Link weight prediction method and system based on network reconstruction and weight perturbation

Abstract

The invention discloses a link weight prediction method and system based on network reconstruction and weight perturbation, and the method comprises the following steps: S1, carrying out the random division of a weight set W in a weighted network, and generating a training set WT and a test set WV; s2, randomly selecting a small part from the training set WT as a disturbance set delta W, and taking the rest part as Wr; s3, performing eigenvalue decomposition operation on the Wr to obtain a disturbed weight matrix W1; s4, reconstructing the weight of the weighted network, and obtaining a weight matrix W2; s5, combining the matrix W1 and the matrix W2 in a linear fusion mode to obtain a link weight prediction matrix; and S6, comparing the weight value corresponding to the test set WV with the predicted weight value, and judging the validity of the algorithm. According to the method, the two major elements of network reconstruction and weight perturbation are ingeniously and linearly integrated, errors in weight information are effectively corrected, and potential new weight information is successfully revealed.

Description

Technical Field

[0001] The present invention relates to the field of bioinformatics, and in particular to a link weight prediction method and system based on network reconstruction and weight perturbation. Background Art

[0002] The problem of data incompleteness has been a persistent challenge in the field of data mining and network science research. In order to more deeply explore the inherent complexity of real-world complex systems, scientists first abstract these systems and construct them into complex network topology models. In this process, the problem of data loss in the original system is inevitably transformed into the phenomenon of missing links in the network topology. Therefore, in the study of network science, link prediction is often used as a prerequisite for research, aiming to fill and improve the gaps in known data sets.

[0003] Link prediction is a core issue in complex network research and has achieved remarkable results. However, with the diversification of research needs, link weight prediction in weighted networks has begun to attract close attention from researchers. Although this is a relatively new research field and related research results are not yet abundant, its theoretical significance and practical application value are profound.

[0004] Theoretically, link weight is an indispensable topological information in the network structure, and reasonable prediction of it can reveal the evolution of network weight information over time. In practical research, researchers often face the problem of incomplete or false positive weight information, and link weight prediction is an effective means to improve the network weight structure. For example, in the study of weighted network synchronization, Zhou et al. found that the synchronization behavior of random networks is significantly affected by the accumulation of link weights and heterogeneity in the network. In addition, link weight prediction also plays a key role in multi-agent consensus, network propagation, protein interaction prediction, and protein complex prediction.

[0005] In practical applications, link weight prediction is also of great significance. It can help researchers to improve the weight information that has not been discovered in the network, so as to refine the network weight information before conducting other studies. Due to various limitations, the weight information is often not fully detected during the network construction process. Therefore, before conducting subsequent studies, the topology and weight information of the network must be constructed first. Taking bioinformatics as an example, protein complexes are usually predicted through protein interaction networks. However, in biological experiments, the weight information of protein interaction networks is easily lost, so it is necessary to restore this weight information through link weight prediction.

[0006] Compared with link prediction, there are relatively few studies on link weight prediction. At present, link weight prediction methods can be roughly divided into two categories: unsupervised and supervised. In the unsupervised method, Zhao et al. proposed a link weight prediction algorithm based on reliable routing, which assumes that the weight of the link in the network is linearly related to its topological similarity. Pech et al. proposed a link weight prediction algorithm based on robust principal component analysis, which mainly considers the sparsity and low-rank characteristics of the weight matrix in the network. In the supervised scheme, Fu et al. used supervised learning methods such as support vector machines, gradient boosted decision trees, and random forests to predict link weights.

[0007] The existing unsupervised learning link weight prediction algorithms are usually evolved from the idea of ​​link prediction. In the process of model design, only a certain evolution mechanism of the network is generally considered. It is suitable for a specific type of network structure, and the prediction accuracy of other types of network structures is difficult to guarantee, that is, the robustness to the network type is weak. In contrast, the advantage of supervised learning is that it defines the link weight prediction problem as a regression problem, and the prediction accuracy for different types of networks is relatively stable, but the disadvantage is that the evolution mechanism of different types of networks is not fully considered when building the model, and the ability to infer new weight information in the network is weak. Summary of the invention

[0008] In view of the remarkable achievements of the robust network reconstruction model in deeply exploring the deep structural characteristics of the network, and the unique advantages of the first-order perturbation theory of Hamiltonian in quantum mechanics in accurately characterizing the regularity of weight information of weighted networks, the present invention innovatively proposes a new link weight prediction method based on network reconstruction and weight perturbation to solve the problems raised in the above background technology.

[0009] To achieve the above-mentioned object of the invention, one aspect of the present invention provides a link weight prediction method based on network reconstruction and weight perturbation, comprising the following steps:

[0010] Step S1: randomly divide the weight set W in the weighted network to generate a training set W T With the test set W V Two parts;

[0011] Step S2, from the training set W T A small part is randomly selected as the perturbation set ΔW, and the rest is denoted as W r ;

[0012] Step S3, for W r Perform eigenvalue decomposition to obtain the corresponding eigenvalue and eigenvector matrix, and use the perturbation model to perturb the matrix W through the perturbation set ΔW r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1;

[0013] Step S4, based on the network reconstruction model, through the VGAE (Variational Graph Autoencoders) encoding link and the MLP (Multilayer Perceptron) decoding link, the weighted network weights are reconstructed to obtain the weight matrix W2;

[0014] Step S5, using linear fusion to combine matrices W1 and W2 to obtain a link weight prediction matrix, which is expressed as: W = α·W1+(1-α)·W2, and where θ and υ are hyperparameters, σ w represents the weight consistency index;

[0015] Step S6: test set W V The corresponding weight values ​​are compared with the predicted weight values ​​to determine the effectiveness of the algorithm.

[0016] Furthermore, in step S3, the calculation formula of the disturbed weight matrix W1 is:

[0017]

[0018] where x i and λ i are the eigenvectors and eigenvalues ​​corresponding to the matrix, Indicates the increment of the eigenvalue.

[0019] Furthermore, the network reconstruction model obtains the structural feature representation of the node by mining the weighted network weight matrix, uses compression loss to constrain the node embedding, and then restores the link weight information in the network through the node embedding.

[0020] Furthermore, the weight reconstruction encoding process of the weighted network in step S4 is expressed as the following formula through the VGAE encoding link:

[0021]

[0022] in, And Z∈R N×D Represents the latent variable matrix of VGAE, where the i-th row represents the latent variable representation of the i-th node with dimension D. VGAE uses two GCNs (Graph Convolution Neural Networks) to learn the mean μ and variance σ of the Gaussian distribution. 2 , where μ = GCN μ (X,A), element μ in μ i Represents the mean of the feature distribution of the i-th node, logσ=GCNσ (X, A); In order to make the model converge in a gradient descent manner, the reparameterization technique is used, that is: Z = μ + σ * ε, where ε ~ N (0, 1).

[0023] Furthermore, the weight reconstruction decoding process of the weighted network in step S4 uses two fully connected layers to obtain the network's reconstruction weight matrix W', embedding vector After training the MLP model, we get W i ′∈R 1×N .

[0024] Furthermore, in step S5, in order to balance the proportion of the weight perturbation model and the network reconstruction model, after the weight perturbation model is run, the weight consistency index σ of each network is checked. w , expressed as the following formula: Where N ΔW represents the mean of all elements in the perturbation weight matrix ΔW, and RMSE(ΔW,ΔW) represents the root mean square error between the original perturbation weight matrix ΔW and its value ΔW predicted by the weight perturbation model.

[0025] Furthermore, the weight information reconstruction loss function formula is:

[0026]

[0027] where W∈R N×N The i-th row W i ∈R 1×N is regarded as the initial feature representation of the i-th node covering the neighbor information, P i W i The penalty factor of

[0028] Define node v i The embedding of non-adjacent nodes is represented as an anchor vector, the embedding of non-adjacent nodes is represented as a negative sample, and the positive sample is aggregated from neighboring nodes, represented as Aggre i ,Right now:

[0029]

[0030] Among them, D w is a diagonal weighted degree matrix,

[0031] Then define node v i The contrast loss function is:

[0032]

[0033] Among them, S x,y and κ represent the cosine similarity of vectors x and y, respectively, and the temperature coefficient,

[0034] The contrast loss function of all nodes is obtained, and the formula is expressed as:

[0035]

[0036] Then the formula of the overall loss function is:

[0037] L=L reconstruct +γL con .

[0038] Another aspect of the present invention provides a link weight prediction system based on network reconstruction and weight perturbation, comprising a partitioning module, a training module, a weight module, a reconstruction module and a fusion module, wherein:

[0039] The partitioning module is used to randomly partition the weight set W in the weighted network to generate a training set W T With the test set W V Two parts;

[0040] The training module is used to extract the T A part of it is randomly selected as the perturbation set ΔW, and the rest is denoted as W r ;

[0041] Weight module, for W r Perform eigenvalue decomposition to obtain the corresponding eigenvalue and eigenvector matrix, and use the defined perturbation model to perturb the matrix W through the perturbation set ΔW r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1;

[0042] A reconstruction module is used to reconstruct the network weights according to the network reconstruction model through the VGAE encoding link and the MLP decoding link, and obtain the weight matrix W2;

[0043] The fusion module is used to combine the matrices W1 and W2 in a linear fusion manner to obtain a link weight prediction matrix, which is expressed as: W = α·W1+(1-α)·W2, and α = θ·arctan(υ·δ w ), where θ and υ are hyperparameters, σ w Represents the weight consistency index.

[0044] Compared with the prior art, the present system and method have the following advantages:

[0045] 1. The present invention utilizes a robust network reconstruction model to efficiently capture the deep structural characteristics of links and weights, and enhances feature expression by comparing the similarities of adjacent nodes.

[0046] 2. The invention generates prediction weights by randomly selecting a small number of weights in the network for perturbation and ensuring the stability of the main network feature vector, allowing only slight changes in the feature value.

[0047] 3. The present invention cleverly linearly integrates the two major elements of network reconstruction and weight perturbation, which not only effectively corrects the errors in the weight information, but also successfully reveals potential new weight information.

[0048] 4. The present invention combines the advantages of the network reconstruction model, which can not only mine the deep structural characteristics of the network in depth, but also capture the characteristic information of neighbor nodes in breadth. At the same time, it draws on the idea of ​​the first-order perturbation theory of Hamiltonian in quantum mechanics, and uses tiny weight perturbations to effectively reconstruct and optimize the weight distribution of the entire network. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart of the link weight prediction method based on network reconstruction and weight perturbation.

[0050] Figure 2 Schematic diagram of the WPNR algorithm framework.

[0051] Figure 3 Schematic diagram of the network reconstruction model.

[0052] Figure 4 RMSE evaluation of the tested algorithm on 8 tested networks.

[0053] Figure 5 The PCC evaluation diagram of the tested algorithm on 8 tested networks. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] like Figure 1Shown is a flow chart of the method of the present invention. An embodiment of the present invention provides a link weight prediction method based on network reconstruction and weight perturbation. The present invention first evaluates the weight consistency of the weighted network. High consistency means that the weight information can be well restored through perturbation theory. Then, a network reconstruction model that integrates variational graph autoencoders and contrastive learning is used to mine the deep structural features of the network, and the idea of ​​contrastive learning is used to constrain the latent vector representation of the nodes, and then the weight information of the network is reconstructed through the MLP model of the decoding link. Finally, the weight perturbation and network reconstruction technology are innovatively integrated to form the WPNR algorithm, whose core structure is divided into two major modules: one is the weight perturbation model (Weight Perturbation Method, WPM), and the other is the network reconstruction model (Network Reconstruction Model, NRM), which realizes the recovery of missing weights in the network and the discovery of new link weight information. The schematic diagram of the WPNR algorithm framework is shown in the figure. Figure 2 This method combines network reconstruction and weight perturbation technology, which not only ensures high accuracy of predictions for various types of networks, but also deeply explores and fully utilizes the deep structural characteristics of the network, thereby significantly enhancing the model's ability to detect emerging link weights.

[0056] The specific steps are as follows:

[0057] Step S1: randomly divide the weight set W in the weighted network to generate a training set W T With the test set W V Two parts;

[0058] Step S2, from the training set W T A part of it is randomly selected as the perturbation set ΔW, and the rest is denoted as W r ;

[0059] Step S3, for W r Perform eigenvalue decomposition to obtain the corresponding eigenvalue set Λ and eigenvector matrix Q. Use the defined perturbation model to perturb the matrix W through the perturbation set ΔW. r Apply influence, calculate the incremental matrix ΔΛ of the eigenvalue, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1. The eigenvalue matrix Λ is a set that contains all the eigenvalues ​​λ i ; The eigenvector matrix Q is also a set, containing all the eigenvectors x i ;

[0060] Step S4, based on the network reconstruction model, the network weights are reconstructed through the VGAE encoding link and the MLP decoding link, and the weight matrix W2 is obtained;

[0061] Step S5, using linear fusion to combine matrices W1 and W2 to obtain a link weight prediction matrix, which is expressed as: W = α·W1+(1-α)·W2, and α = θ·arctan(υ·δ w ), where θ and υ are hyperparameters, δ w Represents the weight consistency index.

[0062] Step S6: The link weight prediction matrix W is obtained by W T Inferred, and will generate predicted weight values ​​for all edges in the network, select the test set W V The corresponding weight value is compared with the weight value predicted by the corresponding edge to determine the effectiveness of the algorithm.

[0063] The weight perturbation model is implemented in step S3. T A small number of links in the perturbation set ΔW, and the remaining links are defined as W r , then: W T =W r +ΔW, and where x i and λ i are the eigenvectors and eigenvalues ​​corresponding to the matrix respectively.

[0064] According to the first-order perturbation theory of Hamiltonian, when a matrix undergoes a small perturbation, the eigenvalues ​​and eigenvectors of the original matrix should also change, that is:

[0065] (W r +ΔW)(x i +Δx i )=(λ i +Δλ i )(x i +Δx i )

[0066] Where Δx i and Δλ i They correspond to the increments of the original eigenvector and eigenvalue respectively.

[0067] In addition, multiply both sides of the above equation by And ignore the equation containing Δx i , we can get:

[0068]

[0069] Assuming that after the weight perturbation, the eigenvector of the new matrix changes little, then the weight matrix restored after the perturbation can be defined as:

[0070]

[0071] The network reconstruction model in step S4 mainly obtains the structural feature representation of the node by mining the weighted network weight matrix, and uses compression loss to constrain node embedding, and then restores the link weight information in the network through node embedding. Its overall framework is as follows: Figure 3 As shown. Figure 3 It can be seen that the model only uses the structural information of the original observation graph, and the weighted adjacency matrix W is used as the input of the model. N×N The i-th row W i ∈R 1×N is regarded as the initial feature representation of the ith node covering the neighbor information.

[0072] The weight reconstruction encoding process of the weighted network is expressed as follows through the VGAE encoding link:

[0073]

[0074] in, And Z∈R N×D Represents the latent variable matrix of VGAE, whose i-th row represents the latent variable representation of the i-th node with dimension D. VGAE uses two GCNs to learn the mean μ and variance σ of the Gaussian distribution 2 , where μ = GCN μ (X,A), element μ in μ i Represents the mean of the feature distribution of the i-th node. Similarly, logσ=GCN σ (X,A).

[0075] In order to make the model show the convergence mode of gradient descent, the reparameterization technique is used, that is: Z = μ + σ * ε, where ε ~ N (0, 1).

[0076] The weight reconstruction of the weighted network can be regarded as a machine learning regression problem. If the decoding process uses the same "node representation, inner product multiplication, and then sigmoid transformation" as the link reconstruction, which maps the output value to [0,1], it will not be able to accurately predict the weight value of each link. Therefore, this method uses two fully connected layers to obtain the network's reconstructed weight matrix W′, that is, the embedding vector After training the MLP model, we get W i ′∈R 1×N .

[0077] Considering that the original weight matrix W of the network is sparse, this method adds a penalty factor P to the non-zero elements in the matrix so that the output values ​​of the reconstructed weights do not tend to 0. That is, if W ij If P is greater than 0, ij =η>1, otherwise P ij =1. Therefore, the weight information reconstruction loss function of this method is:

[0078]

[0079] The above reconstruction method regards the feature vector of each node as an independent element, and rarely considers the dependencies between neighboring nodes in the network. Based on this, the present invention uses node-level contrast loss to constrain the embedding vector, so that the anchor vector is close to the positive sample and far away from the negative sample. Its formal definition is as follows:

[0080] Define node v i The embedding of non-adjacent nodes is represented as an anchor vector, the embedding of non-adjacent nodes is represented as a negative sample, and the positive sample is aggregated from neighboring nodes, represented as Aggre i ,Right now:

[0081]

[0082]

[0083] Among them, D w is a weighted degree matrix in diagonal form.

[0084] Based on this, this model intends to define node v i The contrast loss function is:

[0085]

[0086] Among them, S x,y and κ represent the cosine similarity of vectors x and y, and the temperature coefficient, respectively.

[0087] Therefore, the contrast loss function of all nodes is:

[0088]

[0089] The overall loss function is defined as: L = L reconstruct +γL con , where γ is a hyperparameter.

[0090] The present invention selects 8 different types of networks for experimental verification, namely: Windsurfers, BKFRAT, Highschool, Lesmis, Corum, Health, HasPPI and Geom networks, including social relationship networks, scientific research cooperation networks, protein interaction networks, etc. At the same time, the ratio of training sets and test sets for all networks in the following experiments is 9:1. Table 1 lists the basic topological features of the tested network data sets, where N, |E|, <k> 、 <d>and C represent the total number of nodes, total number of links, average degree, average shortest path length, and average clustering coefficient of the network respectively; σ w Represents the weight consistency indicator of the network. The details are as follows:

[0091] Table 1 Basic topological characteristics of the tested network dataset

[0092]

[0093] At the same time, 11 classic algorithms are selected for comparative analysis, including: 1) algorithms based on shallow features: pWSBM, ZHU, lWCN, lrWRA, lWRA, lrWCN, lrWAA, lWAA and RPCA, etc., 2) algorithms based on matrix analysis: WPLF, NNMF, etc.

[0094] In terms of verification, this experiment selected the root mean square error (RMSE) and Pearson correlation coefficient (PCC) of the predicted weight value and the true weight value for comparative analysis. In addition, this experiment also evaluated the overall performance of the algorithm based on the prediction accuracy ranking indicators of RMSE and PCC. This indicator requires that the performance of each algorithm on each network be arranged in descending order, and the mean ranking of each prediction algorithm on all networks is calculated to reflect the overall performance of the algorithm on all networks.

[0095] Figure 4 The RMSE evaluation results of 12 algorithms on 8 networks are shown. The algorithms are arranged from small to large according to their average ranking, and the average RMSE value is marked above each algorithm. Figure 4 It can be seen that the algorithms can be roughly divided into two levels: the first level includes WPNR, WPLF, pWSBM and ZHU, and the rest of the algorithms are classified into the second level. In particular, the WPNR algorithm performs best among the four networks, and ranks first based on the average ranking of RMSE, showing strong robustness to different network types. Among the algorithms in the first level, the WPLF algorithm recovers the weighted matrix through latent factor decomposition, and the prediction effect is good. The pWSBM and ZHU algorithms also have high prediction accuracy because they assume that the network weights conform to the normal distribution (which is consistent with the actual distribution of weight values ​​of most networks). In summary, the WPNR algorithm has significant advantages over other algorithms.

[0096] Table 2 shows the average ranking of the 12 algorithms in various types of networks, based on the RMSE evaluation index. Among them, the WPNR algorithm ranks first with a Mean ranking of 1.63. This result highlights that the algorithm proposed in this invention has a significant competitive advantage across multiple network types.

[0097] Table 2 RMSE ranking evaluation of the tested algorithms

[0098]

[0099] Table 3 presents the Cohen's d statistical results based on the t-test, which is used to evaluate the statistical difference effect size of the RMSE values ​​of each pair of algorithms in all test networks. Specifically, the Cohen's d values ​​of the WPNR algorithm compared with the WPLF algorithm and the pWSBM algorithm are 0.397 and 0.452, respectively. Both values ​​are below the medium effect threshold of 0.5, indicating that there are perceptible but non-extreme differences between the WPNR algorithm and these two algorithms, showing a slight advantage of the WPNR algorithm. It is worth noting that when the WPNR algorithm is compared with other algorithms, its effect size exceeds the large effect size threshold of 0.8, which clearly shows that the WPNR algorithm has a more significant advantage over other algorithms. In summary, the data analysis in Table 3 reveals that the WPNR algorithm shows obvious superiority in performance compared with most of the comparison algorithms.

[0100] Table 3 Cohen's d statistics based on RMSE values ​​of the comparison algorithms

[0101]

[0102] Figure 5 Table 4 and Table 5 show the performance of each tested algorithm based on the PCC evaluation index, among which the WPNR algorithm shows a significant advantage. Specifically, Figure 5 It reveals that the average PCC value of the WPNR algorithm on 8 different networks reached 0.617, ranking first. Furthermore, the data in Tables 4 and 5 also support this conclusion, which strongly proves the superiority of the WPNR algorithm in ensuring a high correlation trend between the predicted weights and the true weights.

[0103] Table 4 PCC ranking evaluation of the tested algorithms

[0104]

[0105]

[0106] Table 5 Cohen's d statistics based on PCC values ​​of the comparison algorithms

[0107]

[0108] The WPNR algorithm proposed in the present invention has shown strong competitiveness in comparison with many classic link weight prediction algorithms. Starting from the two major evaluation indicators of RMSE and PCC, and comprehensively considering the three dimensions of prediction accuracy, average ranking and statistical analysis, the WPNR algorithm and the three algorithms of WPLF, pWSBM and ZHU have jointly demonstrated excellent link weight recovery performance, and the advantages of WPNR are more obvious than other algorithms. In addition, in tests of various network types, the WPNR algorithm can continue to show its superiority compared with these three leading unsupervised link weight prediction algorithms, which further proves the ability of the WPNR algorithm in link weight recovery.

[0109] By comparing and analyzing the algorithm with 11 classic link weight prediction algorithms on 8 different types of networks, it is found that the algorithm proposed in the present invention has obvious advantages, which verifies that the algorithm proposed in the present invention generally has high prediction accuracy in different types of networks.

[0110] This invention innovatively proposes a new link weight prediction method based on network reconstruction and weight perturbation. This method first uses a robust network reconstruction model to efficiently capture the deep structural characteristics of links and weights, and enhances feature expression by comparing the similarities of adjacent nodes. Subsequently, a small number of weights in the network are randomly selected for perturbation, and the stability of the main network feature vector is ensured, allowing only slight changes in the eigenvalues ​​to generate predicted weights. Finally, this method cleverly linearly integrates the two major elements of network reconstruction and weight perturbation, which not only effectively corrects the errors in the weight information, but also successfully reveals potential new weight information.

[0111] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.< / d> < / k>

Claims

1. A link weight prediction method based on network reconstruction and weight perturbation, characterized in that: The following steps are involved: Step S1: randomly divide the weight set W in the weighted network to generate a training set W T With the test set W V Two parts; Step S2, from the training set W T A small part is randomly selected as the perturbation set ΔW, and the rest is denoted as W r ; Step S3, for W r Perform eigenvalue decomposition to obtain the corresponding eigenvalue and eigenvector matrix, and use the perturbation model to perturb the matrix W through the perturbation set ΔW r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1; Step S4, based on the network reconstruction model, the weighted network weights are reconstructed through the VGAE encoding link and the MLP decoding link, and the weight matrix W2 is obtained; Step S5, using linear fusion to combine matrices W1 and W2 to obtain a link weight prediction matrix, which is expressed as: W = α·W1+(1-α)·W2, and α = θarctan(υ·δ w ), where θ and υ are hyperparameters, σ w represents the weight consistency index; Step S6: test set W V The corresponding weight values ​​are compared with the predicted weight values ​​to determine the effectiveness of the algorithm.

2. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: In step S3, the calculation formula of the disturbed weight matrix W1 is: where x i and λ i are the eigenvectors and eigenvalues ​​corresponding to the matrix, Indicates the increment of the eigenvalue.

3. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: The network reconstruction model obtains the structural feature representation of the node by mining the weighted network weight matrix, uses compression loss to constrain node embedding, and then restores the link weight information in the network through node embedding.

4. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: The weight reconstruction encoding process of the weighted network in step S4 is expressed as follows through the VGAE encoding link: in, And Z∈R N×D Represents the latent variable matrix of VGAE, whose i-th row represents the latent variable representation of the i-th node with dimension D. VGAE uses two GCNs to learn the mean μ and variance σ of the Gaussian distribution 2 , where μ = GCN μ (X,A), element μ in μ i Represents the mean of the feature distribution of the i-th node, logσ=GCN σ (X, A); In order to make the model converge in a gradient descent manner, the reparameterization technique is used, that is: Z = μ + σ * ε, where ε ~ N (0, 1).

5. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: The weight reconstruction decoding process of the weighted network in step S4 uses two fully connected layers to obtain the network's reconstruction weight matrix W', embedding vector After training the MLP model, we get W i ′∈R 1×N .

6. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: In step S5, in order to balance the proportion of the two modules of the weight perturbation model and the network reconstruction model, after the weight perturbation model is run, the weight consistency index σ of each network is checked. w , expressed as the following formula: Where N ΔW represents the mean of all elements in the perturbation weight matrix ΔW, and RMSE(ΔW,ΔW) represents the root mean square error between the original perturbation weight matrix ΔW and its value ΔW predicted by the weight perturbation model.

7. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1 is characterized in that: The formula for weight information reconstruction loss function is: where W∈R N×N The i-th row W i ∈R 1×N is regarded as the initial feature representation of the i-th node covering the neighbor information, P i W i The penalty factor of Define node v i The embedding of non-adjacent nodes is represented as an anchor vector, the embedding of non-adjacent nodes is represented as a negative sample, and the positive sample is aggregated from neighboring nodes, represented as Aggre i ,Right now: Among them, D w is a diagonal weighted degree matrix, Then define node v i The contrast loss function is: Among them, S x,y and κ represent the cosine similarity of vectors x and y, respectively, and the temperature coefficient, The contrast loss function of all nodes is obtained, and the formula is expressed as: Then the formula of the overall loss function is: L=L reconstruct +γL con 。 8. A link weight prediction system based on network reconstruction and weight perturbation, characterized in that: It includes partition module, training module, weight module, reconstruction module and fusion module, among which, The partitioning module is used to randomly partition the weight set W in the weighted network to generate a training set W T With the test set W V Two parts; The training module is used to extract the T A part of it is randomly selected as the perturbation set ΔW, and the rest is denoted as W r ; Weight module, for W r Perform eigenvalue decomposition to obtain the corresponding eigenvalue and eigenvector matrix, and use the defined perturbation model to perturb the matrix W through the perturbation set ΔW r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1; A reconstruction module is used to reconstruct the network weights according to the network reconstruction model through the VGAE encoding link and the MLP decoding link, and obtain the weight matrix W2; The fusion module is used to combine the matrices W1 and W2 in a linear fusion manner to obtain a link weight prediction matrix, which is expressed as: W = α·W1+(1-α)·W2, and α = θ·arctan(υ·δ w ), where θ and υ are hyperparameters, σ w Represents the weight consistency index.

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