Link weight disturbance method based on feature selection and evolutionary algorithm

Abstract

The invention provides a link weight perturbation method based on feature selection and an evolutionary algorithm. The method comprises the following steps: step 1, extracting features of connecting edges; the features of the connecting edges comprise node similarity features of the original network and node centrality features of the line graph network; step 2, performing prediction by using a link weight prediction model of multi-element network feature fusion; step 3, outputting feature importance ranking by using a random forest; and 4, disturbing the important features, and modifying corresponding weights by using an evolutionary distributed estimation algorithm. According to the invention, through an intelligent evolutionary algorithm and a feature selection method, the link weight can be adjusted in a targeted manner, so that disturbance can be dynamically adapted according to the characteristics of different networks, and the privacy protection requirements in different network environments can be flexibly met.

Description

Technical Field

[0001] The present application relates to the technical field of machine learning and network analysis, and in particular to a link weight perturbation method based on feature selection and evolutionary algorithm. Background Art

[0002] With the rapid development of big data and network analysis technology, weighted networks, as an important network representation method, have been widely used in many fields. The link weights in weighted networks reflect the strength of the relationship between nodes or some physical properties. Application scenarios include social networks, financial networks, biological networks, transportation networks, etc. For example, in social networks, the weight of a link represents the closeness of the relationship between users; in financial networks, the weight represents the transaction volume between financial institutions; in biological networks, the weight may reflect the strength of interaction between proteins. Therefore, link weight prediction has become one of the important tasks in network analysis, especially in the presence of missing or incomplete information. How to predict the missing link weights through the existing network structure has become an important direction to promote network integrity analysis and evolution prediction.

[0003] Most methods for predicting link weights are based on the structural features of the network, such as local similarity, node centrality, adjacency matrix, etc., and use these features to predict the corresponding weights. At present, some studies use a multi-feature fusion method to convert the original network into an edge network, use the node centrality features in the edge network to represent the importance of the edge, and then combine the node similarity features for comprehensive analysis. Finally, the link weights are predicted through machine learning algorithms (such as random forests, support vector machines, gradient boosting trees, etc.). Although these methods have improved the prediction accuracy to a certain extent, they often focus on accuracy optimization and ignore the need for privacy protection. For example, some link weights may involve sensitive information (such as private relationships in social networks, financial transaction data, etc.). If these weights are inferred by attackers through link weight prediction algorithms, it will seriously threaten data security and privacy protection.

[0004] Most existing link weight prediction methods focus on improving prediction accuracy, but do not fully consider how to protect sensitive information in the network. Current link weight prediction models usually input the structure and related features of the entire network into the machine learning model for training. If the network contains private links, attackers may infer the weights of private links through model training. Especially in open or semi-open network environments, attackers can gradually recover hidden sensitive information through multiple queries and model training, which in turn leads to privacy leakage, commercial espionage, and even identity theft. Therefore, traditional link weight prediction methods cannot effectively prevent this privacy leakage risk.

[0005] Currently, there are relatively few studies on perturbations for link weight prediction, which makes the problem of privacy link leakage particularly prominent. At the same time, in the field of adversarial defense, the researchers' goal is to improve the robustness of link weight prediction methods. Analyzing and learning the perturbation mechanism and attack characteristics of malicious attackers is the top priority for achieving adversarial defense. Only by deeply exploring the intentions and means of attackers can we truly achieve targeted results. In view of this, it is extremely important to study adversarial attack strategies for network data mining algorithms. Summary of the invention

[0006] The present application provides a link weight perturbation method based on feature selection and evolutionary algorithm, which can be used to solve the technical problem that there are relatively few perturbation studies on link weight prediction.

[0007] The present application provides a link weight perturbation method based on feature selection and evolutionary algorithm, the method comprising:

[0008] Step 1, extracting edge features; edge features include node similarity features of the original network and node centrality features of the line graph network;

[0009] Step 2: Use the link weight prediction model fused with multiple network features to make predictions;

[0010] Step 3: Use random forest to output feature importance ranking;

[0011] Step 4: Perturb the important features and modify the corresponding weights using the evolutionary distributed estimation algorithm.

[0012] Furthermore, the node similarity features include CN, SA, JAC, HPI, HDI, SI, LHN, AA, RA, PA, FM, LP, and LRW;

[0013] Among them, the Common Neighbors Index (CN) is defined as follows:

[0014]

[0015] Where Γ(i) represents the neighbor set of node i, Γ(j) represents the neighbor set of node i, and |·| represents the number of elements in the set. In network science, the CN index of each node pair is calculated through the adjacency matrix A, that is, s CN =h 2 ;

[0016] Salton Index (SA), the Salton Index is defined as the cosine similarity of the common neighbor sets of two nodes; SA is defined as follows:

[0017]

[0018] Among them, k i represents the degree of node i, k j represents the degree of node j, SA is the normalized index of common neighbors;

[0019] Jaccard Index (JAC), the definition of JAC index is as follows:

[0020]

[0021] Hub Promoted Index (HPI), the definition of HPI is as follows:

[0022]

[0023] Hub Depressed Index (HDI), the definition of HDI is as follows:

[0024]

[0025] Furthermore, node centrality features include DC, CC, BC, EC, PR, H, and CO;

[0026] Among them, degree centrality (DC) is defined as the normalized degree value of the node; the definition of degree centrality is as follows:

[0027]

[0028] Closeness Centrality (CC), closeness centrality is defined as the reciprocal of the average distance from a node to all other nodes; closeness centrality is defined as follows:

[0029]

[0030] Betweenness Centrality (BC): Betweenness centrality is defined as the ratio of the number of shortest paths between all node pairs in the network that pass through a certain point to all shortest paths; the definition of betweenness centrality is as follows:

[0031]

[0032] where g st Represents the number of shortest paths between nodes s and t, indicating The number of shortest paths between nodes s and t that pass through node i.

[0033] Furthermore, step 2, using a link weight prediction model fused with multiple network features to perform prediction, includes:

[0034] By converting the original network into an edge network, the node centrality features of the edge network are used to represent the edge importance features of the original network. Then, the node similarity features of the original network are combined with the importance features of the edge network as the overall features of the edges in the original network. Finally, random forest is used to regress the predicted value of the target and evaluate the importance of the features.

[0035] Furthermore, in step 3, the training process of random forest is as follows:

[0036] Step 31, construct multiple decision trees: the generation process of each decision tree is to randomly select samples from the data set with replacement, and each tree randomly selects a feature subset when splitting a node;

[0037] Step 32, calculate the contribution of each feature: in each tree splitting process, evaluate the effect of each feature on the model prediction performance; the greater the information gain, the greater the corresponding feature can significantly reduce the uncertainty of the model when splitting, and the greater the impact on the prediction result;

[0038] Step 33, output feature importance ranking: After all trees are trained, random forest summarizes the importance of all features and gives an importance score for each feature; the score is obtained by calculating the sum of the contributions of each feature in all trees;

[0039] Finally, the random forest outputs a ranking of feature importance, where the higher the ranking, the greater the impact on the predicted target.

[0040] Furthermore, step 4 is to perturb the important features and modify the corresponding weights using the evolutionary distributed estimation algorithm; including:

[0041] Step 41, select important features: select the features that have the greatest impact on the prediction based on the feature importance ranking;

[0042] Step 42, determining important node pairs: based on the most important features, selecting a preset number of node pairs according to the ranking;

[0043] Step 43, adjusting the weight value: perturbing the selected node pair, modifying the weight value of the corresponding node pair, thereby disturbing the relationship between the important feature and the link weight;

[0044] The weights of some edges in the original network are modified in the network. The perturbed network will become new input data for subsequent training and prediction.

[0045] The link weight perturbation has the following restrictions: the modified weight value must be one of the original network weight set to avoid unreasonableness of the modified weight.

[0046] Furthermore, in step 43, an evolutionary computing method - a distributed estimation algorithm is introduced to perform intelligent perturbations on the weights of the edges to be modified in the network by simulating evolution; the estimation process of EDA is as follows:

[0047] Step 431, chromosome encoding:

[0048] Each chromosome represents a set of edge weights selected from the network. The number of genes in the chromosome is equal to the number of edges to be modified. Each gene in the chromosome is a weight value, representing the weight to be assigned to the corresponding edge.

[0049] Step 432, determine the fitness function:

[0050] The evaluation index of link weight prediction is RMSE, which is defined as follows:

[0051]

[0052] Where y is the predicted value, is the actual value;

[0053] The fitness function is calculated as follows:

[0054] Step 4321, modifying and selecting the weight of the edge according to the chromosome;

[0055] Step 4322, using a link weight prediction model based on multi-network feature fusion to perform training on the modified network structure;

[0056] Step 4323, using the model to predict the weight of the target edge in the network, i.e., the privacy edge, and calculating the root mean square error between the predicted value and the actual value;

[0057] Use RMSE as the fitness function value f of the chromosome i ;

[0058] Step 433, select an operation:

[0059] The roulette wheel method is used for selection. The probability p of being selected from the parent generation is determined according to the fitness value. The larger the fitness value, the greater the probability of being selected, that is, p∝f i At the same time, in each generation of evolving population, a part of elite individuals are selected according to the fitness value and retained in the next generation of population.

[0060] Step 434, mutation operation:

[0061] Through the selection operation, the chromosome with better scores is selected for mutation; the gene position on each chromosome is traversed, and then the weight on the corresponding gene is randomly replaced according to the mutation rate pm; at the same time, the legitimacy of the mutation needs to be ensured, and the weights that need to be replaced are selected from the weight set of the original network for replacement;

[0062] Step 435, distribution statistics:

[0063] Through the selection operation sampling, the probability distribution of the gene is statistically calculated, and then new chromosomes are generated based on the probability distribution: first, some chromosomes are selected through the selection operation, and then the distribution of the selected weight values ​​in these chromosomes is statistically calculated. Finally, according to their respective distributions, new weight values ​​are generated through sampling to form new chromosomes;

[0064] The new set of weights represented by the new chromosome will be used to directly replace the weights of the node pairs selected by the original network; after multiple rounds of iterations, the algorithm gradually optimizes the weight perturbation strategy to achieve the purpose of reducing the model's prediction accuracy for the target link weight.

[0065] Compared with the prior art, the present invention has the following significant advantages:

[0066] 1. The present invention uses an intelligent evolutionary algorithm and feature selection method to specifically adjust link weights, so that disturbances can dynamically adapt to the characteristics of different networks and flexibly respond to privacy protection requirements in different network environments.

[0067] 2. The method provided by the present invention not only effectively reduces the prediction accuracy of the weight prediction model for the privacy link weight, thereby effectively preventing the leakage of the privacy link, but also provides a reference for enhancing the robustness of the prediction model, enabling it to better resist various attack methods.

[0068] 3. This invention provides a new privacy protection solution that does not rely on traditional encryption or data perturbation technology, but balances the contradiction between privacy protection and prediction accuracy through multi-level perturbation and intelligent adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of the present invention.

[0070] Figure 2 Schematic diagram of the conversion of the original network into an edge network.

[0071] Figure 3 This is a framework diagram of the weight prediction algorithm based on multi-feature fusion.

[0072] Figure 4 Flowchart of the EDA algorithm.

[0073] Figure 5The prediction results of the link weight prediction model based on multi-feature fusion in different scenarios.

[0074] Figure 6 The prediction results of the GCN-based weight prediction model in different scenarios. DETAILED DESCRIPTION

[0075] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0076] The present invention proposes a link weight perturbation method based on feature selection and evolutionary algorithm, which is used to achieve privacy protection in the process of link weight prediction. The method effectively interferes with the attacker's prediction of sensitive link weights by introducing intelligent perturbations in the network. Specifically, the method includes proposing node similarity features of the original network and node centrality features of the edge network, then using a random forest algorithm for regression prediction and evaluating the importance of the features, then selecting a certain number of edges based on the most influential features, and generating a weight adjustment scheme through an evolutionary algorithm to perturb their weights. The present invention can effectively prevent the leakage of sensitive information and ensure that the prediction accuracy of privacy link weights is reduced in the process of link weight prediction.

[0077] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0078] Step 1, extract edge features; edge features include node similarity features of the original network and node centrality features of the line graph network.

[0079] In the original graph (OG), node similarity features are extracted, namely CN, SA, JAC, HPI, HDI, SI, LHN, AA, RA, PA, FM, LP and LRW. For ease of understanding, several of these indicators are briefly introduced.

[0080] (1) Common Neighbors Index (CN)

[0081] The common neighbor index is the simplest and best understood similarity index. In sociology, it is common sense that the more common friends two people have, the more likely they are to know each other. That is, in a social network, if there are more common neighbors between two nodes, the greater the probability that the two nodes will form an edge. CN is defined as follows:

[0082]

[0083] Where Γ(i) represents the neighbor set of node i, Γ(j) represents the neighbor set of node i, and |·| represents the number of elements in the set. In network science, the CN index of each node pair is calculated through the adjacency matrix A, that is, s CN =A 2 ;

[0084] (2) Salton Index (SA)

[0085] The Salton index is defined as the cosine similarity of the common neighbor sets of two nodes; SA is defined as follows:

[0086]

[0087] Among them, k i represents the degree of node i, k j represents the degree of node j, SA is the normalized index of common neighbors;

[0088] (3) Jaccard Index (JAC)

[0089] The Jaccard index is a classic statistical index used to compare sample similarity. In network science, the definition of the JAC index is as follows:

[0090]

[0091] (4) Hub Promoted Index (HPI)

[0092] The high-degree node index takes into account the degree of the node. If a node with a small degree has a large similarity with the Hub node, the probability of the two nodes forming an edge is high. The definition of HPI is as follows:

[0093]

[0094] (5) Hub Depressed Index (HDI)

[0095] Similarly, the high degree node disadvantage index also takes into account the node's degree, but the definition is opposite to the previous indicator. The definition of HDI is as follows:

[0096]

[0097] Secondly, in order to extend the node centrality feature to the edge importance feature, we use the Line Graph (LG) model in the field of complex networks, such as Figure 2As shown in the figure, the original network is converted into an edge network, and finally the node importance features in the edge network, namely DC, CC, BC, EC, PR, H and CO, are extracted as the important features for predicting edge connections. Similarly, for ease of understanding, several indicators are briefly introduced.

[0098] (4) Degree Centrality (DC)

[0099] Degree centrality is defined as the normalized degree value of a node; obviously, degree centrality is the simplest indicator to measure the importance of a node. The definition of degree centrality is as follows:

[0100]

[0101] (5) Closeness Centrality (CC)

[0102] Closeness centrality is defined as the inverse of the average distance from a node to all other nodes; the greater the closeness centrality of a node, the closer the node is to other nodes and the more central it is. The definition of closeness centrality is as follows:

[0103]

[0104] (6) Betweenness Centrality (BC)

[0105] Betweenness centrality is defined as the ratio of the number of shortest paths between all node pairs in the network that pass through a certain point to all shortest paths; the definition of betweenness centrality is as follows:

[0106]

[0107] where g st Represents the number of shortest paths between nodes s and t, indicating The number of shortest paths between nodes s and t that pass through node i.

[0108] The node importance features in the edge network, namely DC, CC, BC, EC, PR, H and CO, are extracted as the importance features for predicting edge weights.

[0109] Step 2: Use the link weight prediction model based on multi-network feature fusion to make predictions;

[0110] The link weight prediction model based on multi-feature fusion is a model with relatively good weight prediction effect. Specifically, it converts the original network into an edge network, uses the node centrality feature of the edge network to represent the edge importance feature of the original network, and then combines the node similarity feature of the original network with the importance feature of the edge network as the overall feature of the edge in the original network. Finally, traditional supervised learning is used, such as random forest, gradient boosting tree, support vector machine and other common supervised learning algorithms. Here, random forest is used to regress the predicted value of the target. Figure 3 The figure shows the system block diagram of the model. The main innovation of this method is to map the node centrality feature to the edge importance feature through network transformation, and then put the two types of features together into the traditional machine learning model to obtain better prediction accuracy. Using this model to train on the original network, the model can fit our network well. The significant advantage of the random forest in the model is that the random forest can evaluate the importance of features, and then find the features that have a greater impact on weight prediction, so as to perturb them.

[0111] Step 3: Use random forest to output feature importance ranking;

[0112] Random forest is a powerful ensemble learning method that improves the accuracy and stability of the model by building multiple decision trees and aggregating the prediction results of these trees. A significant advantage is that random forest can evaluate the importance of features, which is very useful for feature selection, feature optimization, and model improvement.

[0113] This feature importance ranking identifies the features that have the greatest impact on the prediction results. Based on these feature rankings, we can specifically adjust or modify the features of the model input, thereby reducing the model's prediction accuracy.

[0114] Specifically, the training process of random forest is as follows:

[0115] Step 31, construct multiple decision trees: The generation process of each decision tree is to randomly select samples from the data set with replacement (i.e., Bootstrap sampling), and each tree randomly selects a feature subset when splitting a node;

[0116] Step 32, calculate the contribution of each feature: During each tree split, evaluate the improvement of each feature on the model prediction performance; usually, this contribution is measured by calculating the "information gain" or "Gini index improvement" caused by the feature. The greater the information gain, the greater the impact of the corresponding feature on the prediction result.

[0117] Step 33, output feature importance ranking: After all trees are trained, Random Forest summarizes the importance of all features and gives each feature's importance score; the score is obtained by calculating the sum of each feature's contribution in all trees; for example, for regression problems, feature importance is usually calculated by observing the effect of the feature on reducing model error (such as mean square error). If a feature frequently appears in node splits in all trees and significantly reduces the error, the feature's importance score will be high.

[0118] Finally, the random forest outputs a ranking of feature importance, where the higher the ranking, the greater the impact on the predicted target. This ranking provides a feasible feature selection scheme and identifies which features play a key role in model training.

[0119] Step 4: Perturb the important features and modify the corresponding weights using the evolutionary distributed estimation algorithm;

[0120] After obtaining the feature importance ranking through the random forest model, the features that have the greatest impact on link weight prediction can be identified. Next, these features will be perturbed to affect the prediction accuracy of the model. The perturbation process is as follows:

[0121] Step 41, select important features: select the features that have the greatest impact on the prediction based on the feature importance ranking obtained in step 3. For example, if a feature (such as the common neighbor indicator CN) occupies a high position in the feature ranking, it means that it plays a key role in link weight prediction.

[0122] Step 42, determine important node pairs: based on the most important feature, select a preset number of node pairs according to the ranking; for example, if the important feature is CN, the top 10% of node pairs with the highest CN similarity index can be selected from all node pairs.

[0123] Step 43, adjusting the weight value: perturbing the selected node pair, modifying the weight value of the corresponding node pair, thereby disturbing the relationship between the important feature and the link weight;

[0124] The weights of some edges in the original network are modified in the network, and the perturbed network will become the new input data for subsequent training and prediction. In this way, the model is trained on the perturbed network, which can maximally disrupt the model training process, thereby affecting the prediction accuracy of the link weight model. For example, to predict the interaction intensity between two people in a social network, that is, the link weight, through the previous steps, the features that have the greatest impact on weight prediction are selected, such as the number of common neighbors CN: the number of common friends between two nodes. Generally speaking, if the CN index of a node pair is relatively large, that is, the two nodes have more common neighbors, then their corresponding link weight (interaction intensity) should be larger. When perturbing the network, if this weight is reduced, the model may not be able to effectively fit the wrong data because the intervention destroys the natural relationship between the original feature and the target weight, and the correlation between the CN index and the weight is reduced, resulting in a decrease in prediction accuracy.

[0125] Obviously, the more unreasonable the modification of the edge weight is, such as modifying it to a very large or very small value, the better the perturbation effect. However, in order to ensure the concealment of the perturbation and data availability, the following restrictions are imposed on the link weight perturbation: the modified weight value must be one of the original network weight set to avoid the irrationality of the modified weight; if the weight of the link is arbitrarily modified and is not in the weight set in the original network, it is likely to be discovered by others. For this reason, when we modify the weight of a node pair, the selected weight should be one of the original network weight set.

[0126] Select a certain number of weights from the original network weight set and assign them to the selected node pairs. This problem is considered a combinatorial optimization problem. At the same time, in order to avoid the opposite or unexpected effects of simply adjusting the link weights manually, it is necessary to flexibly adjust the weights according to the network characteristics. Therefore, the evolutionary computing method - Estimation of Distribution Algorithm (EDA) is introduced to intelligently perturb the weights of the edges to be modified in the network by simulating evolution. The algorithm flow chart of EDA is shown below: Figure 4 shown.

[0127] The estimation process of EDA is as follows:

[0128] Step 431, chromosome encoding:

[0129] Each chromosome represents a set of edge weights selected from the network. The number of genes in the chromosome is equal to the number of edges to be modified. Each gene in the chromosome is a weight value, representing the weight to be assigned to the corresponding edge.

[0130] Step 432, determine the fitness function:

[0131] The evaluation index of link weight prediction is RMSE, which is defined as follows:

[0132]

[0133] Where y is the predicted value, is the actual value; obviously, the smaller the RMSE, the smaller the gap between the predicted value and the actual value, and the more accurate the algorithm prediction is.

[0134] The fitness function is calculated as follows:

[0135] Step 4321, modify the weight of the edge we choose according to the chromosome;

[0136] Step 4322, using a link weight prediction model based on multi-network feature fusion to perform training on the modified network structure;

[0137] Step 4323, using the model to predict the weight of the target edge (i.e., the privacy edge) in the network, and calculating the root mean square error between the predicted value and the actual value;

[0138] Use RMSE as the fitness function value f of the chromosome i ;

[0139] Step 433, select an operation:

[0140] The roulette wheel method is used for selection. The probability p of being selected from the parent generation is determined according to the fitness value. The larger the fitness value, the greater the probability of being selected, that is, p∝f i At the same time, in each generation of evolving population, a part of elite individuals are selected according to the fitness value and retained in the next generation of population.

[0141] Step 434, mutation operation:

[0142] Through the selection operation, the chromosome with better scores is selected for mutation; the gene position on each chromosome is traversed, and then the weight on the corresponding gene is randomly replaced according to the mutation rate pm; at the same time, the legitimacy of the mutation needs to be ensured, and the weights that need to be replaced are selected from the weight set of the original network for replacement;

[0143] Step 435, distribution statistics:

[0144] Through the selection operation sampling, the probability distribution of the gene is statistically calculated, and then new chromosomes are generated based on the probability distribution: first, some chromosomes are selected through the selection operation, and then the distribution of the selected weight values ​​in these chromosomes is statistically calculated. Finally, according to their respective distributions, new weight values ​​are generated through sampling to form new chromosomes;

[0145] The new set of weights represented by the new chromosome will be used to directly replace the weights of the node pairs selected by the original network; after multiple rounds of iterations, the algorithm gradually optimizes the weight perturbation strategy to achieve the purpose of reducing the model's prediction accuracy for the target link weight.

[0146] Execute steps 1, 2, 3, and 4 in sequence. After the perturbation is completed, retrain the model and evaluate its prediction accuracy. By comparing the changes in model accuracy before and after the perturbation, you can verify whether the perturbation has successfully reduced the prediction accuracy of the model. If the perturbation is effective, you can see that the prediction performance of the model has dropped significantly, proving that the perturbation has achieved the desired effect.

[0147] Example

[0148] An embodiment of the invention is described in detail as follows. The simulation platform runs on the Windows 11 operating system, and the algorithm is implemented using Python 3.10. During the experiment, for the random forest, we set the number of trees to 3000. The main parameters of the evolutionary computation EDA are shown in Table 1.

[0149] Table 1 Main parameters of Evolutionary Computing EDA

[0150] parameter Value Population size pop_size 100 Mutation probability pm 0.1 Iterations of the algorithm 2000 Number of elite individuals 5 The number of populations used to estimate the distribution in EDA 150

[0151] In order to test the performance of the present invention, this embodiment is tested on the Celegans network, and the network topology is shown in Table 2.

[0152] Celegans: A neural network of worms. Nodes represent neurons, edges represent synaptic contacts between neurons, and edge weights represent the number of synapses.

[0153] Use the exponential transformation method to normalize all edge weights to the interval [0,1], that is:

[0154]

[0155] Table 2 Basic topological characteristics of Celegans weighted network

[0156] feature value V 297 ∣E∣ 2148 k 14.465 C 0.308 d 2.455

[0157] Two traditional evaluation indicators are used to compare the effects of different algorithms, as follows:

[0158] (1) Pearson Correlation Coefficient (PCC)

[0159]

[0160] Where n is the number of samples, andx are the mean and standard deviation of sample x respectively. The value range of PCC is between -1 and 1. If the two sample variables x and y are positively correlated, then the value of PCC is greater than 0; conversely, if the two variables are negatively correlated, then the value of PCC is less than 0; if the two variables are unrelated, then the value of PCC is equal to 0.

[0161] (2) Root Mean Squared Error (RMSE)

[0162] The definition of RMSE is as follows:

[0163]

[0164] Where y is the predicted value, is the actual value. Obviously, the smaller the RMSE, the smaller the gap between the predicted value and the actual value, and the more accurate the algorithm prediction is.

[0165] Divide all the links in the network into ten non-adjacent parts, select one of them as the test set, and regard the test set as the private links that need to be hidden, in order to prevent the weights on them from being predicted, and use the remaining nine as training sets. Use the above algorithms to generate link perturbations, and then use the ten-fold cross-validation method to calculate the RMSE and PCC of link weight prediction.

[0166] A link weight prediction model based on multi-network feature fusion was selected to evaluate the perturbation effect, and the model was named LG-RF. To verify the effectiveness of the method, prediction experiments were conducted in the following three scenarios: prediction based on the original graph, prediction after random perturbation on the original graph, and prediction based on the proposed perturbation method. The prediction results in each scenario are shown in Figure 2. Figure 5 shown.

[0167] Judging from the prediction results, the prediction performance based on the original graph is the best (RMSE=0.13, PCC=0.41), indicating that the model has good prediction ability on undisturbed data. Random perturbation slightly reduces the prediction accuracy of the model (RMSE=0.14, PCC=0.31), but still retains a certain correlation. The perturbation method proposed in the present invention further reduces the prediction ability of the model (RMSE=0.16, PCC=0.11), effectively weakening the model's dependence on network features. This shows that the method provided by the present invention can more significantly disrupt the model's learning of link weights. Compared with random perturbations, the proposed perturbation method is more targeted. By giving priority to adjusting the features that have the greatest impact on weight prediction, it not only effectively weakens the impact of the features on the model, but also reduces the overall prediction performance of the model. This method can dynamically adapt to different network characteristics and has strong versatility and practical value.

[0168] Previously, we assumed that the attacker used LG-RF to predict link weights, but in reality, we know which link weight prediction algorithm the attacker uses. So we want to test the perturbation solution obtained by evolutionary computing, especially EDA, to see how well the defense is transferred to different link weight prediction algorithms. Therefore, we added the link weight perturbation obtained by the final evolution of the EDA algorithm to the training set, used the graph neural network GCN to predict the weights, and calculated the RMSE and PCC of the test set. The graph neural network GCN learns the features of the nodes, and then fuses the node features of the node pairs corresponding to the edges to predict the corresponding weights. The results are as follows: Figure 6 shown.

[0169] The experimental results show that the method provided by the present invention has good migration performance on the GCN model. It adjusts the weights based on the important features selected by random forest, and the generated perturbation solution significantly weakens the GCN's prediction ability for link weights. Compared with random perturbations, the weight adjustment scheme formulated by EDA combined with the feature selection results is more targeted and effective, indicating the superiority of the evolutionary computing algorithm. Overall, the weight perturbation method has high migration ability and defense effect between different models, and provides a reliable strategy for solving unknown attack scenarios. Through the above experiments, it can be seen that the strategy we proposed reduces the correlation between weights and network structure characteristics, and can effectively perturb the existing weight prediction model, protecting the weights of some privacy links.

[0170] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

[0171] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A link weight perturbation method based on feature selection and evolutionary algorithm, characterized in that: The method comprises: Step 1, extracting edge features; edge features include node similarity features of the original network and node centrality features of the line graph network; Step 2: Use the link weight prediction model fused with multiple network features to make predictions; Step 3: Use random forest to output feature importance ranking; Step 4: Perturb the important features and modify the corresponding weights using the evolutionary distributed estimation algorithm.

2. The method according to claim 1, characterized in that The node similarity features include CN, SA, JAC, HPI, HDI, SI, LHN, AA, RA, PA, FM, LP, and LRW; Among them, the Common Neighbors Index (CN) is defined as follows: Where Γ(i) represents the neighbor set of node i, Γ(j) represents the neighbor set of node i, and |·| represents the number of elements in the set. In network science, the CN index of each node pair is calculated through the adjacency matrix A, that is, s CN =A 2 ; Salton Index (SA), the Salton Index is defined as the cosine similarity of the common neighbor sets of two nodes; SA is defined as follows: Among them, k i represents the degree of node i, k j represents the degree of node j, SA is the normalized index of common neighbors; Jaccard Index (JAC), the definition of JAC index is as follows: Hub Promoted Index (HPI), the definition of HPI is as follows: Hub Depressed Index (HDI), the definition of HDI is as follows:

3. The method according to claim 1, characterized in that: node centrality features, including DC, CC, BC, EC, PR, H, and CO; Among them, degree centrality (DC) is defined as the normalized degree value of the node; the definition of degree centrality is as follows: Closeness Centrality (CC), closeness centrality is defined as the reciprocal of the average distance from a node to all other nodes; closeness centrality is defined as follows: Betweenness Centrality (BC): Betweenness centrality is defined as the ratio of the number of shortest paths between all node pairs in the network that pass through a certain point to all shortest paths; the definition of betweenness centrality is as follows: where g st Represents the number of shortest paths between nodes s and t, indicating The number of shortest paths between nodes s and t that pass through node i.

4. The method according to claim 1, characterized in that: Step 2: Use the link weight prediction model based on multi-network feature fusion to make predictions; including: By converting the original network into an edge network, the node centrality features of the edge network are used to represent the edge importance features of the original network. Then, the node similarity features of the original network are combined with the importance features of the edge network as the overall features of the edges in the original network. Finally, random forest is used to regress the predicted value of the target and evaluate the importance of the features.

5. The method according to claim 1, characterized in that In step 3, the training process of random forest is as follows: Step 31, construct multiple decision trees: the generation process of each decision tree is to randomly select samples from the data set with replacement, and each tree randomly selects a feature subset when splitting a node; Step 32, calculate the contribution of each feature: during each tree splitting process, evaluate the effect of each feature on the model prediction performance; The greater the information gain, the more the corresponding feature can significantly reduce the uncertainty of the model when splitting, and the greater the impact on the prediction results; Step 33, output feature importance ranking: After all trees are trained, the random forest summarizes the importance of all features and gives the importance score of each feature; The score is obtained by calculating the sum of the contribution of each feature in all trees; Finally, the random forest outputs a ranking of feature importance, where the higher the ranking, the greater the impact on the predicted target.

6. The method according to claim 1, characterized in that Step 4: perturb the important features and modify the corresponding weights using the evolutionary distributed estimation algorithm; including: Step 41, select important features: select the features that have the greatest impact on the prediction based on the feature importance ranking; Step 42, determining important node pairs: based on the most important features, selecting a preset number of node pairs according to the ranking; Step 43, adjusting the weight value: perturbing the selected node pair, modifying the weight value of the corresponding node pair, thereby disturbing the relationship between the important feature and the link weight; The weights of some edges in the original network are modified in the network. The perturbed network will become new input data for subsequent training and prediction. The link weight perturbation has the following restrictions: the modified weight value must be one of the original network weight set to avoid unreasonableness of the modified weight.

7. The method according to claim 6, characterized in that In step 43, an evolutionary computing method - a distributed estimation algorithm is introduced to perform intelligent perturbations on the weights of the edges to be modified in the network by simulating evolution. The estimation process of EDA is as follows: Step 431, chromosome encoding: Each chromosome represents a set of edge weights selected from the network. The number of genes in the chromosome is equal to the number of edges to be modified. Each gene in the chromosome is a weight value, representing the weight to be assigned to the corresponding edge. Step 432, determine the fitness function: The evaluation index of link weight prediction is RMSE, which is defined as follows: Where y is the predicted value, is the actual value; The fitness function is calculated as follows: Step 4321, modifying and selecting the weight of the edge according to the chromosome; Step 4322, using a link weight prediction model based on multi-network feature fusion to perform training on the modified network structure; Step 4323, using the model to predict the weight of the target edge in the network, i.e., the privacy edge, and calculating the root mean square error between the predicted value and the actual value; Use RMSE as the fitness function value f of the chromosome i ; Step 433, select an operation: The roulette wheel method is used for selection. The probability p of being selected from the parent generation is determined according to the fitness value. The larger the fitness value, the greater the probability of being selected, that is, p∝f i At the same time, in each generation of evolving population, a part of elite individuals are selected according to the fitness value and retained in the next generation of population. Step 434, mutation operation: Through the selection operation, the chromosome with better scores is selected for mutation; the gene position on each chromosome is traversed, and then the weight on the corresponding gene is randomly replaced according to the mutation rate pm; at the same time, the legitimacy of the mutation needs to be ensured, and the weights that need to be replaced are selected from the weight set of the original network for replacement; Step 435, distribution statistics: Through the selection operation sampling, the probability distribution of the gene is statistically calculated, and then new chromosomes are generated based on the probability distribution: first, some chromosomes are selected through the selection operation, and then the distribution of the selected weight values ​​in these chromosomes is statistically calculated. Finally, according to their respective distributions, new weight values ​​are generated through sampling to form new chromosomes; The new set of weights represented by the new chromosomes will be used to directly replace the weights of the node pairs selected by the original network; After multiple rounds of iterations, the algorithm gradually optimizes the weight perturbation strategy to achieve the goal of reducing the model's prediction accuracy for the target link weight.

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