Influence maximization method based on bottom-up community merging

Abstract

The invention discloses an influence maximization method based on bottom-up community merging, and belongs to the technical field of complex network analysis. The method comprises the steps of 1, identifying an initial community in a network; 2, in each community, identifying bridge nodes and core nodes as candidate nodes; 3, for the initial communities, combining the communities based on community attraction to obtain a new community; 4, iteratively executing the candidate node identification and community merging process until a community containing all nodes of the network is obtained; and 5, calculating the ranking of the candidate nodes by using a ranking measure by considering the propagation influence and the minimum distance of the candidate nodes, and then selecting the top k nodes to be added into the seed set S. According to the method, the problem of influence maximization is solved based on the community structure information of the network, the final influence scale of the seed node is improved, and reasonable time complexity is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network analysis, and in particular relates to an influence maximization method based on bottom-up community merging. Background Art

[0002] Influence maximization (IM) aims to select the minimum number of initial spreaders, i.e., seed nodes, from the network, in the expectation of obtaining the maximum spread influence at the lowest cost. With the rapid growth of network users and data volume, the IM problem has become increasingly important, and many different methods have been proposed. The greedy algorithm iteratively selects the most influential node, which is accurate but has a high time complexity. Although a large number of studies have improved the performance of the greedy algorithm, it is still very time-consuming when dealing with large and complex networks. Centrality-based methods select influential nodes according to various centrality indicators, but these methods are susceptible to overlapping influence and show performance differences in different networks. Random sampling-based methods solve the problem of time-consuming Monte Carlo simulation by sampling with approximately linear time complexity. However, the sampling results may be biased, which in turn affects the accuracy. Metaheuristic optimization-based methods replace Monte Carlo simulation by simulating natural phenomena or biological behaviors. They usually require efficient and discrete evolutionary mechanisms to seek the optimal solution through multiple iterations.

[0003] It has been proven that communities tend to form naturally in social networks, with sparse connections between communities and close connections within them. Community structure plays a vital role in the information propagation of the entire network. Therefore, community-based IM methods have received more attention. These methods aim to use community structure information to narrow the search space and thus solve the IM problem more efficiently, but their effectiveness depends on the results of community detection and the accuracy of selecting candidate nodes and seed nodes. Therefore, it is crucial to accurately and efficiently select candidate nodes from communities and seed nodes from candidate nodes. Summary of the invention

[0004] In order to overcome the above technical problems, the purpose of the present invention is to provide an influence maximization method based on bottom-up community merging, which regards both bridge nodes and core nodes in the community as candidate nodes, and discovers potential candidate nodes by iteratively merging communities. When selecting seed nodes, the propagation influence and minimum distance of candidate nodes are considered, thereby reducing influence overlap.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] An influence maximization method based on bottom-up community merging includes the following steps:

[0007] Step 1: Identify the initial community and use the Louvain algorithm to divide a network with n nodes into several non-overlapping communities;

[0008] Step 2: In each community, identify bridge nodes and core nodes as candidate nodes;

[0009] Step 3: For the initial communities, merge the communities based on community attractiveness to obtain new communities;

[0010] Step 4: Iteratively perform the process of identifying candidate nodes and merging communities until a community containing all nodes in the network is obtained;

[0011] Step 5: Use a ranking metric to rank candidate nodes by considering their propagation influence and minimum distance, and select the top k nodes to join the seed set S.

[0012] In step 2, the following community diversity indicators are used to identify bridge nodes that can promote cross-community information dissemination:

[0013]

[0014] This indicator takes into account the heterogeneity of the node's external connections, that is, the number of edges between the node and nodes outside the community and the number of different communities to which the external node belongs, where q is the number of communities and p is the number of communities. vc =k vc / k v represents the probability that the neighbors of node v belong to community c.

[0015] Identify core nodes in a community using the following neighborhood-based centrality metrics:

[0016]

[0017] This indicator considers three topology-based centrality indicators, namely DC, H-index and K-shell. The parameter μ is the ratio of the average H-index and the average K-shell of all nodes in the network, which is used to balance the difference between the two indicators.

[0018] In step 3, for each community, the community with the greatest attraction to it is identified, and the corresponding communities are merged. The community attraction is calculated as follows:

[0019] CAF ij =c ij ×(SI(c i )+SI(c j ))

[0020] Specifically, community attraction takes into account the community communication impact and the attraction coefficient between communities. The communication impact of a community is determined by its size (number of internal nodes), the number of internal edges, and the number of edges connected to other communities:

[0021]

[0022] Community j To the community i The attraction coefficient of the two communities is related to the number of edges between them and the community c i The scale is related to:

[0023]

[0024] In step 4, the initial community obtained by the Louvain algorithm is located in the first layer. After each round of merging, the number of layers of the community increases by one. The candidate nodes of the initial community are in the first layer. The number of layers of the candidate nodes identified in communities of different layers is different. The final candidate node is the union of the candidate nodes of all communities of different layers.

[0025] In step 5, when selecting a seed node, the propagation influence and the minimum distance of the candidate node are considered, and the seed node selection process includes:

[0026] Step 5.1: Based on the number of layers and K-shell value of the candidate node, use r v = l v +ks v Represents its position in the network, and the attraction coefficient of candidate node v to candidate node u is defined as:

[0027]

[0028] Step 5.2: Combine the attraction coefficient, cross information and distance of candidate node v and candidate node u to represent the mutual influence between them:

[0029]

[0030] Step 5.3: Use information entropy to represent the amount of information carried by the candidate node v itself. By considering the information carried by the candidate node v and its mutual influence with other candidate nodes, the propagation influence of the candidate node v is calculated as follows:

[0031]

[0032] Step 5.4: Calculate the propagation influence of each candidate node. The minimum distance of a candidate node v is defined as the minimum distance from it to all candidate nodes with greater propagation influence than it. Combining the propagation influence and minimum distance of the candidate node, a ranking metric is used to calculate the ranking of the candidate nodes, and the top k nodes are added to the seed set S. The ranking metric is calculated as follows:

[0033] RM(v)=SI(v)×d min (v)

[0034] Among them, SI(v) and d min (v) are the propagation influence and minimum distance of candidate node v respectively.

[0035] Beneficial effects of the present invention:

[0036] The present invention provides an influence maximization method based on bottom-up community merging. First, the initial community is divided using the Louvain algorithm; second, the heterogeneity of external connections is considered to select bridge nodes, and different centrality metrics are combined to select core nodes; then the community is iteratively merged based on community propagation influence and attraction coefficient to discover potential candidate nodes; finally, the seed node is selected considering the propagation influence and minimum distance of the candidate node. This method not only has a high final influence scale and low influence overlap, but also has a reasonable time complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is the overall calculation process of the influence maximization method of the present invention.

[0038] Figure 2 This is the candidate node selection process of the influence maximization method of the present invention.

[0039] Figure 3 It is the community merging process of the influence maximization method of the present invention.

[0040] Figure 4 This is the seed node selection process of the influence maximization method of the present invention.

[0041] Figure 5 It is a process schematic diagram of the influence maximization method of the present invention. DETAILED DESCRIPTION

[0042] In the embodiments of the present invention, the specific implementation process of the technical solution is clearly described by means of diagrams. The diagrams include the processes of identifying the initial community, selecting candidate nodes, merging communities, and selecting seed nodes. The diagrams can help readers better understand the technical implementation details of the present invention and obtain clear operational guidance from them. It should be clear that the technical solutions described in the embodiments of the present invention only represent some embodiments, not all embodiments. All other embodiments that can be obtained by ordinary technicians in this field without performing creative work are within the scope of protection of the present invention.

[0043] Therefore, the present invention, through detailed description and illustration, shows the technical personnel an innovative influence maximization method based on bottom-up community merging. The method combines network community detection, bridge node and core node identification, community merging and seed node identification technology, effectively improving the final influence scale of seed nodes.

[0044] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0045] An influence maximization method based on bottom-up community merging includes the following steps:

[0046] Step 1: Identify the initial community and use the Louvain algorithm to divide a network with n nodes into several non-overlapping communities;

[0047] Step 2: In each community, identify bridge nodes and core nodes as candidate nodes;

[0048] Step 3: For the initial communities, merge the communities based on community attractiveness to obtain new communities;

[0049] Step 4: Iteratively perform the process of identifying candidate nodes and merging communities until a community containing all nodes in the network is obtained;

[0050] Step 5: Use a ranking metric to rank candidate nodes by considering their propagation influence and minimum distance, and select the top k nodes to join the seed set S.

[0051] In step 2, the following community diversity indicators are used to identify bridge nodes that can promote cross-community information dissemination:

[0052]

[0053] This indicator takes into account the heterogeneity of the node's external connections, that is, the number of edges between the node and nodes outside the community and the number of different communities to which the external node belongs, where q is the number of communities and p is the number of communities. vc =k vc / k vrepresents the probability that the neighbors of node v belong to community c.

[0054] Identify core nodes in a community using the following neighborhood-based centrality metrics:

[0055]

[0056] This indicator considers three topology-based centrality indicators, namely DC, H-index and K-shell. The parameter μ is the ratio of the average H-index and the average K-shell of all nodes in the network, which is used to balance the difference between the two indicators.

[0057] In step 3, for each community, the community with the greatest attraction to it is identified, and the corresponding communities are merged. The community attraction is calculated as follows:

[0058] CAF ij =c ij ×(SI(c i )+SI(c j ))

[0059] Specifically, community attraction takes into account the community communication impact and the attraction coefficient between communities. The communication impact of a community is determined by its size (number of internal nodes), the number of internal edges, and the number of edges connected to other communities:

[0060]

[0061] Community j To the community i The attraction coefficient of the two communities is related to the number of edges between them and the community c i The scale is related to:

[0062]

[0063] In step 4, the initial community obtained by the Louvain algorithm is located in the first layer. After each round of merging, the number of layers of the community increases by one. The candidate nodes of the initial community are in the first layer. The number of layers of the candidate nodes identified in communities of different layers is different. The final candidate node is the union of the candidate nodes of all communities of different layers.

[0064] In step 5, when selecting a seed node, the propagation influence and the minimum distance of the candidate node are considered, and the seed node selection process includes:

[0065] Step 5.1: Based on the number of layers and K-shell value of the candidate node, use r v = l v +ks v Represents its position in the network, and the attraction coefficient of candidate node v to candidate node u is defined as:

[0066]

[0067] Step 5.2: Combine the attraction coefficient, cross information and distance of candidate node v and candidate node u to represent the mutual influence between them:

[0068]

[0069] Step 5.3: Use information entropy to represent the amount of information carried by the candidate node v itself. By considering the information carried by the candidate node v and its mutual influence with other candidate nodes, the propagation influence of the candidate node v is calculated as follows:

[0070]

[0071] Step 5.4: Calculate the propagation influence of each candidate node. The minimum distance of a candidate node v is defined as the minimum distance from it to all candidate nodes with greater propagation influence than it. Combining the propagation influence and minimum distance of the candidate node, a ranking metric is used to calculate the ranking of the candidate nodes, and the top k nodes are added to the seed set S. The ranking metric is calculated as follows:

[0072] RM(v)=SI(v)×d min (v)

[0073] Among them, SI(v) and d min (v) are the propagation influence and minimum distance of candidate node v respectively.

Claims

1. A method for maximizing influence based on bottom-up community merging, characterized in that: The steps include: Step 1: Identify the initial community and use the Louvain algorithm to divide a network with n nodes into several non-overlapping communities; Step 2: In each community, identify bridge nodes and core nodes as candidate nodes; Step 3: For the initial communities, merge the communities based on community attractiveness to obtain new communities; Step 4: Iteratively perform the process of identifying candidate nodes and merging communities until a community containing all nodes in the network is obtained; Step 5: Use a ranking metric to rank candidate nodes by considering their propagation influence and minimum distance, and select the top k nodes to join the seed set S; In step 2, the following community diversity indicators are used to identify bridge nodes that can promote cross-community information dissemination: This indicator takes into account the heterogeneity of the node's external connections, that is, the number of edges between the node and nodes outside the community and the number of different communities to which the external node belongs, where q is the number of communities and p is the number of communities. vc =k vc / k v represents the probability that the neighbors of node v belong to community c; Identify core nodes in a community using the following neighborhood-based centrality metrics: This index considers three topology-based centrality indices, namely DC, H-index and K-shell. The parameter μ is the ratio of the average H-index and the average K-shell of all nodes in the network, which is used to balance the difference between the two indices. In step 3, for each community, the community with the greatest attraction to it is identified, and the corresponding communities are merged. The community attraction is calculated as follows: CAF ij =c ij ×(YES(c i )+SI(c j )) Specifically, community attraction takes into account the community communication impact and the attraction coefficient between communities. The communication impact of a community is determined by its size (number of internal nodes), the number of internal edges, and the number of edges connected to other communities: Community j To the community i The attraction coefficient of the two communities is related to the number of edges between them and the community c i The scale is related to: In step 4, the initial community obtained by the Louvain algorithm is located at the first layer. After each round of merging, the number of layers of the community increases by one. The candidate nodes of the initial community are at the first layer. The number of layers of the candidate nodes identified in communities of different layers is different. The final candidate node is the union of the candidate nodes of all communities of different layers. In step 5, when selecting a seed node, the propagation influence and the minimum distance of the candidate node are considered, and the seed node selection process includes: Step 5.1: Based on the number of layers and K-shell value of the candidate node, use r v = l v +ks v Represents its position in the network, and the attraction coefficient of candidate node v to candidate node u is defined as: Step 5.2: Combine the attraction coefficient, cross information and distance of candidate node v and candidate node u to represent the mutual influence between them: Step 5.3: Use information entropy to represent the amount of information carried by the candidate node v itself. By considering the information carried by the candidate node v and its mutual influence with other candidate nodes, the propagation influence of the candidate node v is calculated as follows: Step 5.4: Calculate the propagation influence of each candidate node. The minimum distance of a candidate node v is defined as the minimum distance from it to all candidate nodes with greater propagation influence than it. Combining the propagation influence and minimum distance of the candidate node, a ranking metric is used to calculate the ranking of the candidate nodes, and the top k nodes are added to the seed set S. The ranking metric is calculated as follows: RM(v)=SI(v)×d min (in) Among them, SI(v) and d min (v) are the propagation influence and minimum distance of candidate node v respectively.

Images