Network embedding-based random network topology accurate reconstruction method and system

Abstract

The application discloses a random network topology accurate reconstruction method based on network embedding, which comprises the following steps: S1: expressing the adjacency matrix M(G) of a high-dimensional sparse random network graph G as a low-dimensional dense feature matrix Φ through feature embedding, wherein the dimension of the adjacency matrix M(G) is n*n, the dimension of the low-dimensional dense feature matrix Φ is n*r, and r<<n; S2: reconstructing the adjacency matrix by using the low-dimensional dense feature matrix; and S3: clustering and quantizing the reconstructed adjacency matrix, mapping the discrete matrix elements with errors to accurate values of the cluster centers, eliminating the reconstruction disturbance error, and obtaining the accurate reconstructed adjacency matrix of the random network. The application can quickly and accurately reconstruct the random network topology information, and guarantees the timeliness and accuracy of the reconstruction result.

Description

Technical Field

[0001] This invention belongs to the field of mobile communication technology and mainly relates to a method for accurate reconstruction of random network topology. Specifically, it is a method and system for accurate reconstruction of random network topology based on network embedding and vector quantization theory. Background Technology

[0002] A random network is a network whose topology changes randomly. Its communication mode uses a "store-carry-forward" message forwarding mechanism. Specifically, nodes communicating with each other move randomly within a certain range. These nodes can independently act as terminals to perform data storage and forwarding tasks. When two communicative nodes move into each other's communication range, they can transmit data. If no next communicative node can be found, the data is temporarily stored locally, and the nodes continue to move randomly until they enter the communication range of another node before forwarding the message. Unlike the traditional network protocol MANET, this mode does not require a complete communication path between the two endpoints, allowing the network to be in a partially connected state at certain times. This makes it more suitable for the needs of real-world network deployments, especially in special scenarios where infrastructure has been damaged due to earthquakes or military attacks.

[0003] The topology of a random network contains much important information about the network, directly related to its performance, reliability, and communication costs. Therefore, timely and accurate acquisition of the random network topology is crucial. However, because the topology of a random network is dynamic, topology information obtained through routing protocols may not accurately reflect the actual network topology due to node movement. While a global or local network topology might have been constructed at one moment, the topology may have changed due to node movement, making it difficult for routing protocols to maintain a true random network topology. Nevertheless, with the deepening research into random networks, some progress has been made.

[0004] Currently, the mainstream topology reconstruction methods are distributed and centralized. Distributed estimation requires real-time acquisition of information such as the speed and direction of each node, consuming significant communication resources and leading to network congestion. Centralized methods for obtaining random network topologies primarily utilize signal filtering techniques to achieve real-time estimation of the characteristic parameters of the adjacency matrix, then reconstruct the network adjacency matrix using Equation 1. Assuming the random network reaches a steady state within a certain timeframe during node movement... This represents the adjacency matrix of a network snapshot within a given time slice. Existing spectral decomposition methods for accurate reconstruction utilize feature parameters for this purpose.

[0005]

[0006] Where G represents the random network at the current moment, N is the number of nodes in the network, and the feature parameters include the feature values ​​of network adjacency obtained through a correlation estimation algorithm. and the corresponding feature vector in express The transpose of .

[0007] In the network accurate reconstruction method of Equation 1, when the network node scale is large, there are two problems that urgently need to be solved: 1) First, the time complexity of its algorithm is O(n^2). 3 1) Therefore, the computation time required cannot guarantee the timeliness of reconstructing the network topology; 2) Secondly, there are errors in the prediction of all feature spectrum parameters of large-scale random networks, so the accuracy of the reconstruction results needs to be improved.

[0008] To address, or at least partially address, the problems of excessive computation time and low reconstruction accuracy of existing network reconstruction algorithms when the network size is large. Summary of the Invention

[0009] To address the problems of long running time and low reconstruction accuracy in existing random network topology recovery methods when reconstructing large-scale random networks, this invention provides a method and system for fast and accurate reconstruction of random network topologies.

[0010] The technical solution adopted in this invention is:

[0011] A method for accurate reconstruction of random network topology based on network embedding is provided, including the following steps:

[0012] S1: The adjacency matrix M(G) of the high-dimensional sparse random network graph G is represented as a low-dimensional dense feature matrix Φ through feature embedding, where the dimension of the adjacency matrix M(G) is n×n, the dimension of the low-dimensional dense feature matrix Φ is n×r, and r<<n.

[0013] S2: Initially reconstruct the adjacency matrix using the low-dimensional dense feature matrix.

[0014] S3: Convert the adjacency matrix Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

[0015] Following the above technical solution, step S1 specifically includes the following steps:

[0016] S11: Assume that the adjacency matrix M(G) of a high-dimensional sparse random network G has a dimension of n×n. After the network reaches a steady state at a certain time, obtain all the eigenvalues ​​λ of its adjacency matrix. iand the corresponding eigenvector x i Arrange Eig{λ1, λ2, ..., λ3} in descending order of eigenvalue set. n}, and its corresponding feature vector is {x1, x2, ..., x}. n If the embedding dimension is represented by the first r feature components, then the eigenvalue matrix Λ and the eigenvector matrix X are represented as Λ=[λ1,λ2…λ r ], X = [x1, x2, ... x r ];

[0017] S12: Initialize a low-dimensional matrix And initialize a unitary matrix Q = I to obtain the low-dimensional embedding target matrix Φ0 = BQ, where the dimension of the target matrix Φ0 is n×r and r << n, and initialize the solution matrix as U = rand(n, r), which represents a random matrix of dimension n×r;

[0018] S13: Define the loss function as follows Iteratively solve U = max(0, BQ) and Q = VH T , where H, V T For U T B yields the unitary matrix U through singular value decomposition. T B=H∑V T When the iteration termination condition is met When ε is found, the solution matrix U is the low-dimensional dense characteristic matrix Φ, and ε is the upper bound of the tolerance error for accurate reconstruction.

[0019] Following the above technical solution, step S2 specifically involves:

[0020] The adjacency matrix can be initially reconstructed using the obtained solution matrix U. Where i, j∈1,2,...,n.

[0021] Following the above technical solution, step S3 specifically includes the following steps:

[0022] S31: Based on the preliminary reconstruction of the adjacency matrix The maximum element value m divides the matrix elements into K clusters. A partitioning threshold θ = m / K is set, representing the initial distance between the centers of each cluster. First, the n elements in the adjacency matrix are... 2 Each element is placed into an initial set S0, and the two elements with the smallest distance in the initial set are calculated and their center value is taken as the first cluster center. Then, according to the cluster center distance threshold θ, all elements within the threshold range are placed into set S1, and the remaining elements are placed into set S2, i.e., S2 = S0 - S1. This process is repeated for S2 until K cluster centers c1, c2, ..., c3 are initially selected. k ;

[0023] S32: Initialize cluster centers C = {c1, c2, ..., c...} k} and membership matrix U(0)=μ k (a ij ), μ k Define the clustering objective function to represent the membership degree. For μ respectively k and c k Taking the partial derivative, we obtain the cluster center update expression. and membership update expression The expression is solved iteratively until the cluster center value remains unchanged or the element allocation cluster remains unchanged.

[0024] S33: According to the principle of maximum membership, elements are assigned to different subclusters, if μ p (a ij )>μ q (a ij ), then a ij The elements are divided into the p-th cluster, p, q = 1, 2, ..., K'p ≠ q. The cluster center value is then used to assign values ​​to the elements in the cluster to obtain the final accurate reconstruction of M(G).

[0025] Following the above technical solution, the specific calculation process for ε is as follows:

[0026] Assumption To reconstruct the network matrix, where A is the adjacency matrix of the actual network topology, the error between them is calculated using the following formula:

[0027]

[0028] in, Assuming the maximum difference between corresponding elements of the reconstructed network adjacency matrix and the original adjacency matrix is ​​ΔE, we obtain... Due to symmetry, we know that m = n, then The upper bound of the tolerance error for accurate reconstruction of random networks is obtained:

[0029]

[0030] Following the above technical solution, |ΔE| is solved as follows:

[0031] According to the membership degree partitioning principle, the membership degree value U k (a ij ) represents element a in the original matrix ij Belongs to a certain cluster C k The probability value is used to assign each element to its respective cluster.

[0032] Suppose that within a certain cluster, the element farthest from the cluster center among all elements before quantization is considered the perturbation threshold. When the matrix is ​​perturbed, if the perturbation error of an element is lower than this perturbation threshold, then the reconstructed matrix after quantization is accurate. The average of the sums of the upper bounds of errors for all clusters is taken as the upper bound of the element's perturbation. Therefore, it is deduced that accurate reconstruction results can be obtained through quantization when the following conditions are met:

[0033]

[0034] In this formula, U k It is an element for cluster C i membership degree x is the distance between the element and the cluster center. ij Let be the j-th element of the i-th cluster, where i = 1, 2, ..., K; j = 1, 2, ..., numk, and numk is the number of elements contained in the i-th cluster.

[0035] Following the above technical solution, the maximum sparsity ratio of the random network graph G does not exceed 0.3.

[0036] The present invention also provides a system for accurate reconstruction of random network topology based on network embedding, comprising:

[0037] The low-dimensional transformation module is used to represent the adjacency matrix M(G) of a high-dimensional sparse random network graph G as a low-dimensional dense feature matrix Φ through feature embedding, where the dimension of the adjacency matrix M(G) is n×n, the dimension of the low-dimensional dense feature matrix Φ is n×r, and r<<n.

[0038] The adjacency matrix reconstruction module is used to initially reconstruct the adjacency matrix using a low-dimensional dense feature matrix.

[0039] The clustering quantization module is used to quantize the adjacency matrix. Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

[0040] Following the above technical solution, the random network graph G is a random network model with a maximum sparsity ratio not exceeding 0.3.

[0041] The present invention also provides a computer storage medium storing a computer program executable by a processor, the computer program performing the network embedding-based random network topology accurate reconstruction method described in the above technical solution.

[0042] The beneficial effects of this invention are as follows: This invention applies network embedding and vector quantization theory to achieve fast and accurate reconstruction of random network topology. First, based on the feature parameters, the high-dimensional random network is embedded into a low-dimensional feature representation space. Reconstructing the original random network using the learned low-dimensional feature representation can greatly reduce the reconstruction time. In addition, to ensure the reconstruction accuracy, vector quantization theory is used to quantize the reconstruction result to eliminate errors caused by disturbances. Therefore, random network topology information can be reconstructed quickly and accurately, ensuring the timeliness and accuracy of the reconstruction result.

[0043] Furthermore, due to the existence of objective factors such as noise and perturbation, the elements of the reconstructed adjacency matrix, in addition to the accurate values, also contain other values ​​within a certain range, which will produce errors in the reconstruction process. This invention addresses this by clustering and quantizing the adjacency matrix. The quantization process involves dividing these perturbation elements into different clusters according to their distance. Each element in a cluster corresponds to the cluster center value. Then, the cluster center value is used to cover these discrete perturbation elements to achieve a many-to-one mapping, which can obtain accurate reconstruction results. Therefore, the reconstruction results are accurate, solving the accuracy problem of reconstruction results for large-scale random networks. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart illustrating a method for accurate reconstruction of random network topology based on network embedding, provided in an embodiment of the present invention;

[0046] Figure 2 The graphs show the sparsity ratios of three random network models in this invention; where r0 = 0.1 in graph (a), r0 = 0.2 in graph (b), and r0 = 0.3 in graph (c).

[0047] Figure 3 This is a distribution diagram of the singular value magnitudes of the adjacency matrices of the three random network models in this embodiment of the invention;

[0048] Figure 4 This is a comparison of the time consumption of three random network reconstruction methods based on network embedding in this embodiment of the invention with the original reconstruction method;

[0049] Figure 5 This is a graph showing the accuracy of random network reconstruction based on network embedding reconstruction algorithms for three types of random networks according to embodiments of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment of the method for accurate reconstruction of random network topology based on network embedding includes the following steps:

[0053] S1: The adjacency matrix M(G) of the high-dimensional sparse random network graph G is represented as a low-dimensional dense feature matrix Φ through feature embedding, where the dimension of the adjacency matrix M(G) is n×n, the dimension of the low-dimensional dense feature matrix Φ is n×r, and r<<n.

[0054] S2: Initially reconstruct the adjacency matrix using the low-dimensional dense feature matrix to obtain the reconstructed adjacency matrix.

[0055] S3: Reconstruct the adjacency matrix Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

[0056] In this embodiment, the high-dimensional sparse network graph G is first represented as a low-dimensional dense feature matrix through feature embedding. Since r is much smaller than N, therefore reconstruction The time required will be greatly reduced, and then... Cluster quantization is performed to map discrete, erroneous matrix elements to their accurate values ​​at the center of their respective clusters, thereby eliminating reconstruction perturbation errors and achieving accurate reconstruction of random networks.

[0057] Example 2

[0058] This embodiment, based on embodiment 1, refines each step using specific methods to achieve the innovative purpose of embodiment 1.

[0059] Step S1 specifically includes the following steps:

[0060] S11: Assume that the adjacency matrix M(G) of a high-dimensional sparse random network G has a dimension of n×n. After the network reaches a steady state at a certain time, obtain all the eigenvalues ​​λ of its adjacency matrix. i and the corresponding eigenvector x i Arrange Eig{λ1, λ2, ..., λ3} in descending order of eigenvalue set. n}, and its corresponding feature vector is {x1, x2, ..., x}. n If the embedding dimension is represented by the first r feature components, then the eigenvalue matrix Λ and the eigenvector matrix X are represented as Λ=[λ1,λ2…λ r ], X = [x1, x2, ... x r ];

[0061] S12: Initialize a low-dimensional matrix And initialize a unitary matrix Q = I to obtain the low-dimensional embedding target matrix Φ0 = BQ, where the dimension of the target matrix Φ0 is n×r and r << n, and initialize the solution matrix as U = rand(n, r), which represents a random matrix of dimension n×r;

[0062] S13: Define the loss function as follows Iteratively solve U = max(0, BQ) and Q = VH T , where H, V T For U T B yields the unitary matrix U through singular value decomposition. T B=H∑V T When the iteration termination condition is met When ε is found, the solution matrix U is the low-dimensional dense characteristic matrix Φ, and ε is the upper bound of the tolerance error for accurate reconstruction.

[0063] Furthermore, step S2 specifically includes:

[0064] The adjacency matrix can be initially reconstructed using the obtained solution matrix U. Where i, j∈1,2,...,n.

[0065] Step S3 specifically includes the following steps:

[0066] S31: Based on the preliminary reconstruction of the adjacency matrix The maximum element value m divides the matrix elements into K clusters. A partitioning threshold θ = m / K is set, representing the initial distance between the centers of each cluster. First, the n elements in the adjacency matrix are... 2 Each element is placed into an initial set S0, and the two elements with the smallest distance in the initial set are calculated and their center value is taken as the first cluster center. Then, according to the cluster center distance threshold θ, all elements within the threshold range are placed into set S1, and the remaining elements are placed into set S2, i.e., S2 = S0 - S1. This process is repeated for S2 until K cluster centers c1, c2, ..., c3 are initially selected. k ;

[0067] S32: Initialize cluster centers C = {c1, c2, ..., c...} k} and membership matrix U(0)=μ k (a ij), μ k Define the clustering objective function to represent the membership degree. For μ respectively k and c k Taking the partial derivative, we obtain the cluster center update expression. and membership update expression The expression is solved iteratively until the cluster center value remains unchanged or the element allocation cluster remains unchanged.

[0068] S33: According to the principle of maximum membership, elements are assigned to different subclusters, if μ p (a ij )>μ q (a ij ), then a ij The elements are divided into p-th clusters, where p, q = 1, 2, ..., K, and p ≠ q. The cluster center values ​​are then used to assign values ​​to the elements within the cluster to obtain the final accurately reconstructed M(G).

[0069] According to formula (1) in the background technology, the time complexity of the original network reconstruction algorithm is O(n^2). 3 When the network node scale is large, not only is the computation time cost of the algorithm too high, but the reconstruction error also increases accordingly. For the random network accurate reconstruction algorithm based on network embedding in this invention, the main time overhead is in two parts. The first part is the time cost of iteratively calculating matrix multiplication during the embedding process, which is O(nr). 2 The second part, iteratively solving the membership matrix, has a time complexity of O(nc). 2 dt), where c represents the number of clusters, t is the number of iterations, and d is the element feature dimension, which are usually small constants. Therefore, the time cost of the quantization process is close to the linear time complexity O(n), which is a significant improvement in time performance compared with formula (1), and solves the problem that the computation time consumption is difficult to guarantee the timeliness of reconstructing the network topology.

[0070] Example 3

[0071] This embodiment is based on and further improves upon embodiments 1 and 2. Specifically, the method for accurate reconstruction of random network topology based on network embedding in this embodiment includes the following steps:

[0072] Step 1: Assume the random network G has n nodes and its adjacency matrix M(G) has an dimension of n×n. After the network reaches a steady state at a certain time, all the eigenvalues ​​λ of its adjacency matrix can be obtained. i and the corresponding eigenvector x i The eigenvalues ​​are arranged in descending order as follows: Eig{λ1, λ2, ..., λ... n}, and its corresponding feature vector is {x1, x2, ..., x}. nIf the embedding dimension is represented by the first r feature components, then the eigenvalue matrix Λ and the eigenvector matrix X are represented as Λ=[λ1,λ2…λ r ], X = [x1, x2, ... x r ];

[0073] Step 2: Initialize a low-dimensional matrix We initialize a unitary matrix Q = I to obtain a low-dimensional embedding target matrix Φ0 = BQ, where the dimension of the target matrix Φ0 is n×r and r << n. Therefore, we can initialize the solution matrix as U = rand(n, r), which represents a random matrix with dimension n×r.

[0074] Step 3: Define the loss function as follows Iteratively solve U = max(0, BQ) and Q = VH T , where H, V T For U T B yields the unitary matrix U through singular value decomposition. T B=H∑V T When the iteration termination condition is met When the solution matrix U is obtained, the low-dimensional feature embedding representation Φ is obtained.

[0075] Step 4: Initially reconstruct the adjacency matrix using the obtained matrix U.

[0076] Step 5: Based on the maximum element value m, divide the matrix elements into K clusters. Set the partitioning threshold θ = m / K, representing the initial distance between the centers of each cluster. First, divide the n elements in the adjacency matrix... 2 Each element is placed into the initial set S0, and the two elements with the smallest distance in the set are calculated. The center value of the two elements is taken as the first cluster center. Then, according to the threshold θ, all elements within the range of this distance are placed into set S1, and the remaining elements are placed into set S2, i.e., S2 = S0 - S1. Then, the process is repeated for S2 until K cluster centers are initially selected.

[0077] Step 6: Initialize cluster centers C = {c1, c2, ..., c...} k} and membership matrix U(0)=μ k (a ij ), set the clustering objective function For μ respectively k and c k Taking the partial derivative, we obtain the cluster center update expression. and membership update expression The expression is solved iteratively until the cluster center value remains unchanged or the element allocation cluster remains unchanged.

[0078] Step 7: According to the principle of maximum membership, assign the elements to different subclusters. If μ p (a ij )>μ q (a ij ), then a ij The elements are divided into p-th clusters, p, q = 1, 2, ..., K'p ≠ q. The cluster center value is then used to assign values ​​to the elements within the cluster. This quantization process can eliminate element perturbation errors and obtain the final accurate reconstruction result M(G).

[0079] This embodiment significantly improves network reconstruction performance in terms of time efficiency, solving the problem that computation time consumption makes it difficult to guarantee the timeliness of network topology reconstruction.

[0080] Furthermore, due to the existence of objective factors such as noise and perturbations, the elements of the reconstructed adjacency matrix contain other values ​​within a certain range in addition to the accurate values, which will introduce errors during the reconstruction process. The quantization process involves clustering these perturbation elements into different clusters according to their distance. Each element in the cluster corresponds to the cluster center value. Then, the cluster center value is used to cover these discrete perturbation elements to achieve a many-to-one mapping, which can obtain accurate reconstruction results. Therefore, the accuracy of the reconstruction results is ensured, and the accuracy problem of reconstruction results for large-scale random networks is solved.

[0081] Example 4

[0082] Based on Example 3, this example studies a specific random network model and demonstrates the superiority of the method of the present invention through the specific calculated parameters.

[0083] The specific process of the random network topology accurate reconstruction method based on network embedding in this embodiment is as follows:

[0084] Suppose a random network G has n nodes and its adjacency matrix M(G) has an dimension of n×n. After the network reaches a steady state at a certain time, all the eigenvalues ​​λ of its adjacency matrix can be obtained. i and the corresponding eigenvector x i The eigenvalues ​​are arranged in descending order as follows: Eig{λ1, λ2, ..., λ... n}, and its corresponding feature vector is {x1, x2, ..., x}. n}

[0085] In one embodiment, when performing network embedding, the first r feature components are used to represent the embedding dimension. The eigenvalue matrix Λ and the eigenvector matrix X are then represented as Λ = [λ1, λ2, ..., λ]. r ], X = [x1, x2, ... x rFrom this, we can see that the dimension of the eigenvector matrix is ​​n×r, where the size of r depends on the property of the rank of the random network. A lower rank in the adjacency matrix results in a more accurate recovery matrix. For the embedding method of this invention, the rank of the matrix determines the dimension in which the matrix decomposition can be accurately embedded, and the embedding dimension is related to the reconstruction accuracy. In current theoretical calculations, the formula for judging the low rank of a matrix is:

[0086]

[0087] In Formula 2, σ i Let w(k) be the i-th largest singular value, and w(k) represent the weight percentage of the top k largest singular values ​​among all singular values ​​after sorting the singular values ​​in descending order. To determine the possible values ​​of r in a random network, experimental analysis was conducted on the weight percentages of the top k largest singular values ​​in the random network matrix. The experimental results are as follows: Figure 2 As shown.

[0088] exist Figure 2 In the diagram, the horizontal axis represents the index of all singular values ​​in the network matrix, and the vertical axis represents the magnitude of the singular values. Experimental results show that after sorting the singular values ​​of the random network by magnitude, calculations using Formula 2 reveal that the top 20% (the top 200 singular values ​​arranged from largest to smallest) account for over 90% of the weight of all singular values ​​(shaded area in the figure). Therefore, the adjacency matrix of the random network exhibits low rank. Furthermore, according to spectral graph theory, smaller singular values ​​can be considered network noise, thus a value of 0.2n for r is reasonable. Dimensionality reduction can further remove this noise, resulting in a low-dimensional embedding representation that retains the main information of the network matrix. Reducing the data dimensionality also decreases the computational time cost of the reconstruction algorithm.

[0089] After determining the value of r, a low-dimensional matrix can be initialized based on the eigenvalue matrix Λ and the eigenvector matrix X. We initialize a unitary matrix Q = I to obtain the low-dimensional embedding target matrix Φ0 = BQ, where the target matrix Φ0 has dimensions n × r and r << n. Therefore, we can initialize the solution matrix as U = rand(n, r), representing a random matrix of dimension n × r. The loss function is defined as follows. By iteratively solving U = max(0, BQ) and Q = VH T , where H, V T For U T B yields the unitary matrix U through singular value decomposition. T B=H∑V T When the iteration termination condition is met:

[0090]

[0091] The solution matrix U is then the low-dimensional feature embedding representation Φ. During the iterative solution of the low-dimensional embedding matrix, the matrix needs to satisfy the requirement of sparsity. For sparse low-rank matrices, convergence to a unique solution is fast; therefore, it is necessary to verify the sparse low-rank property of the random network matrix.

[0092] Network sparsity is typically represented by the ratio of the number of edges connected to a node to the total number of nodes. If an adjacency matrix is ​​used to represent the network topology, the sparsity ratio μ is calculated as the ratio of the number of non-zero elements μ0 in the matrix to the total number of elements n in the matrix. 2 The ratio:

[0093]

[0094] This embodiment selects three random network models—RW, RD, and RWP—for research, and the relationship between the sparsity ratio and network-related parameters of the random network can be obtained as follows:

[0095]

[0096]

[0097]

[0098] The experiment set the network range as a circular region with a radius of R = 100m, the node movement speed was [1, 5] m / s, the dwell time of the RWP and RD models was [5, 10] s, the node communication radius was set to 10, 20, 30 respectively, i.e., the value of r0 was 0.1, 0.2, 0.3, and the number of network nodes was set to 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. The sparsity of the obtained random network is as follows: Figure 3 As shown.

[0099] Depend on Figure 3 Experimental results show that, in the three random network models, network size does not affect the sparsity ratio of the network matrix. Under the same network parameters, the sparsity of different node models varies, with the RWP node movement model exhibiting a lower sparsity ratio compared to the RW and RD models. Furthermore, while ensuring that r0 ≤ 0.3, the maximum sparsity ratio of the three network models does not exceed 0.3, and the minimum sparsity ratio is 0.03 when r0 = 0.1. This demonstrates that random networks possess sparsity characteristics.

[0100] To ensure the accuracy of the low-dimensional embedding matrix, it is necessary to analyze the matrix tolerance error. If the obtained embedding matrix can guarantee that the reconstruction error accuracy is lower than the minimum tolerance theoretical value, then the network matrix can be considered to be an accurate reconstruction. Assume... To reconstruct the network matrix, where A is the adjacency matrix of the actual network topology, the error between them can be calculated using the following formula:

[0101]

[0102] The calculation method for the molecule in Formula 8 above is as follows: The method for calculating the denominator is as follows: Assuming the maximum difference between corresponding elements of the reconstructed network adjacency matrix and the original adjacency matrix is ​​ΔE, we can obtain Due to symmetry, we know that m = n, then Therefore, we can obtain the upper bound of the tolerance error for accurate reconstruction of random networks:

[0103]

[0104] Using this upper bound of error tolerance as the termination condition for the iteration in Equation 3, the resulting embedding matrix has high accuracy. The adjacency matrix is ​​then initially reconstructed using the obtained matrix U. Since errors can occur due to noise and interference, the reconstruction results need to be further quantified.

[0105] First, based on the maximum element value m, the matrix elements are divided into K clusters. Then, a partitioning threshold θ = m / K is set to represent the initial distance between the centers of each cluster. Next, the n elements in the adjacency matrix are... 2 Each element is placed into the initial set S0, and the two elements with the smallest distance in the set are calculated. The center value of the two elements is taken as the first cluster center. Then, according to the threshold θ, all elements within the range are placed into set S1, and the remaining elements are placed into set S2, i.e., S2 = S0 - S1. Finally, the process is repeated for S2 until K cluster centers are initially selected.

[0106] Initialize cluster centers C = {c1, c2, ..., c...} k} and membership matrix U(0)=μ k (a ij ), set the clustering objective function For μ respectively k and c k Taking the partial derivative, we obtain the cluster center update expression. and membership update expression The expression is solved iteratively until the cluster center value remains unchanged or the element allocation clusters remain unchanged. Then, according to the maximum membership principle, the elements are assigned to different sub-clusters. For example, if μ... p (a ij )>μ q (a ij ), then a ijDivide into the p-th cluster, p, q = 1, 2, ..., K, p ≠ q. Assign values ​​to the elements in the cluster using the cluster center value. This quantization process can eliminate element perturbation errors and obtain the final accurate reconstruction result M(G).

[0107] The |ΔE| in Formula 9 can be solved as follows: According to the principle of membership degree partitioning, the membership degree value U... k (a ij ) represents element a in the original matrix ij Belongs to a certain cluster C k The probability of each element being assigned to its cluster can be accurately determined based on this probability value. Now, assuming that within a cluster, the element furthest from the cluster center before quantization is considered the perturbation threshold, then when the matrix is ​​perturbed, if the perturbation error of an element is below this threshold, then quantization can be considered to result in an accurate reconstructed matrix. Therefore, the average of the sum of the upper bounds of errors for all clusters is used as the upper bound of the perturbation for each element. From this, it can be deduced that accurate reconstruction results can be obtained through quantization when the following conditions are met:

[0108]

[0109] In this formula, U k It is an element for cluster C i membership degree x is the distance between the element and the cluster center. ij Let j be the j-th element of the i-th cluster (i = 1, 2, ..., K; j = 1, 2, ..., numk, where numk is the number of elements in the i-th cluster). From Formula 10, it can be seen that when a matrix element is perturbed, the membership degree U can be used to determine the perturbation. k Constraining the element to its cluster eliminates disturbance errors, thus the accurate reconstruction condition |ΔE|, as the tolerance error of Equation 9, can guarantee the accuracy of the reconstruction.

[0110] Example 5

[0111] This embodiment primarily aims to implement the above-described method embodiments, providing a system for accurate reconstruction of random network topology based on network embedding, characterized by including:

[0112] The low-dimensional transformation module is used to represent the adjacency matrix M(G) of a high-dimensional sparse random network graph G as a low-dimensional dense feature matrix Φ through feature embedding, where the dimension of the adjacency matrix M(G) is n×n, the dimension of the low-dimensional dense feature matrix Φ is n×r, and r<<n.

[0113] The adjacency matrix reconstruction module is used to initially reconstruct the adjacency matrix using a low-dimensional dense feature matrix.

[0114] The clustering quantization module is used to quantize the adjacency matrix. Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

[0115] Each module is used to implement the method steps of the above-described multiple embodiments, and will not be described in detail.

[0116] Example 6

[0117] This application also provides a computer-readable storage medium, such as flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, server, app store, etc., which stores a computer program, and the program implements corresponding functions when executed by a processor. The computer-readable storage medium of this embodiment, when executed by a processor, implements the network-embedded random network topology accurate reconstruction method of the method embodiment.

[0118] Example 7

[0119] The methods and systems described above can be used in drone swarms.

[0120] In a drone swarm, each drone acts as a node in the communication network, possessing both router and host functions. For example, when a drone swarm performs search and rescue missions, it needs to collect a large amount of image and sensor data in real time and transmit this data to a remote command center. Simultaneously, the remote command center needs to issue motion control commands. During communication, the movement of drones can alter the network topology, potentially causing communication breakdowns between drones or between drones and commanders. This can lead to reduced efficiency, missed critical rescue opportunities, and other problems. Therefore, it is necessary to reconstruct the drone communication network topology to promptly restore data transmission and communication links.

[0121] Example 8

[0122] The methods and systems described in the above embodiments can be used in vehicle-mounted ad hoc networks.

[0123] In the Internet of Vehicles (IoV), various intelligent devices, sensors, and microcomputers are installed in automobiles, and all devices inside and outside the vehicle are connected via wireless networks. This enables comprehensive connectivity and data interaction between vehicles, between vehicles and people, and between vehicles and service platforms. IoV is characterized by rapid changes in network topology and frequent network segmentation. These characteristics significantly impact the communication capabilities and data transmission within the IoV system. Therefore, rapidly and accurately reconstructing the network topology through network reconstruction technology can improve network performance.

[0124] Example 9

[0125] The methods and systems described in the above embodiments can be used for industrial automation.

[0126] In fields such as smart manufacturing and logistics, robots often need to perform collaborative operations. Each robot can act as a node in a communication network. Since the positions of robots are not fixed, real-time acquisition of network topology can better handle networking needs such as network node expansion and emergency recovery. Furthermore, in large-scale warehousing scenarios, where various devices are dispersed, multiple sensors are often needed to monitor the production environment. Network topology can optimize routing, ensuring reliable and stable communication links and improving the monitoring accuracy and efficiency of equipment. Additionally, in the event of emergencies, it is necessary to quickly establish a wireless communication network to address temporary deployment scenarios and rapid response needs, enabling wireless communication and emergency rescue.

[0127] In these specific applications, the network topology is constantly changing due to the movement of nodes. In order to obtain the accurate network topology, the success rate, transmission speed, latency and signal-to-noise ratio of data messages sent and received by nodes in the network can be monitored to evaluate the state information of nodes and the connection quality between nodes. By using the historical data of the recorded traffic matrix or the adjacency matrix of the topology, the characteristic parameters of the network matrix can be estimated and the network topology can be reconstructed to ensure network security, stability and other aspects to optimize network performance.

[0128] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0129] The order of the steps in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0130] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for accurate reconstruction of random network topology based on network embedding, characterized in that, Includes the following steps: S1: Transform high-dimensional sparse random network graphs adjacency matrix The feature embedding is represented as a low-dimensional dense feature matrix. The adjacency matrix The dimension is Low-dimensional dense feature matrix The dimension is ,and ; S2: Initially reconstruct the adjacency matrix using the low-dimensional dense feature matrix to obtain the initially reconstructed adjacency matrix. ; S3: Convert the initially reconstructed adjacency matrix Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

2. The method for accurate reconstruction of random network topology based on network embedding according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Assume a high-dimensional sparse random network adjacency matrix The dimension is After the network reaches a steady state at a certain time, obtain all the eigenvalues ​​of its adjacency matrix. and the corresponding feature vector Arranged in descending order of eigenvalue set Its corresponding feature vector is , adopt before Each feature component represents an embedding dimension, then the eigenvalue matrix... and eigenvector matrix Represented as ; S12: Initialize a low-dimensional matrix and initialize a unitary matrix. Used to obtain low-dimensional embedding target matrix , where the target matrix The dimension is and The initial solution matrix is: , indicating a dimension is A random matrix; S13: Define the loss function as follows Iterative solution and ,in To Unitary matrix obtained by singular value decomposition When the iteration termination condition is met When, then solve the matrix. It is a low-dimensional dense feature matrix , To accurately reconstruct the upper bound of the tolerance error.

3. The method for accurate reconstruction of random network topology based on network embedding according to claim 2, characterized in that, Step S2 is as follows: Using the obtained solution matrix Preliminary reconstruction of the adjacency matrix ,in .

4. The method for accurate reconstruction of random network topology based on network embedding according to claim 2, characterized in that, Step S3 specifically includes the following steps: S31: Based on the initially reconstructed adjacency matrix Maximum element value Divide the matrix elements into Each cluster is assigned a partitioning threshold. , representing the initial distance between the cluster centers, first the adjacency matrix in Add the elements to the initial set. In the initial set, the two elements with the smallest distance are calculated and the center value of the two elements is taken as the first cluster center. Then, the cluster center distance threshold is used as the basis for further calculations. Add all elements within the distance threshold range to the set. The remaining elements are placed into the collection. ,Right now Then to Repeat this process until preliminary selections are made. Cluster center ; S32: Initialize cluster center and membership matrix , Define the clustering objective function to represent the membership degree. , respectively and Taking the partial derivative, we obtain the cluster center update expression. and membership update expression The expression is solved iteratively until the cluster center value remains unchanged or the element allocation cluster remains unchanged. S33: According to the principle of maximum membership, elements are assigned to different subclusters. Then Divided into the first Clusters, , =1,2,...,K, However, the cluster center value is then used to assign values ​​to the elements within the cluster, resulting in the final accurately reconstructed adjacency matrix.

5. The method for accurate reconstruction of random network topology based on network embedding according to claim 2, characterized in that, The specific calculation process is as follows: Assumption To reconstruct the network matrix, Let the adjacency matrix be the actual network topology, then the error between them is calculated using the following formula: in, , Assume that the maximum difference between the corresponding elements of the reconstructed network adjacency matrix and the original adjacency matrix is ​​. ,get It can be known from symmetry ,but We obtain the upper bound of the tolerance error for accurate reconstruction of random networks: 。 6. The method for accurate reconstruction of random network topology based on network embedding according to claim 5, characterized in that, Solve as follows: According to the principle of membership degree partitioning, the membership degree value Represents the elements in the original matrix Belongs to a certain cluster The probability value is used to assign each element to its respective cluster. Suppose that within a certain cluster, the element farthest from the cluster center among all elements before quantization is considered the perturbation threshold. When the matrix is ​​perturbed, if the perturbation error of an element is lower than this perturbation threshold, then the reconstructed matrix after quantization is accurate. The average of the sums of the upper bounds of errors for all clusters is taken as the upper bound of the element's perturbation. Therefore, it is deduced that accurate reconstruction results can be obtained through quantization when the following conditions are met: In this formula It is an element for a cluster membership degree It is the distance between the element and the cluster center. Let be the j-th element of the i-th cluster, where i = 1, 2, ..., K; j = 1, 2, ..., numk, and numk is the number of elements contained in the i-th cluster.

7. The method for accurate reconstruction of random network topology based on network embedding according to any one of claims 1-6, characterized in that, Random network graph The maximum sparsity ratio does not exceed 0.

3.

8. A system for accurate reconstruction of random network topology based on network embedding, characterized in that, include: The low-dimensional transformation module is used to transform high-dimensional sparse random network graphs. adjacency matrix The feature embedding is represented as a low-dimensional dense feature matrix. The adjacency matrix The dimension is Low-dimensional dense feature matrix The dimension is ,and ; The adjacency matrix reconstruction module is used to initially reconstruct the adjacency matrix using a low-dimensional dense feature matrix, obtaining the initially reconstructed adjacency matrix. ; The clustering quantization module is used to convert the initially reconstructed adjacency matrix into a single data structure. Cluster quantization is performed to map discrete matrix elements with errors to the accurate values ​​of their respective cluster centers, eliminating reconstruction perturbation errors and obtaining the adjacency matrix after accurate reconstruction of the random network.

9. The system for accurate reconstruction of random network topology based on network embedding according to claim 8, characterized in that, Random network graph It is a random network model with a maximum sparsity ratio not exceeding 0.

3.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer program that can be executed by a processor, which performs the method for accurate reconstruction of random network topology based on network embedding as described in any one of claims 1-6.

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