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

Abstract

The present invention discloses a link weight prediction method and system based on network reconstruction and weight perturbation, comprising the following steps: Step S1, randomly dividing 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 W r ; Step S3, W r Perform eigenvalue decomposition to obtain the perturbed weight matrix W1; Step S4, reconstruct the weighted network weights and obtain the weight matrix W2; Step S5, combine the matrices W1 and W2 using linear fusion to obtain the link weight prediction matrix; Step S6, combine the test set W V The corresponding weight values ​​are compared with the predicted weight values ​​to determine the effectiveness of the algorithm. This method cleverly linearly integrates the two elements of network reconstruction and weight perturbation, effectively correcting the errors in the weight information and successfully revealing potential new weight information.

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 remains a persistent challenge in data mining and network science research. To more deeply explore the inherent complexity of complex real-world systems, scientists first abstract these systems and construct complex network topology models. This process inevitably translates data loss in the original system into missing links in the network topology. Therefore, link prediction is often considered a prerequisite for network science research, aiming to fill and complete gaps in known datasets.

[0003] Link prediction is a core issue in complex network research, with significant progress already achieved. However, with the diversification of research needs, link weight prediction in weighted networks has begun to attract close attention. Although this is a relatively new research field with limited research results, its theoretical significance and practical application value are profound.

[0004] Theoretically, link weights are essential topological information in network structures, and their reasonable prediction can reveal how network weight information evolves 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 of improving network weight structure. For example, in their 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. Furthermore, link weight prediction plays a key role in multi-agent consensus, network propagation, protein interaction prediction, and protein complex prediction.

[0005] Link weight prediction is also crucial in practical applications. It can help researchers refine previously undiscovered weight information within a network, allowing them to refine the network's weights before conducting further research. Due to various limitations, comprehensive weight information is often not readily available during network construction. Therefore, prior to conducting further research, the network's topology and weight information must be constructed. For example, in bioinformatics, protein complexes are often predicted using protein interaction networks. However, in biological experiments, the weight information within protein interaction networks is easily lost, necessitating the use of link weight prediction to recover this information.

[0006] Compared to link prediction, there is relatively little research on link weight prediction. Currently, 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 boosting decision trees, and random forests to predict link weights.

[0007] Existing unsupervised learning link weight prediction algorithms are typically derived from the idea of ​​link prediction. During model design, they typically only consider certain network evolution mechanisms, making them suitable for specific network structures. Prediction accuracy for other types of network structures is difficult to guarantee, resulting in weak robustness across network types. In contrast, supervised learning has the advantage of defining the link weight prediction problem as a regression problem, resulting in relatively stable prediction accuracy across different network types. However, its disadvantage is that the model construction fails to fully consider the evolution mechanisms of different network types, resulting in a weak ability to infer new weight information within the network. 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 the 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, 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, the weighted network weights are reconstructed through the VGAE (Variational Graph Autoencoders) encoding link and the MLP (Multilayer Perceptron) decoding link to obtain the weight matrix W2;

[0014] Step S5, using linear fusion method, combine matrices W1 and W2 to obtain the 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 perturbed 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 nodes 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.

[0020] Furthermore, the weight reconstruction encoding process of the weighted network in step S4 is expressed as follows 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', the embedding vector After training the MLP model, we get W i ′∈R 1×N .

[0024] Furthermore, in step S5, in order to balance the proportions 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;

[0028] Define node v i The embedding of non-adjacent nodes is represented as negative samples, and the positive samples are aggregated from neighboring nodes and 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] 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] Training module, used to extract the T A part of the perturbation set ΔW is randomly selected, and the rest is represented 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 the 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 eigenvector, allowing only slight changes in the eigenvalues.

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

[0048] 4. This invention combines the advantages of network reconstruction models, enabling both deep exploration of the network's underlying structural characteristics and broad capture of neighboring node information. Furthermore, it draws on the first-order perturbation theory of the Hamiltonian in quantum mechanics, employing 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 graph of the tested algorithm on 8 tested networks. DETAILED DESCRIPTION

[0054] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall 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 as follows. Figure 2 This method combines network reconstruction and weight perturbation techniques, which not only ensures high-precision predictions for various network types, 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 the perturbation set ΔW is randomly selected, and the rest is represented as W r ;

[0059] Step S3, 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: linearly combine the matrices W1 and W2 to obtain the 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] In step S4, the network reconstruction model mainly obtains the structural feature representation of the node by mining the weighted network weight matrix, and uses compression loss to constrain the 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. 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 that covers 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, where the 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 will not tend to 0. That is: if W ij If it is greater than 0, then P ij =η>1, otherwise P ij = 1. Therefore, the weight information reconstruction loss function of this method is:

[0078]

[0079] The above reconstruction methods treat the feature vector of each node as an independent element, and rarely consider the dependencies between neighboring nodes in the network. Based on this, the present invention uses a node-level contrastive loss to constrain the embedding vector, making the anchor vector close to positive samples and away from negative samples. Its formal definition is as follows:

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

[0081]

[0082]

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

[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] This paper selects eight 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 set to test set for all networks in the following experiments is 9:1. Table 1 lists the basic topological features of the tested network datasets, 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 validation, this experiment compared and analyzed the root mean squared error (RMSE) and Pearson correlation coefficient (PCC) between the predicted and true weight values. Furthermore, this experiment evaluated the overall performance of the algorithms using the prediction accuracy ranking metrics of RMSE and PCC. This metric requires ranking each algorithm's performance on each network in descending order and calculating the mean ranking of each prediction algorithm across all networks to reflect the algorithm's overall performance across all networks.

[0095] Figure 4 The RMSE evaluation results of 12 algorithms on 8 networks are shown. The algorithms are arranged in ascending order by average, and the average RMSE value is marked above each algorithm. Figure 4 The algorithms can be roughly divided into two tiers: the first tier includes WPNR, WPLF, pWSBM, and ZHU, with the remaining algorithms grouped into the second tier. In particular, the WPNR algorithm performed best among the four networks, ranking first in average RMSE, demonstrating strong robustness across different network types. Among the first-tier algorithms, the WPLF algorithm, which recovers the weight matrix through latent factor decomposition, achieves good prediction results. The pWSBM and ZHU algorithms also have high prediction accuracy due to their assumption that network weights follow a normal distribution (which is consistent with the actual distribution of weight values ​​in most networks). In summary, the WPNR algorithm offers significant advantages over the other algorithms.

[0096] Table 2 shows the average rankings of the 12 algorithms across various network types, based on the RMSE metric. The WPNR algorithm takes the top spot with a mean ranking of 1.63. This result highlights the significant competitive advantage of the proposed algorithm across a wide range of network types.

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

[0098]

[0099] Table 3 presents the Cohen's d statistic, derived from a t-test. This metric assesses the statistical difference in the RMSE effect size between pairs of algorithms across all tested networks. Specifically, the Cohen's d values ​​for the WPNR algorithm compared to the WPLF and pWSBM algorithms were 0.397 and 0.452, respectively. Both values ​​are below the medium effect size threshold of 0.5, indicating a perceptible but not extreme difference between the WPNR algorithm and these two algorithms, demonstrating a slight advantage for the WPNR algorithm. Notably, when the WPNR algorithm is compared to the other algorithms, its effect size exceeds the large effect size threshold of 0.8, clearly demonstrating a significant advantage for the WPNR algorithm over the other algorithms. In summary, the data analysis in Table 3 reveals that the WPNR algorithm exhibits significant performance superiority over most of the compared algorithms.

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

[0101]

[0102] Figure 5 Tables 4 and 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 The results reveal 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, strongly proving 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 this paper has demonstrated 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, together with the WPLF, pWSBM, and ZHU algorithms, has demonstrated excellent link weight recovery performance, and the advantages of WPNR are more obvious than those of other algorithms. In addition, in tests of various network types, the WPNR algorithm can also continue to demonstrate 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 proposed in this invention with 11 classic link weight prediction algorithms on 8 different types of networks, it is found that the algorithm proposed in this invention has obvious advantages, which verifies that the algorithm proposed in this 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 eigenvector is ensured, allowing only slight changes in the eigenvalues ​​to generate predicted weights. Ultimately, 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] While 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 these embodiments without departing from the principles and spirit of the invention, and that the scope of the 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 △W, and the rest is represented as W r ; Step S3, 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 △W r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1; Among them, the calculation formula of the perturbed weight matrix W1 is: where x i and λ i are the eigenvectors and eigenvalues ​​corresponding to the matrix, represents the increment of eigenvalue; 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; The weight reconstruction encoding process of the weighted network is expressed as follows through the VGAE encoding link: 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 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, a reparameterization technique is used, namely: Z = μ + σ * ε, where ε ~ N (0, 1); Step S5: linearly combine the matrices W1 and W2 to obtain the 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; Step S6: test set W V Compare the corresponding weight value with the predicted weight value to determine the effectiveness of the algorithm; 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; Define node v i The embedding of non-adjacent nodes is represented as negative samples, and the positive samples are aggregated from neighboring nodes and 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: The formula of the overall loss function is: L=L reconstruct +γL con 。 2. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1, characterized in that: The network reconstruction model obtains the structural feature representation of nodes 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.

3. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1, 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', the embedding vector After training the MLP model, we get W i ′∈R 1×N .

4. The link weight prediction method based on network reconstruction and weight perturbation according to claim 1, characterized in that: In step S5, in order to balance the proportions 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 △W represents the mean of all elements in the perturbation weight matrix △W, and RMSE(ΔW,ΔW) represents the root mean square error between the original perturbation weight matrix △W and its value ΔW predicted by the weight perturbation model.

5. A link weight prediction system based on network reconstruction and weight perturbation, characterized in that: It includes partitioning 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; Training module, used to extract the T A part of the set is randomly selected as the perturbation set △W, and the rest is represented 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 △W r Apply influence, calculate the incremental matrix of eigenvalues, and keep the eigenvector unchanged to obtain the perturbed weight matrix W1; Among them, the calculation formula of the perturbed weight matrix W1 is: where x i and λ i are the eigenvectors and eigenvalues ​​corresponding to the matrix, represents the increment of eigenvalue; 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 weight reconstruction encoding process of the weighted network is expressed as follows through the VGAE encoding link: 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 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, a reparameterization technique is used, namely: Z = μ + σ * ε, where ε ~ N (0, 1); The fusion module is used to combine the matrices W1 and W2 in a linear fusion manner to obtain the 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 Representative weight consistency index 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; Define node v i The embedding of non-adjacent nodes is represented as negative samples, and the positive samples are aggregated from neighboring nodes and 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, and the temperature coefficient, respectively, and the contrast loss function of all nodes is obtained, which is expressed as follows: The formula of the overall loss function is: L=L reconstruct +γL con 。

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