Link prediction algorithm based on network local topology weight
By introducing a link prediction algorithm with local topological weights, combined with local and global information, the existing link prediction algorithms are solved in terms of accuracy and complexity, and efficient and accurate prediction in large-scale networks are achieved.
Patent Information
- Application Number
- CN202510286953.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-12
- Publication Date
- 2025-07-18
AI Technical Summary
The existing link prediction algorithms have shortcomings in prediction accuracy, parameter dependence and computational complexity. They ignore local topology structure and node weights, lack consideration of structural enhancement values, and it is difficult to predict potential links efficiently and accurately in large-scale networks.
A link prediction algorithm based on the local topological weight of the network is proposed. By calculating the aggregation coefficient, structural enhancement value, topological edge weight, local structure edge weight and expanding the local structure edge weight, combining local and global information, link prediction scores are generated to adapt to different network types and reduce the computational complexity.
It improves the accuracy and efficiency of link prediction, can operate efficiently in large-scale networks, and is suitable for social networks, protein interaction networks, and traffic networks, improving the ability to identify potential connections.
Smart Images
Figure CN120342883A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of network science and complex network analysis, and more specifically relates to a link prediction algorithm based on network local topology weights. Background Art
[0002] Link prediction is an important task in complex network analysis, and its goal is to predict new links that may form in the network, or existing hidden links in the network. This has important application values for understanding the evolution of the network and realizing network recommendation, etc. Common link prediction algorithms mainly include methods based on shared numbers, resource allocation, Jaccard coefficients, etc.
[0003] However, these traditional link prediction methods usually only focus on the global topological information between nodes and ignore the local topological structure of the network. The local topological structure of the network, such as clustering coefficient, neighboring nodes, etc., is also very important for link prediction. For example, if two users are both active members of a certain community, then the possibility of a link existing between them will be relatively large.
[0004] In addition, the link prediction algorithm needs to consider the proportional relationship between the actual connection number of a node and the theoretically possible maximum connection number. In this way, the local clustering of the node can be effectively characterized and used as the weight value of the node. At the same time, by combining the neighbor weights of the nodes, the structural enhancement value of each node can be calculated to reflect its influence in the local network.
[0005] There are also some methods that are prediction algorithms based on machine learning. Common ones include decision trees, logistic regression, random forests, neural networks, etc. These methods often require a large amount of training data and have a relatively high computational complexity, and are not suitable for large-scale network data.
[0006] In summary, the existing link prediction algorithms based on network topology face some challenges, including: ignoring the influence of the local topological structure on link prediction, lacking a weight calculation method for nodes and the consideration of the structural enhancement value, etc. The global and local topological information needs to be effectively fused to improve the accuracy and efficiency of link prediction. Therefore, there is an urgent need for a link prediction algorithm that can fully consider the global and local topological information, and at the same time consider the node weights and the structural enhancement value. Summary of the Invention
[0007] The present invention mainly solves the problems existing in the existing link prediction methods in terms of prediction accuracy, parameter dependence, and computational complexity. The present invention proposes a link prediction algorithm based on network local topology weights, which improves the calculation accuracy and prediction ability of node similarity by introducing topological edge weights and combining local structure enhancement values and global information. At the same time, the algorithm can adaptively calculate the topological weights without manual intervention, enabling the algorithm to adapt to different network types, thus having strong generality. In addition, the algorithm mainly uses local topological information, avoiding the complexity of calculating global shortest paths, so the computational efficiency is high and it is suitable for efficient calculation on large-scale networks. Generally speaking, the present invention aims to provide a method for more comprehensive, accurate, and efficient network link prediction to solve the problems existing in the prior art.
[0008] To achieve the above object, the present invention is implemented by the following technical solutions: The algorithm includes:
[0009] Node assignment calculation: Calculate the clustering coefficient of each node according to the degree of the node and the actual number of connections as the weight value of the node;
[0010] Structure enhancement value calculation: Calculate the structure enhancement value of each node through the sum of the neighbor weights of the node to characterize its influence in the local network;
[0011] Topological edge weight calculation: Calculate the topological edge weight by combining the number of common neighbors of two nodes and their structure enhancement values;
[0012] Local structure edge weight calculation: Quantify the potential connection strength of the indirect path based on the product of the topological edge weights of the common neighbors;
[0013] Extended local structure edge weight calculation: Calculate the extended edge weight through the second-order path of non-common neighbors;
[0014] Link prediction score fusion: Combine the local structure edge weight and the extended local structure edge weight to generate a link prediction score.
[0015] In one solution, in the node assignment calculation:
[0016] Calculate the clustering coefficient through the proportional relationship between the degree of the node and the actual number of existing connections, where the ratio of the actual number of connections to the maximum number of connections that the node may form theoretically is used to measure the local clustering of the node, and nodes with high degrees and many actual connections are assigned higher weight values.
[0017] In one solution, in the structure enhancement value calculation:
[0018] The structural enhancement value of each node is the sum of the weight values of all its neighbor nodes. The higher the weight value of the neighbor nodes, the greater the structural enhancement value of the current node, thereby strengthening the influence of ordinary nodes connected to key nodes in the local network.
[0019] In one solution, in the calculation of the topological edge weight:
[0020] The topological edge weight is jointly determined by the normalized product of the number of common neighbors of two nodes and the structural enhancement values of the two nodes, where the normalization operation balances the dominant effect of high-degree nodes on the edge weight through the degree of the nodes.
[0021] In one solution, in the calculation of the local structural edge weight:
[0022] The cumulative product result of the topological edge weights of all common neighbors shared by two nodes is used to quantify the indirect connection strength formed between nodes through common neighbors. Nodes sharing key neighbors have higher local structural edge weights.
[0023] In one solution, in the calculation of the extended local structural edge weight:
[0024] By traversing the first-order non-common neighbors and second-order non-common neighbors of a node, the potential path weights across communities or domains are calculated to capture the indirect connection relationships not covered by common neighbors in sparse networks.
[0025] In one solution, in the link prediction score fusion:
[0026] The local structural edge weight and the extended local structural edge weight are linearly weighted and summed through a preset weight coefficient to generate the final link prediction score, where the weight coefficient is dynamically adjusted according to the network type, with dense networks emphasizing the local structural edge weight and sparse networks emphasizing the extended edge weight.
[0027] In one solution, the optimization method of the weight coefficient includes:
[0028] Based on cross-validation or grid search, with the goal of maximizing the prediction performance on the training set, the proportional parameters of the local structural edge weight and the extended edge weight are determined, and the parameter value range is from 0 to 1, and the optimal combination is selected through the validation set.
[0029] In one solution, the algorithm only traverses local neighbor nodes during the calculation process, specifically including:
[0030] Node assignment and structural enhancement value calculation depend on first-order neighbors, topological edge weight and local structural edge weight calculation depend on common neighbors, and extended edge weight calculation depends on second-order neighbors. The overall time complexity is linearly related to the network scale, which is suitable for efficient processing of large-scale networks. Advantages of the present invention:
[0031] The present invention introduces the Local Topology Weight (LTW) algorithm into the link prediction method. Different from the traditional methods that only rely on the global structure or simple degree information, it provides a comprehensive network structure evaluation mechanism.
[0032] By enhancing and expanding the calculation method of the local structure through the local structure, it can more accurately identify potential connections, improve the accuracy of link prediction, and overcome the problem that traditional prediction methods ignore indirect connection information.
[0033] The calculation framework proposed by the present invention optimizes the calculation overhead, enabling it to operate efficiently in large-scale network data and enhancing the scalability of the model. Brief Description of the Drawings
[0034] Figure 1 is a flowchart of the method of the present invention;
[0035] Figure 2 is a comparison chart of the AUC results of LTW of the present invention and the comparison algorithm. Detailed Embodiments
[0036] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. The typical embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.
[0037] Unless otherwise defined, all technical and scientific terms used in the present invention have the same meaning as understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. The typical embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.
[0038] As Figure 1 shown, to achieve the above object, the present invention proposes a link prediction algorithm based on network local topology weight. This method combines network topology information with a local structure enhancement mechanism to improve the accuracy of link prediction. The algorithm mainly includes the following parts:
[0039] Step 1. Node assignment calculation. The LTW algorithm first measures the importance of each node in the network by its degree and assigns a weight value to each node to reasonably reflect its influence in subsequent calculations. Specifically, for any node i in the network, if it has k i neighbors and the actual number of connections it has is E i , then the clustering coefficient C i of this node can be calculated by the following formula:
[0040]
[0041] where E i represents the actual number of connections of node i, and k i (k i -1) / 2 represents the maximum number of connections that this node can theoretically form. This formula is used to measure the local clustering of nodes, that is, the tightness of nodes in their neighborhoods. Nodes with higher degrees and more connections to other important nodes will be assigned higher values to reflect their key roles in the network.
[0042] Step 2. Structure enhancement value calculation. The LTW algorithm further calculates the "local information" value of each node, which is used to characterize the overall structural relationship between the node and its neighbor nodes. Specifically, the structure enhancement value SC i of a node is calculated from the sum of the assignments of its neighbor nodes:
[0043] SC i = ∑ z∈τ(i) C z (2)
[0044] where τ(i) represents the set of neighbor nodes of node i, and C z is the assignment of neighbor node z. By considering the weight situation of neighbor nodes, this value further strengthens the influence of the node in the entire network structure. Nodes with higher neighbor assignments will significantly increase the structure enhancement value of the current node, thus reflecting their relative importance in the network.
[0045] Step 3. Topological edge weight calculation. In the LTW algorithm, in order to measure the potential connection strength between nodes, a method for calculating topological edge weights is defined. This method comprehensively considers the number of common neighbors of nodes and the structure enhancement value, and the calculation formula is as follows:
[0046]
[0047] Among them, Γ(x) and Γ(y) represent the neighbor sets of nodes x and y respectively, Γ(x) ∩ Γ(y) represents the number of their common neighbors, and Γ(x) ∪ Γ(y) represents the number of their joint neighbors. The first term of the formula reflects the common neighbor relationship between nodes, and the second term further measures the similarity between nodes through the weighted operation of the structural enhancement value and degree of nodes. Through this calculation method, the LTW algorithm can reasonably quantify the association degree between nodes and provide basic data support for link prediction.
[0048] Step 4. Calculation of local structure edge weights. To further enhance the accuracy of link prediction, the LTW algorithm introduces the calculation of local structure edge weights. This calculation method fully considers the indirect relationship formed between nodes through common neighbors. The specific calculation formula is as follows:
[0049]
[0050] This formula captures their indirect influence by calculating the indirect path between nodes x and y (i.e., the edge through the common neighbor a), thus supplementing the possible deficiencies of the direct edge weight. Based on this calculation method, the LTW algorithm can further improve the coverage of link prediction and enhance the ability to identify potential links.
[0051] Step 5. Extended calculation of local structure edge weights. In addition, the LTW algorithm also introduces the extended calculation of local structure edge weights. This part aims to further utilize the adjacency information in a larger range to improve the prediction accuracy of the algorithm. The calculation formula is as follows:
[0052]
[0053] Among them, This set represents the set of neighbors of node b that do not belong to the direct neighbor set of x. This formula improves the link prediction ability by further expanding the indirect connection relationship and utilizing the adjacency information at a greater distance.
[0054] Step 6. Calculation of the final link prediction score. The final step of the LTW algorithm is to obtain the link prediction score for each pair of nodes xx and yy by synthesizing all calculation results. The formula for the final score is as follows:
[0055]
[0056] This formula first considers the local edge weight Then it is further weighted to obtain the topological local edge weight, and finally a comprehensive link prediction score is obtained. This score comprehensively considers the direct similarity and indirect influence between nodes and provides an efficient calculation method for network structure analysis and link prediction.
[0057] Comparative experiment:
[0058] AUC Results of LTW and Comparative Algorithms
[0059] Networks CN AA RA LGC RLR CN2D NSIM LTW Intes 0.8310 0.8385 0.8419 0.8092 0.8403 0.8277 0.8403 0.8472 BrainNet 0.8716 0.8784 0.8799 0.8561 0.8787 0.8676 0.8799 0.8889 Arizona 0.8452 0.8602 0.8646 0.8866 0.8736 0.8214 0.8672 0.8868 EUAir 0.8919 0.8960 0.8969 0.9108 0.8987 0.8852 0.9099 0.9245
[0060] Precision Results of LTW and Comparative Algorithms
[0061] Networks CN AA RA LGC RLR CN2D NSIM LTW Intes 0.4225 0.4097 0.3357 0.3924 0.3776 0.4299 0.4191 0.4579 BrainNet 0.5474 0.5635 0.5518 0.5550 0.5569 0.5545 0.5586 0.6169 Arizona 0.4773 0.4257 0.3731 0.4303 0.4048 0.4681 0.4649 0.5643 EUAir 0.7058 0.6739 0.5421 0.6412 0.5938 0.7092 0.7038 0.7298
[0062] From the above experimental results Figure 2 it can be seen that the LTW algorithm has the best performance on multiple datasets in terms of AUC and Precision, and is superior to the NSIM algorithm.
[0063] Advantages of the LTW algorithm:
[0064] 1. Incorporating local topological structure information to improve prediction accuracy
[0065] Most existing link prediction methods rely on the global network structure and ignore the contribution of local topological information. The present invention introduces a local topological weight (LTW) calculation method, which fully considers the neighbor structure, connection relationship of each node and its importance in the network, thus improving the accuracy of link prediction.
[0066] By calculating the structure enhancement value (SC), the present invention further quantifies the importance of neighbor nodes to the target node, making the prediction results more consistent with the connection patterns in the real network.
[0067] 2. Adopting a topological edge weight calculation method to better measure the potential connection between nodes
[0068] Traditional link prediction methods, such as Common Neighbors (CN) or Jaccard Similarity, only make predictions based on simple adjacency relationships and fail to fully utilize the topological features of nodes.
[0069] The topological edge weight calculation method proposed by the present invention comprehensively considers the number of shared neighbors, node degrees and their local structure enhancement values, making the edge weights more accurately reflect the potential connections between nodes and improving the rationality of predictions.
[0070] 3. Enhancing the comprehensiveness of link prediction through local and extended structure information
[0071] Existing link prediction methods have poor performance in predicting potential connections between distant nodes. The present invention proposes local structure edge weight (LSW) and extended local structure edge weight (ESW), which improve the coverage ability of potential links by considering indirect neighbors and multi-hop connections. This method is not only applicable to dense networks, but can also effectively improve the prediction effect in sparse network environments.
[0072] 4. Low computational complexity, suitable for large-scale networks
[0073] Traditional path- or walk-based methods, such as the Katz index, Random Walk, etc., usually have a relatively high computational complexity and are not suitable for large-scale networks.
[0074] The present invention performs link prediction based on local topological features, while ensuring high accuracy, maintaining a low computational complexity, enabling it to efficiently process large-scale data sets such as social networks, protein interaction networks, traffic networks, etc.
[0075] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The said program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above various methods. Among them, the said storage medium can be a magnetic disk, an optical disk, a Read-Only Memory (ROM), or a Random Access Memory (RAM), etc.
[0076] It should be understood that the detailed description of the technical solutions of the present invention with the aid of the preferred embodiments above is illustrative rather than restrictive. Those of ordinary skill in the art can modify the technical solutions recorded in each embodiment on the basis of reading the specification of the present invention, or perform equivalent substitution on some of the technical features; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of each embodiment of the present invention.
Claims
1. A link prediction algorithm based on network local topology weight, characterized in that: The described algorithm includes: Node assignment calculation: Calculate the clustering coefficient of each node based on the degree of the node and the actual number of connections, and use it as the weight value of the node. Structure enhancement value calculation: Calculate the structure enhancement value of each node through the sum of the weights of its neighbor nodes, which is used to characterize its influence in the local network. Topological edge weight calculation: Combine the number of common neighbors of two nodes and their structure enhancement values to calculate the topological edge weight. Local structure edge weight calculation: Quantify the potential connection strength of the indirect path based on the product of the topological edge weights of the common neighbors. Extended local structure edge weight calculation: Calculate the extended edge weight through the second-order path of non-common neighbors. Link prediction score fusion: Integrate the local structure edge weight and the extended local structure edge weight to generate a link prediction score.
2. The link prediction algorithm based on network local topology weight according to claim 1, wherein: In the node assignment calculation: Calculate the clustering coefficient through the ratio relationship between the degree of the node and the actual number of existing connections. The ratio of the actual number of connections to the maximum number of connections that the node can theoretically form is used to measure the local clustering of the node. Nodes with high degrees and many actual connections are assigned higher weight values.
3. A link prediction algorithm based on network local topology weight according to claim 1, characterized in that: In the structure enhancement value calculation: The structure enhancement value of each node is the sum of the weight values of all its neighbor nodes. The higher the weight value of the neighbor node, the greater the structure enhancement value of the current node, thereby strengthening the influence of ordinary nodes connected to key nodes in the local network.
4. A link prediction algorithm based on network local topology weight according to claim 1, characterized in that: In the topological edge weight calculation: The topological edge weight is jointly determined by the number of common neighbors of two nodes and the normalized product of the structure enhancement values of the two nodes. The normalization operation balances the dominant effect of high-degree nodes on the edge weight through the degree of the node.
5. The link prediction algorithm based on network local topology weight according to claim 1, characterized in that: In the local structure edge weight calculation: Quantify the indirect connection strength formed between nodes through common neighbors by the cumulative product result of the topological edge weights of all common neighbors shared by the two nodes. Nodes pairs sharing key neighbors have higher local structure edge weights.
6. The link prediction algorithm based on network local topology weight according to claim 1, characterized in that: In the extended local structure edge weight calculation: By traversing the first-order non-common neighbors and their second-order non-common neighbors of the node, calculate the potential path weights across communities or domains, which is used to capture indirect connection relationships not covered by common neighbors in sparse networks.
7. A link prediction algorithm based on network local topology weight according to claim 1, characterized in that: In the link prediction score fusion: Generate the final link prediction score by linearly weighting and summing the local structure edge weight and the extended local structure edge weight with a preset weight coefficient. The weight coefficient is dynamically adjusted according to the network type, with dense networks emphasizing the local structure edge weight and sparse networks emphasizing the extended edge weight.
8. A link prediction algorithm based on network local topology weight according to claim 7, characterized in that: The optimization method of the weight coefficient includes: Based on cross-validation or grid search, with the goal of maximizing the prediction performance on the training set, determine the proportional parameter between the local structure edge weight and the extended edge weight. The parameter value range is from 0 to 1, and select the optimal combination through the validation set.
9. The link prediction algorithm based on network local topology weight according to claim 1, wherein: During the calculation process of the algorithm, only local neighbor nodes are traversed, specifically including: Node assignment and structure enhancement value calculation rely on first-order neighbors, topological edge weight and local structure edge weight calculation rely on common neighbors, extended edge weight calculation relies on second-order neighbors, and the overall time complexity is linearly related to the network scale, which is suitable for efficient processing of large-scale networks.