A method and device for finding a seed set of a two-stage influence maximization problem

Abstract

The application provides a method and device for searching a seed set of a two-stage influence maximization problem, the method comprising: obtaining a social network graph, obtaining a reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule; selecting a target node in the reverse reachable set and adding the target node to a pre-established seed set; obtaining a target function corresponding to the two-stage influence maximization problem, and determining the seed set as a seed set with the most influence if the seed set meets the target function. The application distinguishes different stages, obtains an accurate reverse reachable set, and then selects a target node in the reverse reachable set, so that the result of the seed set is more accurate.

Description

Technical Field

[0001] This invention relates to the field of social network technology, and in particular to a method and apparatus for finding a seed set for a two-stage influence maximization problem. Background Technology

[0002] Social networks are composed of individuals and the relationships between them, and can be viewed as a graph. Our lives are a large graph of social networks, with individuals and their relationships forming the edges. Information transmission is constantly around us. How to achieve maximum impact with minimal human and material resources is a current research hotspot. The Impact Maximization (IM) problem is to find the k seed nodes with the greatest influence in a social network. The IM problem first appeared in 2003, with the theoretical approximation ratio of a greedy algorithm and two basic propagation models: the Independent Cascade (IC) model and the Linear Threshold (LT) model. Subsequently, the IM problem has received more research. The IM problem begins with identifying influential individuals, i.e., opinion leaders. Then, these k influential individuals are selected to experiment with the desired goal. Transforming the IM problem into a mathematical problem is combinatorial optimization. The efficiency of the algorithm and the establishment of the model are important factors in solving this problem. Due to the diversity and complexity of information in social networks, a single social network cannot meet the current needs, thus competitive social networks have emerged, leading to the problem of Competitive Influence Maximization (CIM). The goal of the CIM problem is to find the k nodes with the greatest influence diffusion in a competitive social network, where k is a positive integer.

[0003] The biggest difference between CIM and IM problems lies in the propagation process. CIM propagation only requires whether a node is activated, while CIM considers not only activation but also which node is activated. In real life, once some original products become popular, many similar products emerge to seize market share. At this point, the original product is the seed node, while similar products are competitors. Existing models do not distinguish between different stages, therefore the set of seed nodes with the greatest influence is inaccurate.

[0004] Therefore, existing technologies have shortcomings and need to be improved and developed. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and apparatus for finding the seed set of a two-stage influence maximization problem, in order to address the above-mentioned defects of the prior art. The aim is to solve the problem that the existing model does not distinguish between different stages, and therefore the seed set of the maximum influence is not accurate.

[0006] The technical solution adopted by this invention to solve the technical problem is as follows:

[0007] A method for finding a seed set for a two-stage influence maximization problem, the method comprising:

[0008] Obtain the social network graph and, according to a preset two-stage selection rule, obtain the reverse reachability set corresponding to the social network graph;

[0009] Select a target node from the reverse reachability set and add the target node to a pre-established seed set;

[0010] Obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set conforms to the objective function, then the seed set is determined as the most influential seed set.

[0011] Optionally, the step of obtaining the social network graph, and obtaining the reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule, includes:

[0012] Obtain the social network graph and select the first parent node of each node in the social network graph according to a preset two-stage selection rule;

[0013] If the first parent node has not been visited, then the node corresponding to the first parent node is added to the pre-established reverse reachable set.

[0014] Optionally, after selecting the first parent node of each node in the social network graph according to a preset two-stage selection rule, the process of obtaining the social network graph further includes:

[0015] If the first parent node has been visited, the second parent node corresponding to the first parent node is selected again until no new node is added to the reverse reachable set, and the first influence diffusion degree corresponding to each node in the reverse reachable set is obtained.

[0016] Optionally, the preset two-stage selection rule is as follows:

[0017] If the current node is in a phase without competition during the propagation stage, then the first parent node of the current node is selected with a preset first probability.

[0018] If the current node is in a competitive phase during the propagation stage, the first parent node of the current node will be selected with a preset second probability.

[0019] Optionally, the preset two-stage selection rule is as follows:

[0020] If the number of hops of the current node is less than or equal to the preset hop count threshold, then the first parent node of the current node is selected with a preset first probability.

[0021] If the number of hops of the current node is greater than the preset hop count threshold, then the first parent node of the current node is selected with a preset second probability.

[0022] Optionally, selecting a target node from the reverse reachability set and adding the target node to a pre-established seed set includes:

[0023] Obtain the number of covered nodes corresponding to each node in the reverse reachable set, and take the node corresponding to the maximum value of the number of covered nodes as the initial selected node.

[0024] The second influence diffusion degree corresponding to the initial selected node is calculated using a greedy algorithm with maximum coverage.

[0025] Obtain the first influence diffusion degree corresponding to the initial selected node, and calculate the difference between the first influence diffusion degree and the second influence diffusion degree;

[0026] If the difference between the first influence diffusion degree and the second influence diffusion degree is less than or equal to a preset deviation threshold, then the initial selected node is added as a target node to the pre-established seed set.

[0027] Optionally, the objective function is:

[0028] Where S represents the seed set, |S A0 |=k represents selecting k nodes from the seed set S, where all k nodes belong to the original node A0, σ t This refers to the degree of influence diffusion at each node. It represents the sum of the influence of competing nodes in a social network graph.

[0029] The present invention also provides an apparatus for finding a seed set for a two-stage influence maximization problem, the apparatus comprising:

[0030] The acquisition module is used to acquire the social network graph and obtain the reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule;

[0031] The selection module is used to select a target node in the reverse reachability set and add the target node to a pre-established seed set.

[0032] The determination module is used to obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set meets the objective function, the seed set is determined as the most influential seed set.

[0033] The present invention also provides a terminal, comprising: a memory, a processor, and a program stored in the memory and executable on the processor for finding a seed set of a two-stage influence maximization problem. When the program for finding a seed set of a two-stage influence maximization problem is executed by the processor, it implements the steps of the method for finding a seed set of a two-stage influence maximization problem as described above.

[0034] The present invention also provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program that can be executed to implement the steps of the method described above for finding the seed set of the two-stage influence maximization problem.

[0035] This invention provides a method and apparatus for finding a seed set for a two-stage influence maximization problem. The method includes: acquiring a social network graph; obtaining a reverse reachability set corresponding to the social network graph according to a preset two-stage selection rule; selecting a target node from the reverse reachability set and adding the target node to a pre-established seed set; acquiring a pre-constructed objective function corresponding to the two-stage influence maximization problem; and determining the seed set as the most influential seed set if the seed set conforms to the objective function. This invention obtains an accurate reverse reachability set by distinguishing different stages, and then selects a target node from the reverse reachability set, resulting in a more accurate seed set. Attached Figure Description

[0036] Figure 1 This is a flowchart of a preferred embodiment of the method for finding the seed set of the two-stage influence maximization problem in this invention.

[0037] Figure 2a This is a graph showing the effect of changing k on the diffusion of influence on the Wiki-Talk dataset when the number of competing categories c=5.

[0038] Figure 2b This is a graph showing the effect of changing k on the diffusion of influence on the Email-EuAll dataset when the number of competing categories c=5.

[0039] Figure 2c This is a graph showing the effect of changing k on the influence diffusion degree when the number of competing categories c = 5 on the soc-Epinions1 dataset.

[0040] Figure 2d This is a graph showing the effect of changing k on the influence diffusion degree when the number of competing categories c = 5 on the dataset p2p-Gnutella06.

[0041] Figure 2eThis is a graph showing the effect of changing k on the diffusion of influence on the Wiki-Vote dataset when the number of competing categories c=5.

[0042] Figure 3a This is a graph illustrating the effect of changing k on the diffusion of influence when the number of competing categories c=5 on the facebook-combined dataset.

[0043] Figure 3b This is a graph illustrating the effect of changing k on the diffusion of influence when the number of competing categories c=5 is verified on the CA-GrQc dataset.

[0044] Figure 3c This is a graph illustrating the effect of changing k on the diffusion of influence when the number of competing categories c=5 is verified on the Cit-HepTh dataset.

[0045] Figure 4a This is a graph illustrating the impact of changing the number of competing categories c and k on the influence diffusion in the Wiki-Talk dataset, based on the present invention.

[0046] Figure 4b This is a graph illustrating the impact of changing the number of competing categories c and k on the influence diffusion degree on the Email-EuAll dataset, based on the present invention.

[0047] Figure 4c This is a graph showing the effect of changing the number of competing categories c and k on the influence diffusion degree on the soc-Epinions1 dataset according to the present invention.

[0048] Figure 4d This is a graph showing the effect of changing the number of competing categories c and k on the influence diffusion degree on the p2p-Gnutella06 dataset, as described in this invention.

[0049] Figure 4e This is a graph showing the effect of changing the number of competing categories c and k on the influence diffusion degree on the Wiki-Vote dataset, based on the present invention.

[0050] Figure 5a This is a graph used in this invention to verify the effect of changing the number of competing categories c and k on the influence diffusion on the facebook-combined dataset.

[0051] Figure 5b This is a graph used in this invention to verify the effect of changing the number of competing categories c and k on the influence diffusion degree on the CA-GrQc dataset.

[0052] Figure 5c This is a graph used in this invention to verify the effect of changing the number of competing categories c and k on the influence diffusion on the Cit-HepTh dataset.

[0053] Figure 6 This refers to the experimental running time of each algorithm in this invention during the experiment.

[0054] Figure 7 This is a functional principle block diagram of a preferred embodiment of the device for finding the seed set of the two-stage influence maximization problem in this invention.

[0055] Figure 8 This is a functional principle block diagram of a preferred embodiment of the terminal in this invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0057] Social networks are composed of individuals and their relationships, and can be viewed as a graph. Our lives are a large graph of social networks, with individuals and their relationships forming the edges. Information transmission is constantly around us. How to achieve maximum impact with minimal human and material resources is a current research hotspot. The Impact Maximization (IM) problem is to find the k seed nodes with the greatest influence in a social network. The IM problem first appeared in 2003, proposed by Kempe et al. They not only provided the theoretical approximation ratio of a greedy algorithm but also gave two basic propagation models: the Independent Cascade (IC) model and the Linear Threshold (LT) model. Subsequently, the IM problem has received more research. The IM problem begins with identifying influential individuals, i.e., opinion leaders. Then, these k influential individuals are selected to experiment with the expected target. Transforming the IM problem into a mathematical problem is combinatorial optimization. The efficiency of the algorithm and the establishment of the model are important factors in solving this problem. Due to the diversity and complexity of information in social networks, a single social network cannot meet the current scenario, thus giving rise to competitive social networks. Building upon the work of Kempe and Bharathi, the Competitive Influence Maximization (CIM) problem was proposed, and a multi-player game model was first introduced. He proved that the "competitive price" in this game is at most 2, and the algorithm for calculating the opponent's optimal strategy has a theoretical approximation guarantee of (1-1 / e). Since then, the CIM problem has attracted considerable attention from researchers. The goal of the CIM problem is to find the k nodes with the greatest influence diffusion in a competitive social network, where k is a positive integer.

[0058] The biggest difference between CIM and IM problems lies in the propagation process. CIM propagation only requires whether nodes are activated, while CIM considers not only activation but also who is activated. In real life, once some original products become popular, many similar products will emerge to seize market share. At this point, the original product is the seed node, while similar products are competitors, and the existing model is no longer suitable.

[0059] This invention takes into account that original merchants need to promote their products in two stages to maximize their influence: the first stage of maximizing individual influence and the second stage of maximizing competitive influence. It designs a method to solve the two-stage influence maximization problem.

[0060] This invention extends the IC model to better fit the problem of maximizing two-stage influence with competition. It adds decision states to the model, termed the Two-Stage Independent Cascaded Model (TSIC). The method seamlessly connects two factors: the original product and competing products. To make the TSIC model more realistic, the information propagation distribution is divided into two parts: non-competitive influence (stage one) and competitive influence (stage two). Before time T, a user learns about a message from a friend and decides whether to receive it. During this process, the user has two choices: receive (activate) and reject (do not activate). After time T, other similar messages join, creating a competitive environment. The influence propagation at this point is not a simple acceptance or rejection, but rather involves an intermediate process of consideration and choice, which this invention defines as a decision state.

[0061] Due to the characteristics of information propagation on social networks, the influence maximization (IM) problem has received widespread attention. The IM problem involves the spread of influence from a small group of seed nodes to the widest extent within the network. To better adapt to real-world propagation scenarios, this invention considers both single-product and multi-entity product propagation. Therefore, a two-stage influence maximization problem is proposed. In the first stage, there are no competitors. After time T, competing nodes are added to the second stage. Since existing models do not adequately address the problem, this invention extends the Independent Cascade (IC) model. The two-stage influence maximization (TSIC) problem is theoretically proven to be NP-hard, monotonic, and submodular. Because heuristic algorithms are fast, improvements are made. Combining the divide-and-conquer approach, the Leiden_imrank and Random divide-and-conquerimrank (RDCI) algorithms are proposed, which improve influence diffusion and shorten running time. Greedy algorithms also show good results. Utilizing reverse influence sampling and maximum coverage, the Max-Coverage-RIS-Greedy (MCRG) algorithm is proposed. Experiments were conducted on eight real-world datasets (five datasets of different orders of magnitude and three validation sets) to verify the effectiveness and validity of the algorithm. The experiments conclude that the MCRG algorithm is more suitable for small datasets, while the Leiden_imrank and RDCI algorithms perform well on large datasets.

[0062] For the TSIC model, in daily life, it is common to see some new products in stores. If these products sell well, many similar products will be seen in many other stores. When a new product appears, if there is a certain demand for it, some similar products will emerge to seize the market share and make a profit, which brings competition. From the perspective of the original merchant, how to maximize the promotion of the product and expand its influence in the face of competition is a question worthy of consideration. To address such problems, the present invention proposes a two-stage influence maximization problem, which is more suitable for the current diversified market. For the classical IM problem, the independent cascade model is the basic model. Under the IC model, each activated node will attempt to stimulate its neighbor nodes with a certain probability. To cope with the influence of competing nodes, in the proposed model, a node has three states: inactive, influenced, and determined, and a node has only one chance to choose a definite state. A node being inactive means that no other node sends a message to it. If the node receives information from other nodes, the node is influenced. When this node is influenced, it will decide which influence to receive for transmission, and this state will be determined. There are m + 1 different influences C = {C0, C1, ···, Cm}, where C1, ···, Cm are competitors, and the present invention only considers the influence of set C0. Each node may have multiple different influences, but only one of these influences can be transmitted to the neighbor nodes. In other words, the influenced states of nodes can overlap, but the determined state is unique. The present invention aims to select k seed nodes S = {s1, ···, sk}, and the seed node si (1 ≤ i ≤ k) may receive several different influences, and only the influence of C0 needs to be calculated. First stage: At the beginning, all non-seed nodes are inactive, and the seed nodes have only one influence of C0. When t = 1, the seed nodes diffuse their influence to the inactive neighbor nodes with different probabilities. When t = t + 1 < T, the activated nodes will influence other unactivated nodes. Second stage: When t > T, the remaining unactivated nodes are classified, and i (0 < i < k) selects nodes from each category as competing nodes, and the nodes activated in the first stage continue to influence the non-seed neighbor nodes. Since the competing nodes start to join and have an impact at time T, nodes may be subject to multiple influences during the propagation process, and the present invention calculates the nodes with the decision state of C0 for the next propagation. The criterion for the determined state is as follows: Suppose Ix is the set of influences that x has received, and x decides which influence to choose as the determined state with an equal probability of 1 / |Ix|. The propagation ends until the states of all nodes do not change.

[0063] Please refer to Figure 1 , Figure 1 is the flowchart of the method for finding the seed set of the two-stage influence maximization problem in the present invention. As Figure 1As shown in the embodiment of the present invention, the method for finding the seed set of the two-stage influence maximization problem includes:

[0064] Step S100: Obtain the social network graph and obtain the reverse reachable set corresponding to the social network graph according to the preset two-stage selection rule.

[0065] Specifically, a social network is modeled as a graph G = (V, E), where V and E represent the set of user nodes and the set of edges representing relationships, respectively. Each edge E connects nodes, indicating that users can communicate with each other. Due to the development of social networks, users frequently use them to spread messages. Because of the characteristics of social networks, many businesses utilize them to promote their products and expand their brand influence. However, due to the convenience of social networks, if some products achieve good profits, over time, many businesses will promote similar products to seize market share. This invention primarily helps original product manufacturers expand their product's influence when they initially dominate the market and later face a proliferation of similar products.

[0066] In one implementation, step S100 specifically includes:

[0067] Step S110: Obtain the social network graph and select the first parent node of each node on the social network graph according to the preset two-stage selection rules;

[0068] Step S120a: If the first parent node has not been visited, add the node corresponding to the first parent node to the pre-established reverse reachable set.

[0069] In one embodiment, the step S110 is followed by:

[0070] Step S120b: If the first parent node has been visited, continue to select the second parent node corresponding to the first parent node until no new node is added to the reverse reachable set, and obtain the first influence diffusion degree corresponding to each node in the reverse reachable set.

[0071] First, the social network graph is initialized. Specifically, for each node in the social network graph G, all nodes are marked as uncovered, and the seed set S is set to empty. The reverse reachable set (RR set) is also initialized to empty.

[0072] When selecting a node, the following steps are included:

[0073] Step 1: Randomly select a starting node v in the social network graph G;

[0074] Step 2: For each node u in the social network graph G, before t < T, with a certain probability q1 or when t > T, with probability q2, select its parent node v. If v has not been visited, add v to the RR set; otherwise, continue to the next step.

[0075] Step 3: For each selected parent node v, with a certain probability p, select its parent node w. If w has not been visited, add w to the RR set; otherwise, continue to the next step.

[0076] Step 4: Repeat Step 3 until no new nodes are added to the RR set.

[0077] In one embodiment, the preset two-stage selection rule is as follows: If the current node propagation stage is in the non-competition influence stage, select the first parent node of the current node with the preset first probability; if the current node propagation stage is in the competition influence stage, select the first parent node of the current node with the preset second probability.

[0078] In one embodiment, the preset two-stage selection rule is:

[0079] If the hop count of the current node is less than or equal to the preset hop count threshold, select the first parent node of the current node with the preset first probability;

[0080] If the hop count of the current node is greater than the preset hop count threshold, select the first parent node of the current node with the preset second probability.

[0081] The present invention is divided into two stages. Selecting the hop count threshold T for division is more in line with the actual situation, and merchants can set different hop count thresholds T according to the situation of the product. That is, dividing the stages in two stages is more suitable for the actual situation. The present invention defines that there is no competition before T, which is a conventional IM problem. After reaching T, competitors join, and it becomes a CIM problem.

[0082] As Figure 1 shown, the method for finding the seed set of the two-stage influence maximization problem in this embodiment further includes:

[0083] Step S200: Select a target node from the reverse reachable set and add the target node to the pre-established seed set.

[0084] Specifically, from all uncovered nodes in the reverse reachable set, select the node that can cover the most uncovered nodes and add it to the seed set S. In this way, mark all the nodes covered by the newly added node to the seed set S as the covered state. When the difference between the influence diffusion degree calculated by the greedy algorithm of maximum coverage and the influence diffusion degree calculated by the reverse reachable set is less than (1 + ∈) (in the present invention, 1.1 can be taken), terminate the algorithm and output the current seed set S.

[0085] In one implementation, step S200 specifically includes:

[0086] Step S210: Obtain the number of covered nodes corresponding to each node in the reverse reachable set, and take the node corresponding to the maximum value among the covered node numbers as the initial selected node.

[0087] Step S220: Calculate the second influence diffusion degree corresponding to the initially selected node using a greedy algorithm with maximum coverage;

[0088] Step S230: Obtain the first influence diffusion degree corresponding to the initial selected node, and calculate the difference between the first influence diffusion degree and the second influence diffusion degree;

[0089] Step S240: If the difference between the first influence diffusion degree and the second influence diffusion degree is less than or equal to a preset deviation threshold, then the initially selected node is added as a target node to the pre-established seed set.

[0090] Specifically, the preset deviation threshold can be set to 1.1.

[0091] Traditional greedy algorithms are time-consuming due to continuous simulation iterations. Some heuristic methods can improve efficiency, such as the IMRank algorithm. This invention, based on the original idea, adopts a divide-and-conquer approach and improves the IMRank algorithm by considering the actual situation of competitive classification, proposing the Leiden_imrank algorithm and the Random Divide-and-Conquer IMRank (RDCI) algorithm (Algorithm 1 and Algorithm 2). Specifically, in the second stage, the Leiden_imrank algorithm first selects competing nodes from the node set V, then uses community classification to divide the remaining nodes in V into multiple subsets; finally, it simultaneously calculates the influence diffusion degree of each subset. The RDCI algorithm, on the other hand, forms multiple subsets through random classification and simultaneously calculates the influence diffusion degree of the seed node. To speed up the Monte Carlo simulation, one method is to reduce the variance in the sampling process; resampled importance sampling (RIS) is one of the classic solutions. This algorithm was first applied by Borgs et al. to the instant messaging problem. On the same dataset, RIS can bring a significant speed improvement over Monte Carlo. This invention uses RIS instead of Monte Carlo simulation.

[0092] First, the probability that an edge E in graph G can propagate a message is randomly generated within the interval [0,1]. Given a threshold (0.1), edges below this threshold are removed, and the remaining edges are retained as Random Reverse ReachableSets (RRS). Second, using a greedy algorithm with maximum coverage, k nodes are selected from the RRS and added to the seed set S. The influence diffusion degree Cov(SR) is calculated using Algorithm 3. Then, Algorithm 4 is used to calculate the influence diffusion degree Cov(SR∪v) of the seed nodes and compare it with Cov(SR). When Cov(SR∪v) - Cov(SR) is less than or equal to 0.01 (a value less than 0.1 can be set according to the actual situation), the calculation stops. Finally, Algorithm 5 is used to select the k most influential nodes in the social network graph G and add them to the seed set S. Algorithm 1 is shown in the table below.

[0093]

[0094] Algorithm 2 is shown in the table below.

[0095]

[0096]

[0097] Algorithm 3 is shown in the table below.

[0098]

[0099] Algorithm 4 is shown in the table below.

[0100]

[0101] Algorithm 5 is shown in the table below.

[0102]

[0103] like Figure 1 As shown in the figure, the process of finding the seed set for the two-stage influence maximization problem described in this embodiment also includes:

[0104] Step S300: Obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set meets the objective function, then the seed set is determined as the most influential seed set.

[0105] Specifically, let S be the seed node set, x∈V\S be a seed node, and define f(x|S)=f(S+x)-f(S) as the marginal effect of adding a new seed node x to the seed set. Given a network G=(V,E), where V represents nodes and E represents edges. Assume A0 is the original product, and there are m distinct competing products Ai={A1,A2,...,Am}, where T represents the hop count, a positive integer k. After reaching the hop count T, competing products Ai join the competition against A0. The TSIM problem is to select k nodes from the node set V as the seed set S.

[0106] In one embodiment, the objective function is: Where S represents the seed set, |S A0 |=k represents selecting k nodes from the seed set S, where all k nodes belong to the original node A0, σ t This refers to the degree of influence diffusion at each node. It represents the sum of the influence of competing nodes in a social network graph.

[0107] Specifically, the solution process for the two-stage influence maximization problem of this invention includes: determining the objective function, determining the node selection strategy, implementing the algorithm, and verifying the algorithm. First, an objective function needs to be determined to measure the influence after selecting certain nodes. Then, the node selection strategy under the given objective function is determined, i.e., how to select some nodes to maximize the objective function. In implementing the algorithm, the node selection strategy is transformed into specific algorithm implementations, such as Algorithm 1, Algorithm 2, and Algorithm 5.

[0108] This invention verifies the performance of the algorithm through experiments and compares it with other algorithms.

[0109] This invention selects five datasets from real social networks: Wiki-Vote, p2p-Gnutella06, socEpinions1, Email-EuAll, and Wiki-Talk. These datasets demonstrate various social relationships, such as information exchange between different users, email transmission and sending, etc. To ensure the reliability of the experiment, three real-world datasets are also provided as validation sets: facebook-combined, CA-GrQc, and Cit-HepTh. Tables 3-1 and 3-2 show the experimental datasets.

[0110] Table 3-1 Experimental Dataset

[0111]

[0112] Table 3-2 Experimental Validation Set

[0113]

[0114] For the comparison algorithms, on the one hand, we selected the theoretically sound greedy algorithm and the improved greedy algorithm CELF. On the other hand, we also selected heuristic algorithms with shorter running times: IMRank and IRIE. To compare the diversity of experimental types, we finally chose the IMM algorithm using the reverse reachability set. Details are as follows:

[0115] Leiden_imrank: The dataset is first classified using community classification. Then, each sorted dataset is iteratively sorted. Finally, the distribution of node marginal influence based on the current sort is calculated. See Algorithm 1 for the specific algorithm.

[0116] RDCI: Algorithm 2 is an improvement on the IMRank algorithm. This invention uses a divide-and-conquer approach to randomly classify the dataset. Each node iteratively sorts the dataset for each classification and calculates the marginal influence distribution of the node based on the current sort.

[0117] MCRG: See Algorithm 3-5 for details.

[0118] The comparative experiments were designed with not only advanced algorithms but also different types of algorithms, and the setup was reasonable.

[0119] Parameter setting instructions: ∈1 = 1 / 60; ∈2 = 1 / 20; ∈3 = 1 / 40·(1-1 / e);

[0120] λ1=1+(1+∈2)·(4e-8) / ∈2 2 log(1 / δ2), δ2 < 1;

[0121] λ2=(1+∈1)·(1+∈2)·(4e-8) / ∈3 2 log(3 / δ), δ² = 0.25

[0122] This invention selected five real-world datasets and five comparison algorithms for experiments, and used three datasets to verify the accuracy of the experiments. During the experiments, the results were mainly analyzed by controlling two parameters: the seed set size *k* and the number of competing classifications *c*.

[0123] (1) Results of different algorithms: The size of the seed node k directly affects the degree of diffusion. First, we analyze how the diffusion is affected when k changes, given a fixed number of competing classifications. Figure 1Figure 2(a) shows a dataset of millions of records. When k = 10 and 20, the RDCI algorithm has the largest influence diffusion value. When k = 30, 40, and 50, the influence diffusion value of the RDCI algorithm is smaller than that of the Leiden_imrank and imrank algorithms. The Leiden_imrank algorithm performs better as k increases. The influence diffusion of the Leiden_imrank, RDCI, and IMRank algorithms is much higher than that of the MCRG and IMM algorithms. It can be seen that the MCRG algorithm is generally better than the IMM algorithm. In Figure 2(b), the influence diffusion of the IMRank, IRIE, and RDCI algorithms is similar. The Leiden_imrank algorithm is significantly lower than the IMRank, IRIE, and RDCI algorithms when k = 10 and 20, but the influence value increases significantly as k increases. When k = 40 and 50, the Leiden_imrank algorithm is better than imrank, IRIE, and RDCI. Both the MCRG and IMM algorithms use RRS. It can be seen that the MCRG algorithm performs better than the IMM algorithm. For Figure 2(c), it can be seen that the IMRank, RDCI, and Leiden_imrank algorithms move in the same direction. Leiden_imrank is superior at k=10, 20, and 30. The influence propagation of the MCRC algorithm is significantly higher than that of the IMM algorithm. In Figure 2(d), due to the small dataset and low degree, the greedy algorithm and the CELF algorithm are compared. This invention finds that the MCRG algorithm is significantly better than other algorithms. When k=10, the differences between the CELF, Greedy, IRIE, IMM, and MCRG algorithms are small, but become more pronounced as k increases. Among the five algorithms with small differences in influence diffusion, the MCRG algorithm has the largest influence value, followed by the Greedy, IRIE, and IMM algorithms, and finally the CELF algorithm. In Figure 2(d), the IMRank algorithm outperforms the RDCI and Leiden_imrank algorithms among the other three algorithms. In Figure 2(e), the MCRG algorithm is optimal. As k increases, the influence value of the Leiden_imrank algorithm is smaller than that of the IMM algorithm, but larger than that of the RDCI algorithm. From Figures 3a-3c As shown in the figures, the algorithm is greatly affected by the size of the dataset. The Leiden_imrank algorithm performs best when the dataset is large. As the dataset decreases, the difference in the diffusion of influence between the Leiden_imrank algorithm and the RDCI algorithm narrows. The MCRG algorithm performs best on datasets with values ​​in the thousands, such as p2p-Gnutella06 and Wiki-Vote.

[0124] To verify the optimal performance of the MCRG algorithm on small datasets, three real datasets were selected for validation. Figures 3a-3cThe optimal algorithm is the MCRG algorithm. Figures 4a-4e and Figures 5a-5c The changes in k and c are shown separately. As k increases, the degree of influence diffusion also increases. The increase in c has little impact on the degree of influence diffusion. Because the first stage of influence dissemination has a solid foundation, the number of competitors in the later stages will not significantly affect the outcome. This also corresponds to the fact that original products are generally more popular than imitations in real life.

[0125] (2) Execution time: Execution time is one of the important indicators for judging algorithm performance. From Figure 6 As can be seen from the table, the greedy algorithm is time-consuming, requiring tens of thousands of seconds to obtain results for datasets with thousands of nodes. For example, for the p2p-Gnutella06 dataset with only 8717 nodes and a degree of 3.6, the greedy algorithm takes 114387.083 seconds to obtain the influence diffusion value for k=50. The CELF algorithm is much faster, but still takes 2722.407 seconds. Both the greedy and CELF algorithms are time-consuming when dealing with datasets with high degree and a large number of nodes, such as Wiki-Vote, soc-Epinions1, Email-EuAll, and Wiki-Talk. Therefore, the Greedy and CELF algorithms were only used on the p2p-Gnutella06 dataset. By analyzing the influence propagation results, combined with... Figure 6 It can be concluded that the RDCI algorithm has the shortest execution time, and the Leiden_imrank algorithm is much faster than the IMRank algorithm. The improved RDCI and Leiden_imrank algorithms of this invention outperform the IMRank algorithm in both influence value and runtime.

[0126] This invention proposes a two-stage influence maximization problem. The hop count domain T can be adjusted according to user needs, making it more suitable for everyday scenarios. The IC model is extended by adding decision states, clarifying how to determine whether a node activated in the competition phase is activated by a seed node, and proving that the two-stage influence maximization problem is NP-hard and submodular. Furthermore, to effectively calculate the influence diffusion degree of competing relationships, the Leiden_imrank algorithm, the RandomDivide-and-Conquer IMRank (RDCI) algorithm, and the Max-Coverage-RIS-Greedy (MCRG) algorithm are designed. Experiments on real datasets verify the superiority of the proposed algorithms.

[0127] In one embodiment, such as Figure 7As shown, based on the above method for finding the seed set of a two-stage influence maximization problem, the present invention also provides an apparatus for finding the seed set of a two-stage influence maximization problem, comprising:

[0128] The acquisition module 100 is used to acquire a social network graph and obtain the reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule;

[0129] Selection module 200 is used to select a target node in the reverse reachability set and add the target node to a pre-established seed set;

[0130] The determination module 300 is used to obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set meets the objective function, the seed set is determined as the most influential seed set.

[0131] In one embodiment, the present invention also provides a terminal, such as... Figure 8 As shown, it includes: a memory 20, a processor 10, and a program 30 stored in the memory 20 and executable on the processor 10 for finding a seed set of a two-stage influence maximization problem. When the program 30 for finding a seed set of a two-stage influence maximization problem is executed by the processor 10, it implements the steps of the method for finding a seed set of a two-stage influence maximization problem as described above.

[0132] The present invention also provides a computer-readable storage medium storing a computer program that can be executed to implement the steps of the method described above for finding a seed set for a two-stage influence maximization problem.

[0133] In summary, this invention discloses a method and apparatus for finding a seed set for a two-stage influence maximization problem. The method includes: acquiring a social network graph; obtaining a reverse reachability set corresponding to the social network graph according to a preset two-stage selection rule; selecting a target node from the reverse reachability set and adding the target node to a pre-established seed set; acquiring a pre-constructed objective function corresponding to the two-stage influence maximization problem; and determining the seed set as the most influential seed set if the seed set conforms to the objective function. This invention obtains an accurate reverse reachability set by distinguishing different stages, and then selects a target node from the reverse reachability set, resulting in a more accurate seed set.

[0134] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for finding the seed set of a two-stage influence maximization problem, characterized in that, The method includes: Obtain the social network graph and, according to a preset two-stage selection rule, obtain the reverse reachability set corresponding to the social network graph; Select a target node from the reverse reachability set and add the target node to a pre-established seed set; Obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set conforms to the objective function, then the seed set is determined as the most influential seed set. Selecting a target node from the reverse reachability set and adding the target node to a pre-established seed set includes: Obtain the number of covered nodes corresponding to each node in the reverse reachable set, and take the node corresponding to the maximum value of the number of covered nodes as the initial selected node. The second influence diffusion degree corresponding to the initial selected node is calculated using a greedy algorithm with maximum coverage. Obtain the first influence diffusion degree corresponding to the initial selected node, and calculate the difference between the first influence diffusion degree and the second influence diffusion degree; If the difference between the first influence diffusion degree and the second influence diffusion degree is less than or equal to a preset deviation threshold, then the initial selected node is added as a target node to the pre-established seed set. The objective function is: ; in, Represents the seed set, This means selecting k nodes from the seed set S, where all k nodes are original nodes. 0, This refers to the degree of influence diffusion at each node. This represents the total influence of competing nodes in a social network graph; m indicates that there are m different competing nodes, and V represents the node set.

2. The method for finding the seed set of a two-stage influence maximization problem according to claim 1, characterized in that, The process of obtaining the social network graph, which involves obtaining the reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule, includes: Obtain the social network graph and select the first parent node of each node in the social network graph according to a preset two-stage selection rule; If the first parent node has not been visited, then the node corresponding to the first parent node is added to the pre-established reverse reachable set.

3. The method for finding the seed set of a two-stage influence maximization problem according to claim 2, characterized in that, After selecting the first parent node of each node in the social network graph according to a preset two-stage selection rule, the process of obtaining the social network graph further includes: If the first parent node has been visited, the second parent node corresponding to the first parent node is selected again until no new node is added to the reverse reachable set, and the first influence diffusion degree corresponding to each node in the reverse reachable set is obtained.

4. The method for finding the seed set of a two-stage influence maximization problem according to claim 1, characterized in that, The preset two-stage selection rule is as follows: If the current node is in a phase without competition during the propagation stage, then the first parent node of the current node is selected with a preset first probability. If the current node is in a competitive phase during the propagation stage, the first parent node of the current node will be selected with a preset second probability.

5. The method for finding the seed set of a two-stage influence maximization problem according to claim 1, characterized in that, The preset two-stage selection rule is as follows: If the number of hops of the current node is less than or equal to the preset hop count threshold, then the first parent node of the current node is selected with a preset first probability. If the number of hops of the current node is greater than the preset hop count threshold, then the first parent node of the current node is selected with a preset second probability.

6. An apparatus for finding the seed set of a two-stage influence maximization problem, characterized in that, The device includes: The acquisition module is used to acquire the social network graph and obtain the reverse reachable set corresponding to the social network graph according to a preset two-stage selection rule; The selection module is used to select a target node in the reverse reachability set and add the target node to a pre-established seed set. The determination module is used to obtain the objective function corresponding to the pre-constructed two-stage influence maximization problem. If the seed set meets the objective function, the seed set is determined as the most influential seed set. Selecting a target node from the reverse reachability set and adding the target node to a pre-established seed set includes: Obtain the number of covered nodes corresponding to each node in the reverse reachable set, and take the node corresponding to the maximum value of the number of covered nodes as the initial selected node. The second influence diffusion degree corresponding to the initial selected node is calculated using a greedy algorithm with maximum coverage. Obtain the first influence diffusion degree corresponding to the initial selected node, and calculate the difference between the first influence diffusion degree and the second influence diffusion degree; If the difference between the first influence diffusion degree and the second influence diffusion degree is less than or equal to a preset deviation threshold, then the initial selected node is added as a target node to the pre-established seed set. The objective function is: ; in, Represents the seed set, This means selecting k nodes from the seed set S, where all k nodes are original nodes. 0, This refers to the degree of influence diffusion at each node. This represents the total influence of competing nodes in a social network graph; m indicates that there are m different competing nodes, and V represents the node set.

7. A terminal, characterized in that, include: The memory, the processor, and a program stored in the memory and executable on the processor for finding a seed set of a two-stage influence maximization problem, wherein when the program for finding a seed set of a two-stage influence maximization problem is executed by the processor, the steps of the method for finding a seed set of a two-stage influence maximization problem as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that can be executed to implement the steps of the method for finding a seed set for a two-stage influence maximization problem as described in any one of claims 1 to 5.

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