Target influence maximization method and device based on influence probability joint modeling

Abstract

The invention discloses a target influence maximization method and device based on influence probability joint modeling, and the method comprises the steps: removing non-key user nodes which have small influence on a target user in a social network, and obtaining a simplified target community network; calculating the influence of the candidate seed nodes on the target user in the target community network by using a target influence probability algorithm CATIP; calculating the influence of the candidate seed nodes on the non-target users by using a weighted collective influence algorithm WCI; and comprehensively evaluating the influence of the candidate seed nodes on the target and non-target user groups by using a joint influence probability CIP algorithm, and identifying and obtaining key seed nodes. According to the method, under the condition of equal resource consumption, the influence effect on the target user can be improved, the interference on the non-target user can be reduced, and the accurate access of the information can be realized. In addition, the method is low in time complexity, and is suitable for a target influence maximization task of a large-scale network.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of network science and information processing, and particularly relates to a target influence maximization method and device based on joint modeling of influence probability. BACKGROUND

[0002] In the field of network science, the research and understanding of complex systems occupy a central position, and network models provide a powerful framework for the characterization and analysis of numerous complex systems. For example, online social networks such as Twitter and TikTok have become important channels for efficient communication and information dissemination among individuals, and have become powerful tools for promoting interaction and knowledge sharing. This advertising strategy is referred to as "word-of-mouth communication" in the field of communication studies. To formalize this communication goal, the academic community has proposed the influence maximization problem, the core of which is to accurately identify a limited set of individuals with high influence in social networks, which are referred to as seed nodes.

[0003] Current research is committed to analyzing the influence maximization problem in complex social networks with different strategies. The greedy algorithm proposed in 2003 laid an important foundation, and this pioneering work has promoted the development of efficient greedy algorithms such as CELF and CELF++. In recent years, the research trend has shifted to integrating artificial intelligence technology into influence maximization research: for example, using deep reinforcement learning to combine network dynamics and user behavior for node selection, and GLIE graph neural networks to integrate greedy algorithms and machine learning. In addition, some research has also adopted heuristic algorithms, such as the gravity model and delta-CI algorithm.

[0004] It is worth noting that although the influence maximization problem has received widespread attention, the target influence maximization problem has been relatively understudied. The core of the target influence maximization problem is to propagate information only to target nodes, as non-target nodes may produce unpredictable negative feedback. Therefore, the target influence maximization problem requires identifying super spreaders in complex social networks to maximize the influence of specific target nodes while minimizing the impact on non-target nodes.

[0005] Targeted influence maximization problem has been proven to be NP-hard, which makes heuristic methods more practical. In recent years, the rise of machine learning, deep learning and reinforcement learning has also brought new solutions to the problem of targeted influence maximization. For example, the GLIE model uses graph neural networks (GNNs) to capture complex structural relationships in social networks. Similarly, the S2V-DQN algorithm combines graph embedding techniques with deep Q-learning to iteratively optimize the selection of seed nodes. In addition, the ToupleGDD algorithm uses multiple coupled graph neural networks to simulate the influence propagation process, while the RLEA-IM method combines graph embedding, evolutionary algorithms and deep reinforcement learning to optimize the selection strategy of seed nodes. However, existing research on targeted influence maximization mostly focuses on specific network structures, and is not adaptable to diverse social networks. On the other hand, traditional influence maximization research fails to distinguish the influence of target nodes and only pursues maximum propagation in the entire network. SUMMARY

[0006] In view of the deficiencies in the prior art, the present application aims to provide a targeted influence maximization method and device based on joint modeling of influence probability, which can accurately identify key propagation nodes by eliminating non-key nodes, constructing a target community network, and combining CATIP, WCI and CIP algorithms to comprehensively evaluate the influence of candidate seed nodes on target and non-target users. This method improves the influence effect on target users while ensuring resource efficiency, reduces interference on non-target users, has low time complexity, and is suitable for targeted influence maximization tasks in large-scale social networks.

[0007] In order to achieve the above technical purposes, the following technical solutions are adopted in the present application:

[0008] In one aspect of the present application, a targeted influence maximization method based on joint modeling of influence probability is provided, comprising the following steps:

[0009] S1: Screen the user nodes in the social network, eliminate non-key user nodes with an influence on the target user group below a preset threshold, and generate a simplified target community network;

[0010] S2: In the target community network, calculate the influence of each candidate node on the specified target node set through the candidate node-target node influence probability algorithm CATIP, and output the target influence probability;

[0011] S3: Calculate the potential influence of each candidate node on the non-target node set using the weighted collective influence algorithm WCI, and output the weighted collective influence;

[0012] S4: adopting a joint influence probability CIP algorithm, fusing the target influence probability and weighted collective influence, generating a joint influence probability of each candidate node, so as to improve the influence effect on the target user, reduce the interference on the non-target user, and then realize accurate touch of information, identify and acquire key seed nodes.

[0013] In an embodiment, step S1 comprises:

[0014] For a social network G(V, E), wherein V and E represent a node set and an edge set in the social network respectively;

[0015] Obtain a network influence probability distribution {β u,v}, wherein β u,v represents an influence probability of node u on node v.

[0016] Based on a preset target node set δ, adopt a TC algorithm to construct the target community network.

[0017] In an embodiment, adopting the TC algorithm to construct the target community network comprises:

[0018] S11: initialize a theoretical influence probability TIP as a product of all influence probabilities β u,v on a propagation path; determine a maximum effective propagation distance d imax as a distance whose mathematical expectation of TIP is greater than 0.05;

[0019] S12: starting from the target node set δ, adopt a breadth-first search algorithm to obtain all nodes whose distance to the target node set is less than d imax , and form a target community node set V';

[0020] S13: according to the target community node set V', select edges in the social network G(V, E) with V' as the starting point and the focus, and merge them into a new edge set E';

[0021] S14: output the target community network G s (V', E').

[0022] In an embodiment, the step S2 comprises:

[0023] For a social network G(V, E), wherein V and E represent a node set and an edge set in the social network respectively;

[0024] Obtain a network influence probability distribution {β u,v}, wherein β u,v represents an influence probability of node u on node v.

[0025] Based on the preset target node set δ, the CATIP algorithm is used to calculate the influence probability of each candidate node on the target node set δ.

[0026] In one embodiment, the step S3 includes:

[0027] S21: For each pair of candidate node s and target node μ, the influence probability Y of each propagation path is calculated. sμ,i , where i represents the ith propagation path, and μ ∈ δ;

[0028] S22: For each pair of candidate node s and target node μ, the path with the maximum influence probability is retained, and the maximum influence probability is:

[0029] ω * (s, μ) = max{Y sμ,i}.

[0030] S23: For each pair of candidate node s and target node μ, the target influence probability ε(s) of s is calculated.

[0031] ε(s) = ∑ μ∈δ ω * (s, μ).

[0032] In one embodiment, the step S3 includes:

[0033] S31: The degree centrality k(s) of each candidate node s is initialized, where k(s) is the number of neighbor nodes of the candidate node s.

[0034] S32: The neighbor node set σ(s) of each candidate node s is determined, and the weighted sum of the degrees of the neighbor nodes minus one is calculated, and the weight is the influence probability β of each edge. s,v , where β s,v represents the influence probability of the candidate node s on its neighbor node v, and v ∈ σ(s).

[0035] S33: The weighted collective influence ξ(s) of the candidate node s is calculated, and the calculation method is:

[0036] ξ(s) = (k(s) - 1) × ∑ v∈σ(s) β s,v × (k(s) - 1).

[0037] In one embodiment, the step S4 includes:

[0038] S41: For each candidate node s, the target influence probability ε(s) and the weighted collective influence ξ(s) are normalized to obtain ε'(s) and ξ'(s).

[0039] S42: for each candidate node s, calculate its joint influence probability:

[0040]

[0041] S43: when the termination condition is not reached, perform the following loop: count the current number of seed nodes satisfies wherein n is the number of seed nodes required by the task; select from the candidate node set the node with the largest value to join the seed node set set to a very large negative number;

[0042] S44: end the loop and obtain the seed node set that satisfies the target marketing task

[0043] In another aspect of the present application, an apparatus for target influence maximization based on joint modeling of influence probability is provided, comprising:

[0044] a scaling unit configured to filter non-key user nodes with influence on the target user group lower than a preset threshold, and generate a simplified target community network, for user nodes in the social network;

[0045] a disassembling unit configured to calculate the influence of each candidate node on a specified target node set in the target community network by a candidate node-target node influence probability algorithm CATIP, and output a target influence probability; and calculate the potential influence of each candidate node on a non-target node set by a weighted collective influence algorithm WCI, and output a weighted collective influence;

[0046] a set unit configured to fuse the target influence probability and the weighted collective influence by a joint influence probability algorithm CIP, to generate the joint influence probability of each candidate node, and determine a propagation seed node

[0047] The present application has the following advantages:

[0048] The method of the present application can improve the influence effect on target users and reduce the interference on non-target users under the same resource consumption, thereby achieving precise information reach, by the strategy of community group, the joint modeling of influence probability, and the collective influence algorithm provided by the present application. In addition, the method of the present application has low time complexity and is suitable for target influence maximization tasks in large-scale networks. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a flowchart of the target influence maximization method of the embodiments of the present application;

[0050] Figure 2 This is a schematic diagram of the TC algorithm of an embodiment of the present application;

[0051] Figure 3 This is a schematic diagram of the CATIP algorithm of the embodiment of the present application;

[0052] Figure 4 This is a comparison of the computation time of different seed node selection methods in the embodiments of the present application;

[0053] Figure 5 This is a comparative diagram of different target influence maximization methods in the embodiment of the present application in terms of simulated propagation effects; wherein the ordinate represents the influence ratio (the outer graph is the influence ratio of the target node, and the subgraph is the inverse of the influence ratio of the non-target node), and the abscissa represents the mathematical expectation of the influence probability distribution. size; ∈[0.025,0.5] with equal intervals of 0.025; (a), (e) co-authorship network of scientists in network theory & experiments network; (b), (f) Amazon recommendation network; (c), (g) US power Grid network; (d), (h) web graph network;

[0054] Figure 6 The mathematical expectation of the propagation effect of the embodiment of the present application under different influence probability distributions Frequency histograms of the cases; (a) co-authorship network of scientists in network theory & experiments network; (b) Pretty Good Privacy network; (c) US power Grid network; (d) web graph network;

[0055] Figure 7 : This is the propagation effect under different numbers of seed nodes and target nodes in the embodiment of the present application; where the X-axis represents the number of targets and the Y-axis represents the number of seeds; (ad) co-authorship network of scientists in network theory and experiments network; (eh) US power grid network; (il) web graph network; (mp) Amazon recommendation network;

[0056] Figure 8are the changes of the propagation effect of the embodiments of the present application with the average degree of the network; wherein (a) ER random network; (b) WS random network; (c) BA random network. DETAILED DESCRIPTION

[0057] The technical solutions of the present application will be described clearly and completely in combination with the specific embodiments below, but those skilled in the art will understand that the following described embodiments are part of the embodiments of the present application, not all the embodiments, and are only used to illustrate the present application, and should not be regarded as limiting the scope of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0058] In one embodiment, a target influence maximization method based on joint modeling of influence probability is provided. The network structure is simplified by eliminating non-key user nodes with small influence on the target user in the social network to obtain a target community network. The influence of candidate seed nodes on the target user is calculated and evaluated in the target community network using the target influence probability algorithm CATIP. The influence of candidate seed nodes on non-target users is calculated and evaluated using the weighted collective influence algorithm WCI. The influence of candidate seed nodes on target and non-target user groups is comprehensively evaluated using the joint influence probability algorithm CIP to identify and obtain key seed nodes. This method can improve the influence effect on target users while reducing interference on non-target users under the same resource consumption, thereby achieving precise information reach. In addition, this method has low time complexity and is suitable for large-scale network target influence maximization tasks.

[0059] Specifically, the following steps are included:

[0060] S1: Screening the user nodes in the social network, eliminating non-key user nodes with influence on the target user group lower than a preset threshold, and generating a simplified target community network.

[0061] In some embodiments, for a social network G(V, E), wherein V and E represent the node set and edge set in the social network respectively; the network influence probability distribution {β u,v} is obtained, wherein β u,v represents the influence probability of node u on node v; based on the preset target node set δ, the TC algorithm is used to construct the target community network.

[0062] Specifically, the steps of constructing the target community network using the TC algorithm are as follows:

[0063] S11: Initialize the theoretical influence probability TIP as the sum of all influence probabilities β u,vthe product of the maximum effective propagation distance d imax the distance for which the mathematical expectation of TIP is greater than 0.05;

[0064] S12: Starting from the target node set δ, a breadth-first search algorithm is used to obtain all nodes with a distance to the target node set less than d imax , and a target community node set V' is formed.

[0065] The breadth-first search algorithm is an algorithm for traversing or searching a tree or graph, starting from a starting node and visiting all adjacent nodes layer by layer. In each layer, the algorithm visits all nodes directly connected to the current node, and then continues to visit the adjacent nodes of these newly visited nodes as the starting point, until the termination condition is met.

[0066] Specifically, starting from each node in the target node set δ, the first layer of nodes directly connected to it is searched. During the search process, it is constantly checked whether the distance of the currently visited node is less than d imax . If the distance is less than d imax , the node is added to the target community node set V', and if the distance is equal to or greater than d imax , further search of this branch is stopped.

[0067] S13: According to the target community node set V', the edges in the social network G(V, E) starting and ending with V' are selected and merged into a new edge set E', and the connection relationship between the target community nodes is extracted to remove the edges unrelated to the target community, thereby simplifying the network structure.

[0068] S14: Output the target community network G s (V', E'). Focus on the key nodes and connection relationships that have important influence on the target user group, facilitating more efficient analysis and processing in the future.

[0069] S2: In the target community network, the influence of each candidate node on the specified target node set is calculated by the candidate node-target node influence probability algorithm CATIP, and the target influence probability is output.

[0070] In some embodiments, for a social network G(V, E), where V and E represent the node set and edge set in the social network respectively, a network influence probability distribution {β u,v} is obtained, where β u,v represents the influence probability of node u on node v; based on the preset target node set δ, the CATIP algorithm is used to calculate the influence probability of each candidate node on the target node set δ.

[0071] Wherein, the candidate node belongs to a node set in a social network, is a kind of node which is focused on the analysis of the entire network and has an impact on the target node set δ. By calculating and comparing the influence probability of numerous candidate nodes, key nodes with greater impact on the target node set δ can be screened from the entire social network. These key nodes may have important influence in information dissemination, opinion leader role playing and other aspects.

[0072] The determination of the candidate node can be based on node attributes, random selection or specific rules. Specifically, according to certain attributes of the node, such as activity, number of fans, influence of published content, etc., the nodes meeting certain conditions are selected as candidate nodes. When the number of nodes is large and there is no obvious attribute distinction, random selection can be used to determine the candidate nodes for preliminary influence probability analysis. According to the research purpose or business requirement, specific rules are formulated to select candidate nodes, for example, in the study of the influence of promotion of a certain product, active members in the interest group related to the product are selected as candidate nodes.

[0073] Specifically, the CATIP algorithm is used to calculate the influence probability of each candidate node on the target node set δ as follows:

[0074] S21: For each pair of candidate node s and target node μ, the influence probability Y of each propagation path is calculated sμ,i , wherein i represents the i th propagation path, μ ∈ δ;

[0075] S22: For each pair of candidate node s and target node μ, the path with the maximum influence probability is retained, and the maximum influence probability is

[0076] ω * (s,μ)=max{Y sμ,i};

[0077] S23: For each candidate node s and target node μ, the target influence probability is calculated. Specifically, for each target node μ in the target node set δ, the maximum influence probability ω * (s,μ) from the candidate node s to the target node μ is found, and then these maximum influence probabilities ω * (s,μ) are added to obtain the target influence probability of the candidate node s on the target node set δ:

[0078] ε(s)=∑ μ∈δ ω * (s,μ)。

[0079] S3: The weighted collective influence algorithm WCI is used to calculate the potential influence of each candidate node on the non-target node set, and the weighted collective influence is output.

[0080] Specifically, the following steps are included:

[0081] S31: initialize the degree centrality k(s) of each candidate node s, where k(s) is the number of neighbor nodes of the candidate node s, i.e., the nodes directly connected to the candidate node s;

[0082] S32: determine the neighbor node set σ(s) of each candidate node s, and calculate the weighted sum of the degrees of the neighbor nodes minus one, with the weight being the influence probability β of each edge s,v , where β s,v represents the influence probability of the candidate node s on its neighbor node v, v∈σ(s).

[0083] S33: calculate the weighted collective influence ξ(s) of the candidate node s, by the calculation method:

[0084] ξ(s)=(k(s)-1)×∑ v∈σ(s) β s,v ×(k(s)-1).

[0085] The weighted collective influence calculated through the above steps can identify key candidate nodes that have a large potential influence on a non-target node set in a complex graph structure such as a social network.

[0086] S4: using the joint influence probability CIP algorithm, fusing the target influence probability and the weighted collective influence, generating a comprehensive influence index of each candidate node, identifying and obtaining key seed nodes, to improve the influence effect on target users, while reducing the interference on non-target users, and thus realizing precise reach of information.

[0087] Specifically, the following steps are included:

[0088] S41: for each candidate node s, normalize its target influence probability ε(s) and weighted collective influence ξ(s) to obtain ε'(s) and ξ'(s);

[0089] S42: for each candidate node s, calculate its joint influence probability:

[0090]

[0091] If the value of CIP(s) is large, it indicates that the node has a small interference on non-target users while effectively influencing target users.

[0092] S43: when the termination condition is not met, perform the following loop: count the current number of seed nodes satisfying CIP(s)≥CIPmax where n is the number of seed nodes required by the task; select the candidate node with the maximum CIP from the candidate node set S44: add the selected candidate node to the seed node set, and update the CIPmax value. S45: if the number of seed nodes reaches n, terminate the loop; otherwise, return to S43.The value of the node is added to the seed node set To avoid the nodes selected into the seed node set being selected again in the subsequent loop, the value of the node is set to a very large negative number

[0093] The seed node refers to a key node determined through calculation and screening, which has effective influence on the target user group and less interference on non-target users.

[0094] S44: End the loop to obtain the seed node set meeting the target marketing task

[0095] In another embodiment, an apparatus for target influence maximization based on joint modeling of influence probability is provided, comprising:

[0096] The scaling unit adopts the TC strategy to find and remove nodes with influence less than a set threshold according to the target node distribution and the topology structure information of the basic network, efficiently scales the network structure, and provides the target community network G s (V', E') for subsequent processes. Specifically, the non-key user nodes with influence on the target user group lower than a preset threshold are removed through screening of the user nodes in the social network, and a simplified target community network is generated.

[0097] The disassembling unit calculates the influence of the candidate nodes on the community in the target and non-target community sets respectively, and determines the target influence probability and weighted collective influence of the candidates. Specifically, in the target community network, the influence of each candidate node on the specified target node set is calculated through the candidate node-target node influence probability algorithm CATIP, and the target influence probability is output; the potential influence of each candidate node on the non-target node set is calculated through the weighted collective influence algorithm WCI, and the weighted collective influence is output.

[0098] The set unit sets the two types of influence of the disassembling unit, and determines the propagation seed node Specifically, the joint influence probability CIP algorithm is adopted to fuse the target influence probability and the weighted collective influence, and the joint influence probability of each candidate node is generated.

[0099] Embodiment

[0100] The embodiment is used to solve the problems of large resource consumption or poor target influence effect in the process of network target influence maximization in the prior art. In order to overcome these technical difficulties, the embodiment provides a method for target influence maximization based on joint modeling of influence probability, and the specific implementation scheme is as follows:

[0101] ​In the target community network extraction phase (TC), the network structure is simplified by pruning the propagation paths with small influence, and the simplified target community network is obtained, which reduces the number of candidate nodes and improves the efficiency of subsequent calculations. In measuring the influence of candidate nodes on the target node set, the target influence probability algorithm (CATIP) is used to calculate the target influence probability ε(s) from the target community network. In measuring the influence of candidate nodes on the non-target node set globally, the weighted collective influence algorithm (WCI) is used to further calculate the weighted collective influence ξ(s) of the candidate nodes. Finally, the joint influence probability algorithm (CIP) is further used to evaluate the joint influence probability of the candidate nodes, and the seed nodes are selected accordingly.

[0102] The embodiment can minimize the resource consumption required for controlling propagation while meeting the same propagation effect by using the sub-community group strategy, combining joint modeling of influence probability and collective influence algorithm; or maximize the propagation effect while meeting the same control resource consumption, and avoid adverse feedback from non-target groups. In addition, the method has low time complexity and is suitable for target influence of super large scale network, and can be widely applied to various real scenarios, such as information transmission in social networks, vulnerability analysis of power networks, and intervention strategy formulation of disease transmission networks.

[0103] As Figure 1 , a target influence maximization method based on joint modeling of influence probability is provided, which mainly uses the target community network strategy (TC) to obtain the influence of candidate nodes on the target node set based on the target community network structure, the target influence probability algorithm proposed in the CATIP stage, and the influence of candidate nodes on the non-target node set based on the weighted collective influence algorithm proposed in the WCI stage. Finally, in the CIP stage, the joint influence probability of the candidate nodes is comprehensively evaluated to solve the problems of low efficiency and poor effect of target influence, which specifically includes the following steps:

[0104] Step 1: Define a weighted social network G(V, E) consisting of n = |V| nodes and m = |E| edges, where V and E represent the node set and edge set respectively. Then define the weight (influence probability) of the edge as a Gaussian distribution where η is the mathematical expectation of β, is the variance of β, and u and v are any different nodes.

[0105] Consider a group of nodes, denoted as δ, as the target node set for propagation; the remaining nodes, denoted as are the non-target nodes for propagation and also the initial candidate nodes for word-of-mouth propagation, i.e. Let the propagation path set π sμ l = |π sμ| μ is composed of potential paths propagated by candidate node s. Let τ i (s,μ) contains all the intermediate nodes, which is π sμ In one of the propagation paths, let d i (s,μ) is the path τ i (s,μ). Let For candidate node s through path τ i (s,μ) The probability of successful transmission, calculate Y sμ,i The longest path distance d is less than 0.05 at the 95% confidence level imax Starting from the target node set δ, a breadth-first search algorithm is used to obtain all nodes whose distance from the target node set is less than d imax The target community node V′ is selected according to the target community node V′. The edges with V′ as the starting point and the focus in G(V,E) are merged into a new edge set E′, and the target community network G is output. s (V′,E′).

[0106] Reference Figure 2 The following is a simple example of the TC algorithm process. Before generating a target-based community, the edge E is reversed; the target nodes are gray (t1, t2, t3), assuming that the calculated maximum effective propagation distance d imax =3; Starting from all target nodes, use the breadth-first algorithm to search for all nodes whose distance from the target node set is less than d imax The nodes are marked in black, forming the target community network node set V′, and the edges between these nodes form E′, forming the target community network G s (V′,E′).

[0107] Step 2: Use the target influence probability algorithm CATIP algorithm to calculate the target community network G s In (V′, E′), the success probability of the candidate node affecting the target node is calculated.

[0108] The specific steps of the CATIP algorithm are as follows: First, for each pair of candidate node s and target node μ, calculate the influence probability Y of each propagation path in the target community network. sμ,i Then, retain the path with the maximum impact probability and record the maximum impact probability ω * (s,μ)=max{Y sμ,i Finally, for each pair of candidate nodes s, calculate their target influence probability ε(s) = ∑ μ∈δ ω * (s,μ).

[0109] Figure 3A simple example of the CATIP algorithm process. From all nodes, a reverse search is performed, and each edge records the shortest distance to the target node; when there is a ring, the edge with the largest distance mark is preferentially deleted. The nodes at the starting point of these edges need to be further evaluated, and the evaluation method is to consider the cumulative propagation distance of different propagation paths from the node; for example, the gray-white node v1, the gray-black node v2, and the white node v3 form a ring. v1 has two propagation paths: one with a distance of 3 (pointing to v2) and the other with a distance of 4 (pointing to v3), with a cumulative propagation distance of 7; similarly, the two propagation paths of v2 have distances of 2 and 4, respectively, with a cumulative propagation distance of 6; therefore, the edge from v1 to v3 is deleted; the same method is used to process the other edge (ring mark) in the ring to ensure the formation of the optimal path structure.

[0110] Step 3: Calculate the influence of candidate nodes on non-target nodes using the weighted collective influence algorithm WCI.

[0111] The specific steps of the WCI algorithm are as follows: first, initialize the degree centrality k(s) of each candidate node s, which is the number of neighbor nodes of s. Next, determine the neighbor node set σ(s) of each candidate node s, i.e., the set of nodes directly connected to node s, and calculate the weighted sum of the degree minus one of the neighbor nodes, with the weight being the influence probability β of each edge s,v . Finally, calculate the weighted collective influence ξ(s) of candidate node s, and the calculation method is ξ(s) = (k(s)-1) x ∑ v∈σ(s) β s,v x (k(s)-1).

[0112] Step 4: Balance the theoretical influence of candidate nodes on target and non-target node groups using the joint influence probability CIP algorithm, and identify key nodes.

[0113] The specific steps of the CIP algorithm are as follows: first, for each candidate node s, normalize its target influence probability ε(s) and weighted collective influence ξ(s) to obtain ε'(s) and ξ'(s). Next, for each candidate node s, calculate its joint influence probability After that, when the termination condition is not met, the following loop is executed: count the current number of seed nodes satisfying where n is the number of seed nodes required by the task; select the node with the largest value from the candidate node set and add it to the seed node set Then set to a very large negative number. Finally, end the loop and obtain the seed node set

[0114] Figure 4 A comparison of computational time for different seed node selection methods is presented, focusing on the comparison of computational time between the CATIP and CIP methods and the ΔCI, VE, and VoteRank methods, particularly in terms of efficiency when processing large-scale networks. The cross (x) indicates that VE runs out of memory on RA networks.

[0115] Depend on Figure 4 As can be seen, the CATIP method has a significant advantage in computational time, especially when dealing with large-scale networks. CATIP not only outperforms other methods in solution quality but also excels in computational efficiency. Specifically, CATIP's average computation time is approximately 1,223 times faster than ΔCI, approximately 13,425 times faster than VE, and approximately 1,142 times faster than VoteRank. While CIP performs better on some networks, its overall computational time is longer than CATIP, primarily due to the computational overhead of WCI.

[0116] Figure 5 This paper compares the simulated propagation effects of different target influence maximization methods. Specifically, it shows the proportion of target nodes (outer graph) and non-target nodes (subgraph) affected after simulated propagation when the number of target nodes is 10 (ad) and 20 (eh), respectively, and the number of seed nodes is fixed at 4. This is compared with six methods: HD, HDs, CI, CIs, IMRank, and ΔCI.

[0117] Depend on Figure 5 It can be seen that the CIP method has significant advantages in maximizing the effect of target influence, especially when the mathematical expectation of the probability distribution is affected. When it is smaller, it not only increases the proportion of target nodes affected, but also significantly reduces the number of non-target nodes affected. More specifically, the seed nodes selected by the CIP method have different proportions of target nodes affected in the propagation simulation process. In the case of

[15] , the number of affected nodes is about 3-5 times greater than that of other methods on average, while the proportion of affected non-target nodes is about 15-20 times less than that of other methods. Furthermore, other methods perform well only in certain networks, but poorly in other cases. The algorithm performance fluctuates greatly, while the CIP method is more stable.

[0118] Figure 6 The target impact effect evaluation of different network disassembly methods under fixed seed node and target node numbers is given. When the seed node is fixed at 3 and the target node is fixed at 6, the target impact effect is measured by the ratio of affected target nodes minus the ratio of affected non-target nodes plus one divided by two, and the mathematical expectation of the probability distribution of different impacts is given. The frequency histogram of the case, where The value range is [0.025, 0.5], and the study is conducted with equal intervals of 0.025. It is compared with HDs, IMRank, ΔCI, Voterank and VertexEntanglement methods. The vertical axis represents the probability density. The figure also shows the average propagation effect of 2500 simulations. The numbering sequence is consistent with the legend from top to bottom.

[0119] Depend on Figure 6 It can be seen that in different Under the CIP method The value has significant advantages in different real networks, and its propagation effect Φ is relatively concentrated in multiple simulations, indicating that it performs well in terms of target influence and has good stability. It can effectively increase the influence of target nodes while reducing the influence of non-target nodes. Other methods: HDs, IMRank, and ΔCI methods perform well in some networks, but poorly in other cases. The value fluctuates greatly; Voterank and VertexEntanglement perform poorly in any network.

[0120] Figure 7 The performance comparison of the joint influence probability algorithm (CIP) with HDs, IMRank and ΔCI algorithms on real networks is given, and the target influence effect of the seeds selected by the four algorithms in simulated propagation with different numbers of seed nodes and target nodes is demonstrated.

[0121] Depend on Figure 7 It can be seen that CIP has a significant advantage in propagation effect, especially when seed nodes are scarce. Specifically, for the CIP method, there is a positive correlation between Φ and the scale of target nodes and seed nodes. As the scale of target nodes and seed nodes increases, Φ m (Average difference ) shows a significant upward trend. In contrast, for other methods, the color changes in their corresponding heatmaps are less pronounced, indicating that they lack the ability to effectively maximize the target's influence by scaling up. When the target and seed nodes are of the same size, the CIP method consistently outperforms other methods, demonstrating its robustness.

[0122] Figure 8 The diffusion effect Φ is given on a random network with a network size of n = 1000 and varies with the average degree of the network. <k>The change of the number of different seed nodes, the number of target nodes, and the mathematical expectation of the influence probability distribution shows the propagation effect after the average.

[0123] By Figure 8 It can be seen that the average degree of the random network has a significant impact on the network dynamics, but the CIP method is always superior to other methods under various network types and average degrees. The relationship between the average degree and Φ shows that in the network with sparse connections (low average degree), the value of Φ reaches a peak, highlighting the key role of influential nodes in driving network dynamics. In the network with dense connections, the value of Φ tends to be stable or only has a slight fluctuation, which indicates that the propagation behavior tends to be homogenized, and the target influence of individual nodes is weakened.

[0124] Based on the influence probability joint modeling model and the collective influence algorithm, the application develops an apparatus for maximizing target influence based on influence probability joint modeling. It can minimize the resource consumption required for controlling propagation under the premise of meeting the same propagation effect, or maximize the propagation effect under the premise of the same control resource consumption, while avoiding adverse feedback from non-target groups. In addition, the method has low time complexity and is suitable for target influence maximization in large-scale networks, and can be widely applied to various real-world scenarios, such as information transmission in social networks, vulnerability analysis of power networks, and intervention strategy development for disease transmission networks.

[0125] In summary, the application realizes the target influence maximization based on the influence probability joint modeling, and the proposed double community method can effectively reduce the non-target expenditure in the target influence process, achieving efficient and high-quality target influence maximization.

[0126] Although the embodiments of the application are described above in combination with the drawings, the application is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the inspiration of the present application and without departing from the scope protected by the claims of the present application, which are all within the protection scope of the present application.< / k>

Claims

1. A target influence maximization method based on joint modeling of influence probability, characterized by: include: S1: Screen the user nodes in the social network, remove non-critical user nodes whose influence on the target user group is lower than the preset threshold, and generate a simplified target community network; S2: In the target community network, the influence of each candidate node on the specified target node set is calculated using the candidate node-target node influence probability algorithm CATIP, and the target influence probability is output; S3: Use the weighted collective influence algorithm WCI to calculate the potential influence of each candidate node on the non-target node set and output the weighted collective influence; S4: Using the joint influence probability CIP algorithm, the target influence probability and the weighted collective influence are integrated to generate the joint influence probability of each candidate node, and the key seed nodes are identified and obtained.

2. The target influence maximization method according to claim 1, characterized in that: Step S1 includes: For a social network G(V,E), V and E represent the node set and edge set in the social network respectively; Get the network influence probability distribution {β u,v }, where β u,v represents the probability of node u influencing node v; Based on the preset target node set δ, the target community network is constructed using the TC algorithm.

3. The target influence maximization method according to claim 2, characterized in that: The target community network is constructed using the TC algorithm, including: S11: Initialize the theoretical impact probability TIP to all impact probabilities β on a propagation path u,v The product of ; Determine the maximum effective propagation distance d imax The distance at which the mathematical expectation of TIP is greater than 0.05; S12: Starting from the target node set δ, use the breadth-first search algorithm to obtain all nodes whose distance from the target node set is less than d imax The nodes constitute the target community node set V'; S13: Based on the target community node set V', select the edges in the social network G(V,E) with V' as the starting point and focus, and merge them into a new edge set E'; S14: Output target community network G s (V',E').

4. The method for maximizing target influence according to claim 1, characterized in that: The step S2 comprises: For a social network G(V,E), V and E represent the node set and edge set in the social network respectively; Get the network influence probability distribution {β u,v }, where β u,v represents the probability of node u influencing node v; Based on the preset target node set δ, the CATIP algorithm is used to calculate the influence probability of each candidate node on the target node set δ.

5. The target influence maximization method according to claim 4, characterized in that: The CATIP algorithm is used to calculate the influence probability of each candidate node on the target node set δ, including: S21: For each pair of candidate node s and target node μ, calculate the influence probability Y of each propagation path sμ,i , where i represents the i-th propagation path, μ∈δ; S22: For each pair of candidate node s and target node μ, retain the path with the maximum influence probability. The maximum influence probability is: oh * (s,μ)=max{Y sμ,i }; S23: For each candidate node s and target node μ, calculate its target influence probability: ε(s)=∑ μ∈δ oh * (s,μ).

6. The target influence maximization method according to claim 1, characterized in that: The step S3 comprises: S31: Initialize the degree centrality k(s) of each candidate node s, where k(s) is the number of neighbor nodes of the candidate node s; S32: Determine the neighbor node set σ(s) of each candidate node s, and calculate the weighted sum of the degree of the neighbor nodes minus one, where the weight is the influence probability β of each edge s,v , where β s,v represents the probability of candidate node s influencing its neighbor node v, v∈σ(s). S33: Calculate the weighted collective influence ξ(s) of candidate node s. The calculation method is: ξ(s)=(k(s)-1)×∑ v∈σ(s) b s,v ×(k(s)-1).

7. The target influence maximization method according to claim 1, characterized in that: The step S4 comprises: S41: For each candidate node s, normalize its target influence probability ε(s) and weighted collective influence ξ(s) to calculate ε'(s) and ξ'(s); S42: For each candidate node s, calculate its joint influence probability: S43: When the termination condition is not reached, execute the following loop: count the current number of seed nodes satisfy Among them, n is the number of seed nodes required by the task; from the candidate node set Select the one with the largest The node with the value is added to the seed node set Will Set to a very large negative number; S44: End the loop and obtain the seed node set that meets the target marketing task 8. A device for maximizing target influence based on joint modeling of influence probabilities, characterized in that: include: A scaling unit is used to screen user nodes in the social network, remove non-critical user nodes whose influence on the target user group is lower than a preset threshold, and generate a simplified target community network; A disassembly unit is used to calculate the influence of each candidate node on the specified target node set in the target community network through the candidate node-target node influence probability algorithm CATIP, and output the target influence probability; And the weighted collective influence algorithm WCI is used to calculate the potential influence of each candidate node on the non-target node set and output the weighted collective influence; The collection unit is used to use the joint influence probability CIP algorithm to fuse the target influence probability and the weighted collective influence to generate the joint influence probability of each candidate node and determine the propagation seed node

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