Link prediction method based on node topology characteristics and mutual information

Abstract

The present invention discloses a link prediction method based on node topology features and mutual information. First, self-loops and duplicate edges in the network are removed to eliminate the interference of self-loops and duplicate edges on the prediction results of the method. Then, the local network structure of the node is quantified as the edge structure weight, which is fused with the edge weight through the parameter α to obtain the fusion weight. Next, the method introduces the degree-related weighted node clustering coefficient, mutual information, and path distance to design a weighted link prediction method CWMID based on node topology features and mutual information. The main advantage of the present invention is that by combining multiple topological features of nodes in the network with node mutual information, the utilization of network structure information is more comprehensive. It has good universality and prediction results in different types of networks. At the same time, the prediction accuracy is more accurate than that of most weighted link prediction methods. Experimental results confirm the superiority of the CWMID method designed by the present invention.

Description

Technical Field

[0001] The present invention relates to the technical field of network science link prediction, and is specifically represented by a link prediction method based on node topology features and mutual information. Background Art

[0002] In real life, networks are ubiquitous and can be used to describe and characterize complex systems. Link prediction, a key research branch in network science, aims to predict the likelihood of connections between previously unconnected nodes based on observed network structure. Link prediction has broad applications in a wide range of fields, including biological research, e-commerce, social security, recommender systems, network reconstruction, and label classification.

[0003] With the continuous advancement of link prediction research, undirected, unweighted networks are no longer sufficient for practical applications. Most real-world networks are weighted, and weight is a key characteristic of weighted networks. Edge weights have different meanings in different types of weighted networks. For example, in social networks, weights represent the strength of social relationships; in collaborative networks, weights represent the number of jointly authorized documents by scholars; in food networks, weights represent the carbon flow between species; and in aviation networks, weights represent the volume of transportation between airports. Link prediction methods for weighted networks primarily consider factors such as the natural weights of edges, structural weights, and node attributes. Research on weighted network prediction methods can be categorized into the following: methods based on natural weights, methods based on structural weights, and methods that combine natural and structural weights. Lv et al. proposed a weighted resource allocation method, WRA, by generalizing the unweighted RA method to weighted networks. Experimental results show that considering edge weights can effectively improve the method's prediction accuracy. However, this method utilizes limited information during prediction, which limits its accuracy.

[0004] In recent years, structural weights have been widely used in the study of weighted network link prediction methods. Wang et al. proposed several weighted similarity methods by quantifying the clustering coefficient of edges in a network as the structural weight of the edges. Experiments show that this structural weight plays an important role in improving the prediction accuracy of these methods. Zhu et al. used the normalized clustering coefficient as the structural weight of the edges to construct a weighted network for supervised link prediction. The results show that structural weight can improve the prediction accuracy of the method. Zhu et al. proposed an undirected weighted network model based on mutual information based on local network structural mutual information. They also used edge weights to further enhance the distinguishability of candidate links, thereby improving the prediction accuracy of the method. In response to traditional weighted network link prediction methods that only focus on edge weights and ignore the impact of structural weights on the prediction results, Yuan Rong et al. used the clustering and diffusion characteristics of edges as the structural weights of edges and proposed a WCD weighted link prediction method based on edge structural weights. Compared with weighted methods based on weights and methods based on clustering coefficients, the proposed method has better prediction accuracy. Chen Guangfu et al. proposed a weighted network link prediction model that integrates neighborhood structure and symmetric non-negative matrix factorization to perform tasks such as missing edge prediction and robustness assessment in weighted networks. Experimental results show that the proposed method improves the AUC metric, outperforming existing methods that have high computational complexity and are not applicable to link prediction in large-scale networks. Li Qiaoli et al., building on structural similarity-based methods, introduced topological information coupling and proposed a weighted link prediction method based on topological information coupling. They analyzed the prediction accuracy of the method for different path lengths based on characteristics such as the average shortest path of the network. Experimental results show that the inclusion of differentiated information from different paths significantly improves the prediction performance of the method and demonstrates good robustness. Guo Jingfeng et al., considering that most existing weighted link prediction methods only focus on local or global network features and struggle to balance prediction accuracy and computational complexity, proposed a weighted network link prediction method, STNMP. They validated the method's prediction accuracy and effectiveness on a benchmark dataset, showing that STNMP outperforms existing methods for small-scale networks. Li Ting et al. introduced structural weights into their method. Experimental results show that the method's prediction accuracy is significantly improved after introducing structural weights. Based on the WRA method, the neighborhood network structure of the node is quantified as the edge structure weight, and the fusion weight is obtained by weighted fusion with the edge weight. Secondly, the weighted node clustering coefficient, mutual information and contribution of network path to node similarity related to degree are considered. Summary of the Invention

[0005] A link prediction method based on node topology characteristics and mutual information is provided, which effectively solves the problem of low prediction accuracy of traditional weighted link prediction methods and significantly improves the prediction accuracy of the WRA method.

[0006] The CWMID link prediction method designed in this invention primarily describes node similarity based on network structure weights, weighted clustering coefficients, mutual information, and path information. Liu et al. pointed out that resource transport and information transfer in a network are both related to edge importance, which plays a crucial role in the formation of network topology. Therefore, considering structural weights during link prediction can help improve the accuracy of link prediction methods. Barrat et al., based on the unweighted clustering coefficient, proposed a weighted clustering coefficient to characterize the impact of edge weights on node clustering characteristics, enabling a better estimate of the contribution of each common neighbor node. Furthermore, the goal of link prediction is to predict the probability of an edge between nodes, a probability that can be represented by mutual information. Zhu et al. proposed a mutual information method by combining the common neighbors of a node with the connections between common neighbors. Path information in unweighted networks has a positive impact on the prediction results of the method. For example, the LP method, which considers third-order paths, and the enhanced local path method (ELP), significantly improve prediction accuracy compared to methods based on common neighbors. In weighted networks, paths, as an important means of resource transfer between nodes, play an important role in the generation of edges.

[0007] To achieve the above object, the technical solution adopted by the present invention is: a link prediction method based on node topology characteristics and mutual information, comprising the following steps:

[0008] (1) Training phase

[0009] Step 1: For the weighted network G w , 90% of the edges and all nodes are selected as the training set network by random sampling method The remaining 10% of the edges are used as the test set network Ensure the network connectivity of the training set after division;

[0010] Step 2: Set the parameters α∈(0,1), λ∈(0.001,0.01); according to the parameter value range, use the traversal optimization method to traverse the parameter values. For each set of parameters, calculate the training set The prediction accuracy AUC in train ;

[0011] Step 3: In order to reduce the error caused by random partitioning of the network, given a set of parameter values, loop step 1 T times, and calculate the training set in each loop. The prediction accuracy AUC in train , and then calculate multiple AUC train The average value of the last set of parameters is traversed, according to the AUC train Maximize the network G w The optimal parameter α in * and λ * ;

[0012] (2) Testing phase

[0013] The optimal parameter α obtained by the CWMID method during training * and λ * Substitute into formula (5), in the test set Medium evaluation prediction accuracy AUC test and precision.

[0014] Preferably, for the weighted network G w (V,E,W), where V,E,W represent the node set, edge set and weight set respectively; x and v y The neighborhood structure is quantized into edges (v x ,v y )’s structural weight, denoted as Sw x,y , as shown in formula (1):

[0015]

[0016] In formula (1), k x ,k y Represents node v x ,v y degree; |Γ(v x )∩Γ(v y )| is node v x ,v y The number of common neighbors of

[0017] By parameter α, the edge (v x ,v y ) weight w x,y and structural weight Sw x,y Weighted fusion, denoted by Cw x,y After fusion (v x ,v y ), as shown in formula (2):

[0018] Cw x,y =αw x,y +(1-α)Sw x,y , (2);

[0019] In formula (2), Cw x,y =Cw y,x , α is an adjustable parameter, and α∈(0,1), which is used to measure the relative importance between edge weight and structure weight.

[0020] Preferably, based on the unweighted clustering coefficient, considering the weighted network edge weight, Barrat divides the node v z The clustering coefficient It is defined as (3):

[0021]

[0022] In formula (3), s z Represents node v z Strength; k z Represents node v z The degree of node v is defined as z The number of nodes with direct edges; a z,j 、a j,k 、a z,k Respectively represent the elements at corresponding positions in matrix A; w z,j Represents the edge (v z ,v j ) weight, w z,k Represents the edge (v z ,v k ) weight; Formula (3) only calculates nodes with a degree greater than 1 when calculating the clustering coefficient.

[0023] Preferably, for the weighted network G w Node v in (V,E,W) x and v y , defining the second-order path distance between them As shown in formula (4):

[0024]

[0025] In formula (4), Represents the connection node v x and v y A set of paths of length 2, p is any path in the set, v z is the intermediate node of path p, is the edge weight (v x ,v z ) is the edge weight (v z ,v y )

[0026] By introducing the weighted clustering coefficient, mutual information and node path distance related to node degree into the WRA method, a link prediction method CWMID based on node topology characteristics and mutual information is designed.

[0027] The definition of the CWMID method is as follows: For the weighted network G w Two nodes v in (V,E,W) x ,v y ∈V, defining the similarity between them As shown in formula (5):

[0028]

[0029] In formula (5), k z and s z Node v z Weighted clustering coefficient, degree, and strength of x,z For the edge (v x ,v z )’s fusion weight; For node v x and v y The second-order path distance of represents common neighbors v z When it exists, node v x and v y There is mutual information between the edges; λ is the path control parameter, which is used to adjust the contribution of the second-order path to the node similarity.

[0030] Beneficial effects of the present invention:

[0031] The main process of this method is to first remove self-loops and duplicate edges in the network from a real network dataset to eliminate the interference of self-loops and duplicate edges on the prediction results of the method, then quantify the local network structure of the node into the edge structure weight, and fuse it with the edge weight through the parameter α to obtain the fusion weight. Next, the method introduces the degree-related weighted node clustering coefficient, mutual information and path distance, and designs a weighted network link prediction method CWMID based on node topological features and mutual information. The main advantage of the present invention is that by combining multiple topological features of nodes in the network with node mutual information, the utilization of network structure information is more comprehensive, and it has good universality and prediction results in different types of networks. At the same time, the prediction accuracy is more accurate than that of most weighted link prediction methods. Experimental results confirm the superiority of the CWMID method designed by the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is the prediction accuracy AUC of the eight methods of the present invention in 15 networks;

[0033] Figure 2 is the prediction accuracy of the eight methods of the present invention in 15 networks;

[0034] Figure 3 is the prediction accuracy AUC of the 7 methods of the present invention in 15 networks;

[0035] Figure 4 is the prediction accuracy of the seven methods of the present invention in 15 networks;

[0036] Figure 5It is a flow chart of the present invention. DETAILED DESCRIPTION

[0037] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings.

[0038] The present invention is described in detail with reference to the accompanying drawings, and the specific steps are as follows:

[0039] The present invention is based on the link prediction method of node topology characteristics and mutual information, such as Figure 1 As shown, please follow the steps below:

[0040] Step 1: For a given weighted network G w , preprocess the data, i.e., ignore the direction of the edges in the directed network and delete the self-loops and multiple edges in the network;

[0041] Step 2: Select 90% of the edges and all nodes in the network as the training set network by random sampling The remaining edges and all nodes are used as the test set network Ensure the connectivity of the training set;

[0042] Step 3: According to the range of parameter values, the traversal optimization method is used to traverse the values ​​of each set of parameters and calculate the prediction accuracy AUC in the training set under each set of parameters. train value;

[0043] Step 4: To reduce the error caused by random network partitioning, repeat steps 2 and 3 T times for a given set of parameter values ​​and calculate the AUC under T experiments. train The average value and the maximum AUC train Find the corresponding optimal parameter α * and λ * ;

[0044] Step 5: The best parameter α obtained by the method during the training process * and λ * Substitute into formula (5) to evaluate the prediction accuracy AUC index and precision index of the method in the network.

[0045] In the link prediction method based on node topology features and mutual information designed by the present invention:

[0046] Step 1 removes self-loops and duplicate edges from the network, ensuring that nodes have only one edge between them and no nodes themselves have any edges. This eliminates the interference of self-loops and duplicate edges on the link prediction method, resulting in more accurate prediction results.

[0047] The role of step 2 is to ensure the connectivity of the training set after division, which provides a basis for the accurate prediction of the link prediction method in the complete network;

[0048] The purpose of step 4 is to reduce the error caused by randomly partitioning the network;

[0049] In order to evaluate the prediction precision and accuracy of the design method of the present invention, it is compared with 8 traditional weighted network link prediction methods and 6 weighted network link prediction methods proposed in recent years.

[0050] (1) Comparison of the accuracy of the method designed by the present invention and the traditional weighted link prediction method;

[0051] Table 1 Basic statistical characteristics of 15 weighted networks

[0052]

[0053]

[0054] Where |V| and |E| represent the number of network nodes and edges respectively; <k>is the average degree of the network; C is the network clustering coefficient; H is the degree heterogeneity; ρ is the network density; <d>is the average shortest distance of the network.

[0055] Table 2 Prediction accuracy AUC of 8 methods in 15 networks

[0056]

[0057]

[0058] Table 3 Accuracy of 8 methods in 15 networks

[0059]

[0060]

[0061] Table 2 (continued)

[0062]

[0063] Table 3 (continued)

[0064]

[0065] Table 4 Prediction accuracy AUC of 7 methods in 15 networks

[0066]

[0067]

[0068]

[0069] Table 5 Accuracy of 7 methods in 15 networks

[0070]

[0071]

[0072] Table 5 (continued)

[0073]

[0074] To evaluate the prediction accuracy of the CWMID method, a comparison was conducted on the 15 weighted networks shown in Table 1. Seven different weighted link prediction methods were selected: WRA, rWRA, WAA, rWAA, WLP, rWCN, and WCC. These seven methods primarily describe node similarity based on local topological features such as node strength, degree, edge weights, and path information between nodes. They all demonstrate excellent prediction accuracy. The rWRA, rWAA, and rWCN methods, respectively, introduce reliable routes into the WRA, WAA, and WCN methods. These seven methods are frequently used for comparison in weighted link prediction experiments. The prediction results of the eight methods on the 15 weighted networks are shown in Tables 2 and 3.

[0075] From the results in Tables 2 and 3, we can see that compared with seven different methods, including WRA, rWRA, WAA, rWAA, WLP, rWCN, and WCC, the CWMID method shows better prediction results in most networks. Among the 15 networks, 11 networks have the best AUC performance, and 12 networks have the best Precision performance. The experimental results demonstrate the superiority of the CWMID method.

[0076] (2) Comparison of the accuracy of the method designed by the present invention with other weighted link prediction methods;

[0077] To further evaluate the prediction accuracy of the CWMID method, six weighted link prediction methods, including MPC (L=2, 3), WMI-WCN, WCD-RA, WRALP, and STNMP, were selected for comparison. These six methods characterize node similarity from different perspectives. The prediction results of the seven methods on 15 weighted networks are shown in Tables 4 and 5. As can be seen from the results in the tables, the CWMID method designed in this paper outperforms the comparison methods in prediction accuracy on most networks. Eleven of the 15 networks achieved the best AUC performance, and thirteen achieved the best Precision performance. These experimental results confirm the superiority of the CWMID method.

[0078] Comparing the two methods above demonstrates that the CWMID method designed by the present invention offers superior overall performance, demonstrating superior prediction results across networks of varying scales. The experimental results demonstrate the CWMID method's applicability across diverse network types, significantly improving prediction accuracy compared to most weighted network link prediction methods.

[0079] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.< / d> < / k>

Claims

1. A link prediction method based on node topology features and mutual information, characterized in that: The steps include: (1) Training phase Step 1: For the weighted network G w , 90% of the edges and all nodes are selected as the training set network by random sampling method The remaining 10% of the edges are used as the test set network Ensure the network connectivity of the training set after division; Step 2: Set the parameters α∈(0,1), λ∈(0.001,0.01); according to the parameter value range, use the traversal optimization method to traverse the parameter values. For each set of parameters, calculate the training set The prediction accuracy AUC in train ; Step 3: In order to reduce the error caused by random partitioning of the network, given a set of parameter values, loop step 1 T times, and calculate the training set in each loop. The prediction accuracy AUC in train , and then calculate multiple AUC train The average value of the last set of parameters is traversed, according to the AUC train Maximize the network G w The optimal parameter α in * and λ * ; (2) Testing phase The optimal parameter α obtained by the CWMID method during training * and λ * Substitute into formula (4), in the test set Medium evaluation prediction accuracy AUC test and precision; For the weighted network G w (V,E,W), where V,E,W represent the node set, edge set and weight set respectively; x and v y The neighborhood structure is quantized into edges (v x ,v y )’s structural weight, denoted as Sw x,y , as shown in formula (1): In formula (1), k x ,k y Represents node v x ,v y degree; |Γ(v x )∩Γ(v y )| is node v x ,v y The number of common neighbors of By parameter α, the edge (v x ,v y ) weight w x,y and structural weight Sw x,y Weighted fusion, denoted by Cw x,y After fusion (v x ,v y ), as shown in formula (2): Cw x,y =αw x,y +(1-a)Sw x,y , (2); In formula (2), Cw x,y =Cw y,x , α is an adjustable parameter, and α∈(0,1), which is used to measure the relative importance between edge weight and structure weight; For the weighted network G w Node v in (V,E,W) x and v y , defining the second-order path distance between them As shown in formula (3): In formula (3), Represents the connection node v x and v y A set of paths of length 2, p is any path in the set, v z is the intermediate node of path p, is the edge weight (v x ,v z ) is the edge weight (v z ,v y ) By introducing the weighted clustering coefficient, mutual information and node path distance related to node degree into the WRA method, a link prediction method CWMID based on node topology characteristics and mutual information is designed. The definition of the CWMID method is as follows: For the weighted network G w Two nodes v in (V,E,W) x ,v y ∈V, defining the similarity between them As shown in formula (4): In formula (4), k z and s z Node v z Weighted clustering coefficient, degree, and strength of Cw x,z For the edge (v x ,v z )’s fusion weight; For node v x and v y The second-order path distance of represents common neighbors v z When it exists, node v x and v y There is mutual information between the edges; λ is the path control parameter, which is used to adjust the contribution of the second-order path to the node similarity.

2. The link prediction method based on node topology features and mutual information according to claim 1, characterized in that: Based on the unweighted clustering coefficient, considering the weighted network edge weight, Barrat divides the node v z The clustering coefficient It is defined as (5): In formula (5), s z Represents node v z Strength; k z Represents node v z degree; a z,j 、a j,k 、a z,k Respectively represent the elements at corresponding positions in matrix A; w z,j Represents the edge (v z ,v j ) weight, w z,k Represents the edge (v z ,v k ) weight; Formula (5) only calculates the nodes with degree greater than 1 when calculating the clustering coefficient.

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