head graph attention network is used to extract features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot to obtain the discrete spatial feature matrix of this multi-head graph attention network; wherein, the first multi-head graph attention network is used to extract features from the node feature matrix and the adjacency matrix of each snapshot to obtain the discrete spatial feature matrix of the first multi-head graph attention network; The ordinary differential equation module is used to perform continuous spatial feature extraction on the discrete spatial feature matrices output by the plurality of multi-head graph attention networks to obtain a spatial evolution feature sequence.

2. The network topology inference method according to claim 1, wherein The node feature extraction module is used to extract node features for each input snapshot, specifically including: Using the Node2Vec algorithm to extract node features for each input snapshot, and the specific formula is: ； ； ； ； Among them, represents the random walk probability between the i-th node and the j-th node in the snapshot; represents the number of links experienced between the i-th node and the j-th node in the snapshot; p and q represent parameters for controlling the exploration steps; represents that the number of nodes is and the number of links is of the snapshot; RandomWalk represents the random walk algorithm; represents the random walk sequence starting from the node , ; Word2vec represents the word embedding algorithm; represents the word embedding vector; Concat represents concatenating the word embedding vectors row by row; C represents the node feature matrix of the snapshot.

3. The network topology inference method according to claim 1, wherein Each multi-head graph attention network is used to extract features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot, and the specific formula is: ， ； ； ； ； ； Among them, represents the matrix obtained by performing a linear transformation on the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; C represents the node feature matrix of the snapshot; represents the trainable weight parameter; represents the attention coefficient of the k-th attention head; LeakyReLU represents the leaky rectified linear unit; represents the adjacency matrix of the snapshot; the superscript T represents the matrix transpose; represents the matrix the feature vector of the i-th node in; represents the matrix the feature vector of the j-th node in; represents the concatenation symbol; represents the normalized attention coefficient of the k-th attention head; N i represents the matrix the set of neighbor nodes of the i-th node in; represents the feature matrix updated by the k-th attention head; ELU represents the exponential linear unit; represents the discrete spatial feature matrix output by the m-th multi-head graph attention network; K represents the number of attention heads in each multi-head graph attention network.

4. The network topology inference method according to claim 1, wherein The ordinary differential equation module is used to perform continuous spatial feature extraction on the discrete spatial feature matrices output by the plurality of multi-head graph attention networks, and the specific formula is: ； ； ； Among them, represents the attention calculation function of the m-th multi-head graph attention network; K represents the number of attention heads in the m-th multi-head graph attention network; N i represents the matrix the set of neighbor nodes of the i-th node in; represents the matrix obtained by linearly transforming the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; represents the normalized attention coefficient of the k-th attention head in the m-th multi-head graph attention network; represents the discrete spatial feature matrix output by the (m - 1)-th multi-head graph attention network; represents a trainable parameter tensor; represents the discrete spatial feature matrix output by the m-th multi-head graph attention network; represents an ordinary differential equation; M represents the number of multi-head graph attention networks; represents a composite operator; represents a non-linear activation function; represents the spatial evolution feature sequence of the snapshot; represents the initial feature vector; represents the granularity of solving the ordinary differential equation; represents the granularity variable; represents the discrete spatial feature matrix output by the m-th multi-head graph attention network.

5. The network topology inference method according to claim 1, characterized in that The temporal information extraction module includes a plurality of LSTM units, and each LSTM unit is used to extract features from the normalized result of the hidden state at the current moment output by the previous LSTM unit to obtain the hidden state at the current moment of this LSTM unit; The first LSTM unit is used to extract features from the fused feature matrix to obtain the hidden state at the current moment of the first LSTM unit; the hidden state at the current moment output by the last LSTM unit is the intermediate feature matrix; Among them, the specific calculation formula for the normalization result of the hidden state at the current moment output by each LSTM unit is: ； Among them, represents the hidden state at the current moment output by the LSTM cell; represents the normalization result of the hidden state at the current moment output by the LSTM cell; and represent the scaling factor and the offset factor respectively; and represent the mean and variance of the hidden state at the current moment respectively; represents a constant used to prevent division-by-zero errors.

6. The network topology inference method according to any one of claims 1 to 5, characterized in that Using the sample data set to train the network topology inference model specifically includes: Input the first Q - 1 snapshots and their adjacency matrices of each sample into the network topology inference model to obtain the predicted adjacency matrix of the network topology inference model; Calculate the loss error between the predicted adjacency matrix and the expected label of the sample. The specific calculation formula is: ； Among them, represents the loss error; N e represents the number of links of the predicted adjacency matrix or the expected labels, including existing and non-existing links; V represents the set of nodes of the predicted adjacency matrix or the expected labels; represents the probability that there is a link between the i-th node and the j-th node in the expected labels; represents the probability that there is a link between the i-th node and the j-th node in the predicted adjacency matrix; Adjust the parameters of the network topology inference model according to the loss error to achieve the training of the network topology inference model; Iteratively train until the training termination condition is reached.

7. A network topology inference system, characterized in that The inference system includes: An acquisition unit configured to acquire dynamic network data; A snapshot generation unit configured to sort all the links in the dynamic network data by time and divide all the time - sorted links using a window to generate continuous snapshots; where the link refers to the edge between two nodes; A data set construction unit configured to construct a sample data set with continuous Q snapshots as a sample; where the first Q - 1 snapshots and their adjacency matrices in each sample are used as inputs, and the adjacency matrix of the last snapshot is used as the expected label; A model construction unit configured to construct a network topology inference model; where the network topology inference model includes a node feature extraction module, a spatial evolution information extraction module, a fusion module, a temporal information extraction module, and an output layer; the node feature extraction module is used to extract node features from each input snapshot to obtain the node feature matrix of each snapshot; the spatial evolution information extraction module is used to extract spatial evolution information from the node feature matrix and adjacency matrix of each snapshot to obtain the spatial evolution feature sequence of each snapshot; the fusion module is used to fuse the spatial evolution feature sequences of continuous Q - 1 snapshots to obtain a fused feature matrix; the temporal information extraction module is used to extract temporal information from the fused feature matrix to obtain an intermediate feature matrix; the output layer is used to predict the intermediate feature matrix to obtain a predicted adjacency matrix; A training unit configured to train and test the network topology inference model using the sample data set to obtain a target network topology inference model; An inference unit configured to perform network topology inference using the target network topology inference model; Among them, the spatial evolution information extraction module includes a plurality of multi - head graph attention networks connected in sequence and an ordinary differential equation module provided at the output end of the plurality of multi - head graph attention networks; Each multi-head graph attention network is used to extract features from the discrete spatial feature matrix output by the previous multi-head graph attention network and the adjacency matrix of the snapshot, so as to obtain the discrete spatial feature matrix of this multi-head graph attention network; among them, the first multi-head graph attention network is used to extract features from the node feature matrix and the adjacency matrix of each snapshot, so as to obtain the discrete spatial feature matrix of the first multi-head graph attention network. The ordinary differential equation module is used to perform continuous spatial feature extraction on the discrete spatial feature matrices output by multiple multi-head graph attention networks, so as to obtain a spatial evolution feature sequence.

8. An electronic device, comprising a memory, a processor, and a computer program / instructions stored on the memory, characterized in that, The processor executes the computer program / instructions to implement the network topology inference method according to any one of claims 1 to 6.

9. A computer-readable storage medium having computer programs / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, the network topology inference method according to any one of claims 1 to 6 is implemented.

Images