Self-influence maximization method under linear threshold model

Abstract

The application relates to a self-influence maximization method based on a linear threshold model, and comprises the following steps: sampling a deterministic instance in a Com-LT model; abstracting a self-influence maximization problem in the Com-LT model; finding all nodes adopting a propagation theme B through a forward BFS algorithm; and finding nodes adopting A which can be activated as a seed of the propagation theme A according to the reverse direction of an active edge. The application has the beneficial effects that the application considers the commonly existing multi-theme complementary relationship in social information propagation, proposes a method for researching a self-influence maximization problem, and greatly improves the calculation efficiency of the self-influence maximization problem through sampling when there is no complementary relationship between two user sets.

Description

Technical Field

[0001] This invention relates to the field of influence dissemination technology, and more specifically, to a method for maximizing one's own influence under a linear threshold model. Background Technology

[0002] In recent years, with the rapid development of the Internet, social relationships and ways of socializing between people have undergone significant changes. The field of information and influence dissemination in social networks has received widespread attention, including information dissemination models that study the dissemination methods of information in social networks, such as the path, speed, and scope of information dissemination; influence dissemination models that study the dissemination methods of influence in social networks, such as the path, speed, and strength of influence; and social network analysis that studies the relationships and network structure between nodes in social networks, including indicators such as node degree, clustering coefficient, and betweenness centrality.

[0003] The classic influence maximization problem focuses only on the spread of influence on a single topic. However, in the real world, users are often exposed to information on multiple topics simultaneously. These topics may be competitive or complementary, causing user behavior to deviate from the single-topic influence spread model. Existing research on multi-topic influence spread mainly focuses on purely competitive relationships, failing to fully consider the complementary relationships that are prevalent in social information dissemination, and therefore struggles to effectively represent multi-topic influence spread in social networks. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for maximizing self-influence under a linear threshold model.

[0005] Firstly, a method for maximizing self-influence under a linear threshold model is provided, including:

[0006] S1. In the Com-LT model, a deterministic instance is sampled;

[0007] S2. In the Com-LT model, abstract the problem of maximizing one's own influence;

[0008] S3. Use the forward BFS algorithm to find all nodes that use propagation topic B;

[0009] S4. Follow the opposite direction of the active edge to find the node that can activate v0 to adopt A when it is a seed for propagating topic A.

[0010] Preferably, S1 includes:

[0011] S101. Randomly and uniformly generate thresholds from [0,1] for user nodes in the two seed sets;

[0012] S102. In each time step, calculate the sum of the edge weights corresponding to the activated incoming edge neighbors for each user node v, compare it with two thresholds, and then mark the response.

[0013] S103. If any user node adopted any topic in S102, return to S102 for the next time step; otherwise, the propagation process terminates.

[0014] As a preferred approach, in S2, the definition of the self-influence maximization problem is: for a given social network G(V, E, W) A W B Let V be the set of nodes in the social network, E be the set of directed edges representing the social relationships between individuals, W be the edge weights, A and B be different topics of communication, and B be the seed set. Budget k≤n and a set of globally complementary parameters γ A，B and γ B，A The goal of the problem of maximizing one's own influence is to find a set of seeds A. Satisfying in |S A When |≤k, the expected number σ of users adopting A at the end of diffusion under the Com-LT model. A (S A S B )maximum.

[0015] As a preferred option, in S2, the Com-LT model uses the user complementarity parameter γ A，B and γ B，A In the general case where the value is arbitrary, the expected number σ A (S A S B Regarding S A It does not possess submodality; for γ B，A =0, meaning that B is not affected by A, but B can affect A in the special case where B is not affected by A, the problem of maximizing its own influence has submodality.

[0016] As a preferred embodiment, in S2, for a given user set S B Consider a given instance H and a seed set S. B Consider two seed sets A. A user node u∈V\T and another user node Due to monotonicity, there is According to the definition of v, there must be an active path P of A from some seed node w0∈T∪{u} to v. A ;in, In instance H, T and S BWhen the seed user sets are A and B respectively, the user node set of propagation topic A is used at the end of the diffusion process.

[0017] As a preferred embodiment, in S2, even if w0 is the only A seed, it is represented as S A ={w0}, on path P A For each point on the model, we will still use A to derive w0 = u; otherwise, we have w0 ∈ T. Due to the monotonicity of the model, we obtain... This contradicts the definition of v; w0 = u, therefore according to σ A (S A S B )yes The non-negative linear addition of σ, therefore σ A (S A S B Also about S A It has sub-model properties.

[0018] As a preferred option, in S3, a first-in-first-out queue Q is created, and all B user seed set nodes are inserted into the queue and marked as B-adopted, due to γ B，A =0, so topic A will not affect the diffusion process of topic B.

[0019] Preferably, in S4, starting from the sampling point user v0, the process moves in the opposite direction of the active edges to find nodes that can activate v0 to use A when it is seeded by A, and adds them to the returned set R; while moving in the opposite direction from node u, the process selects edges based on whether u has used B. Or e u A|B Walking; among them, This indicates that user u's diffusion is related to A's and that A's active edge does not use B, e u A|B This represents an active edge of A that is related to the diffusion of user u and A and has adopted B.

[0020] Secondly, a device for maximizing self-influence under a linear threshold model is provided, for executing any of the self-influence maximization methods under the linear threshold model described in the first aspect, including:

[0021] The sampling module is used to sample a deterministic instance in the Com-LT model;

[0022] The abstract module is used in the Com-LT model to abstract the problem of maximizing one's own influence.

[0023] The module is used to find all nodes that adopt the propagation topic B using the forward BFS algorithm;

[0024] The reverse module is used to find nodes that can be activated when v0 adopts A as a seed for propagating topic A by going in the opposite direction of the active edge.

[0025] Thirdly, a computer storage medium is provided, wherein a computer program is stored therein; when the computer program is run on a computer, the computer executes the method for maximizing its own influence under any of the linear threshold models described in the first aspect.

[0026] The beneficial effects of this invention are as follows: This invention considers the multi-topic complementary relationships commonly found in social information dissemination and proposes a method for studying the problem of maximizing one's own influence. When there is no complementary relationship between two user sets, the sampling method significantly improves the computational efficiency of maximizing one's own influence. Applied to practical scenarios such as social media promotion, political elections, commercial marketing, and public welfare, by maximizing one's own influence, and through lower computational costs and faster computation speed, the feasibility of a solution can be quickly and effectively evaluated. This helps to find a potentially better solution from among many options, reducing trial-and-error costs. Attached Figure Description

[0027] Figure 1 A flowchart of a method for maximizing self-influence under a linear threshold model;

[0028] Figure 2 A schematic diagram comparing the running time of the method provided by this invention with that of a greedy algorithm. Detailed Implementation

[0029] The present invention will be further described below with reference to embodiments. The description of the embodiments below is only for the purpose of helping to understand the present invention. It should be noted that those skilled in the art can make several modifications to the present invention without departing from the principle of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0030] Example 1:

[0031] This application's embodiments are based on a novel complementary multi-topic influence propagation model, Com-LT, and propose a method for studying the self-influence maximization problem. By defining the Com-LT model and sampling a deterministic instance from it, the self-influence maximization problem is defined and proven to be a special case of the classic single-topic influence propagation problem, and thus also an NP-hard problem. Subsequently, by proving that the influence function of the self-influence maximization problem under the Com-LT model has monotonicity and submodularity, a ComLT-SIM algorithm with a 1-1 / e-ε approximation ratio under certain conditions is given, such as... Figure 1 As shown in the embodiments of this application, the method for maximizing self-influence under a linear threshold model includes:

[0032] S1. In the Com-LT model, a deterministic instance is sampled.

[0033] For the model and sampling instance described in S1, the following steps are included:

[0034] S101. For propagation topics A and B, define the weight of each edge (u, υ) used in the diffusion process of A as: For use in B, it is denoted as Then the sum of the weights of the incoming edges of the extended node υ is:

[0035]

[0036] u and v are two user nodes on an edge in the network. It represents the weight of the propagation edge between corresponding users during the diffusion process of topic A.

[0037] The threshold for A when node υ has already used B is:

[0038]

[0039] γ A，B It is the parameter of user complementarity, s A (v) is the sum of the weights of the incoming edges A in the network of user v. This is the threshold for propagating topic A when the current user v is not using propagation topic B. The sum of the edge weights corresponding to the activated incoming edge neighbors of node υ is:

[0040]

[0041] Information diffusion process in S102 and Com-LT models: Initially, in the seed set S of A... A The nodes in the array use A, S B The nodes in the array use B. Each node randomly and uniformly generates a threshold from [0, 1]. Then calculate θ of the node. v A|B and θ v B|A In each time step, for each node υ, if A is not used, then calculate c. A (v), and depending on whether B has been adopted, c A (v) and threshold or Comparison, if c A(v) If the value is not less than the threshold, mark it as not having adopted A, and repeat this process symmetrically for B; if any node in this process adopts either topic (A or B), return to the previous step for the next time step. Otherwise, the propagation process terminates.

[0042] S103. Sample a specific instance. For node υ, let in(υ) represent the number of its incoming edges, denoted by z1, z2, ..., z... in (v) represents these incoming edges, b1, b2, ..., b in (v) represent the weights A of these edges respectively. A random real number is generated uniformly from [0, 1] with equal probability. Used for the next sampling step; find the minimum satisfaction. An integer j ∈ [1, in(v)]. If a j that satisfies this condition exists, return 1. Sampling is complete; no further steps are needed. Otherwise, for node U, It does not exist, and proceed to the next step to find e. v A|B Find the minimum satisfaction The integer k ∈ [1, in(v)]. If a k that satisfies the condition exists, return e. v A|B =z k Otherwise e v A|B It does not exist.

[0043] b i A|B This represents the edge weight of A for the i-th user who has already adopted B. Option B was not adopted. User v's diffusion is related to A's and A's active edges do not use B's, e v A|B This represents an active edge of A that is related to the diffusion of user v and A and has adopted B.

[0044] S2. In the Com-LT model, the problem of maximizing one's own influence is abstracted.

[0045] In S2, the problem of maximizing one's own influence is defined as follows: for a given social network G(V, E, W) A W B Seed set B Budget k≤n and a set of globally complementary parameters γ A，B and γ B，A The goal of the problem of maximizing one's own influence is to find a set of seeds A. Satisfying in |S AWhen |≤k, the expected number σ of users adopting A at the end of diffusion under the Com-LT model. A (S A S B )maximum.

[0046] The Com-LT model in the user complementarity parameter γ A，B and γ B，A In the general case where the value is arbitrary, the expected number σ A (S A S B Regarding S A It does not possess submodality; for γ B，A =0, meaning B is not affected by A, but B can affect A. In this special case, the problem of maximizing one's own influence has a submodularity: for a given S A When γ B，A When σ = 0, the propagation of topic B under Com-LT is unaffected by A, which is equivalent to its propagation process under the classical linear threshold model. Since the classical model has submodality, the expectation number σ = 0. B (S A S B Regarding the user set S B It possesses sub-modeling properties.

[0047] For a given set of users S B Consider a given instance H and a seed set S. B Consider two seed sets A. A user node u∈V\T and another user node Due to monotonicity, there is According to the definition of v, there must be an active path P of A from some seed node w0∈T∪{u} to v. A ;in, In instance H, T and S B When the seed user sets are A and B respectively, the user node set of propagation topic A is used at the end of the diffusion process.

[0048] Even if w0 is the only seed of A, it is represented as S. A ={w0}, on path P A For each point on the model, we will still use A to derive w0 = u; otherwise, we have w0 ∈ T. Due to the monotonicity of the model, we obtain... This contradicts the definition of v; w0 = u, therefore according to σ A (S A S B )yes The non-negative linear addition of σ, therefore σ A(S A S B Also about S A It has sub-model properties.

[0049] S3. Use the forward BFS algorithm to find all nodes that use propagation topic B.

[0050] In S3, a first-in-first-out queue Q is created, and all nodes in the seed set of user B are inserted into the queue and marked as B-adopted. Due to γ... B，A =0, so topic A will not affect the diffusion process of topic B. S3 uses... However, using N + B|A (u) is also equivalent. It is an edge for user node u The starting user's ID, This is for VIP users. The user node number in the specified situation.

[0051] S4. Follow the opposite direction of the active edge to find the node that can activate v0 to adopt A when it is a seed for propagating topic A.

[0052] In S4, starting from the sampling point user v0, the process moves in the opposite direction of the active edges to find nodes that can activate v0 to use A when it is seeded by A, and adds them to the returned set R; while moving in the opposite direction from node u, the process selects edges based on whether u has used B. Or e u A|B Walking; among them, This indicates that user u's diffusion is related to A's and that A's active edge does not use B, e u A|B This represents an active edge of A that is related to the diffusion of user u and A and has adopted B.

[0053] The specific environment used in this application embodiment is an Intel Core i7-7700 CPU @ 3.60GHz, an operating system of Ubuntu 20.04.3LTS, 32GB of memory, and experiments were conducted using C++ on several public social network datasets, including NetHept, HepPH (cit-HepPh), Facebook (musae-facebook), and Deezer (feather-deezer-social).

[0054] Since the influence function is difficult to calculate precisely, Monte Carlo simulations were used to evaluate the algorithm's performance. 10,000 simulations were performed in the experiment. Simulations were conducted directly according to the definition of the Com-LT model, using σ... A (SA S B σ serves as an indicator of influence dissemination. A (S A S B ) is the expected number of users adopting A at the end of the diffusion. Each Monte Carlo sampling will first... Perform a simulation once and record the results, then S B Set the desired outcome and simulate again. Table 1 shows a comparison of the improvement in influence propagation between the present invention and various methods on different datasets, with the data representing the percentage improvement of the present invention compared to two commonly used comparative methods. Table 2 shows a comparison of influence propagation between ComLT-SIM and the greedy algorithm.

[0055] Table 1

[0056]

[0057] Table 2

[0058] ComLT-SIM 244.3868 415.2623 546.475 465.7024 greedy 246.4877 417.504 547.7564 465.0453 Compared to greed -0.85％ -0.54％ -0.23％ 0.14％

[0059] As shown in Table 1, Table 2 and Figure 2 As shown, the method provided in this application embodiment effectively improves the propagation of influence on various datasets under the same fixed user set, and achieves a significant improvement in running time while maintaining an effect close to that of a greedy algorithm, fully demonstrating the efficiency of the present invention.

[0060] Example 2:

[0061] Based on Embodiment 1, Embodiment 2 of this application provides a device for maximizing self-influence under a linear threshold model, comprising:

[0062] The sampling module is used to sample a deterministic instance in the Com-LT model;

[0063] The abstract module is used in the Com-LT model to abstract the problem of maximizing one's own influence.

[0064] The module is used to find all nodes that adopt the propagation topic B using the forward BFS algorithm;

[0065] The reverse module is used to find nodes that can be activated when v0 adopts A as a seed for propagating topic A by going in the opposite direction of the active edge.

[0066] Specifically, the device provided in this embodiment is the same as the device corresponding to the method provided in embodiment 1. Therefore, the parts in this embodiment that are the same as or similar to those in embodiment 1 can be referred to each other, and will not be described again in this application.

Claims

1. A method for maximizing self-influence under a linear threshold model, characterized in that, include: S1. In the Com-LT model, a deterministic instance is sampled; For the model and sampling instance described in S1, the following steps are included: S101. For propagation topics A and B, define the weight of each edge (u, ʋ) used in the diffusion process of A as: If used for B, it is denoted as Then the sum of the weights of the incoming edges of the extended node ʋ is: u and v are two user nodes on an edge in the network. It is the weight of the propagation edge between corresponding users in the process of spreading topic A; The threshold for A when node ʋ has already adopted B is: These are parameters related to user complementarity. It is the sum of the weights of the incoming edges A in the network of user v. This is the threshold for propagating topic A when the current user v does not use propagation topic B; the sum of the edge weights corresponding to the activated incoming edge neighbors of node ʋ is: Information diffusion process in S102 and Com-LT models: Initially in the seed set of A The nodes in the diagram are labeled A. The nodes in the array use B; each node randomly and uniformly generates a threshold from [0,1]. , Then calculate the node's and In each time step, for each node ʋ, if A is not used, then calculate... And based on whether B has been adopted, and threshold or Comparison, if If the value is not less than the threshold, mark it as adopted as A, and repeat this process symmetrically for B; if any node in this process adopts any topic A or B, return to the previous step for the next time step; otherwise, the propagation process terminates. S103. Sample a specific instance; for node ʋ, let in(ʋ) represent the number of its incoming edges, and use... , ,..., Indicate these incoming edges, , ,..., Let A represent the weights of these edges respectively; generate a random real number from [0,1] with equal probability and uniformity. Used for the next sampling step; find the minimum satisfaction. integers If a j that satisfies this condition exists, then return... Sampling is complete; no further steps are needed. Otherwise, for node ʋ, It does not exist, and proceed to the next step to find it. Find the minimum satisfaction integers If a k that satisfies the condition exists, then return. ,otherwise It does not exist; This represents the edge weight of A for the i-th user who has already adopted B. Option B was not adopted; This indicates that user v's diffusion is related to A, and that A's active edge does not use B. S1 represents the active edge of user v that is related to the diffusion of A and has adopted B; S2, in the Com-LT model, abstract the problem of maximizing one's own influence; in S2, for a given social network Let V be the set of nodes in the social network, E be the set of directed edges representing the social relationships between individuals, W be the edge weights, A and B be different topics of communication, and B be the seed set. ,Budget and a set of globally complementary parameters and The goal of the problem of maximizing one's own influence is to find a set of seeds A. , satisfying In the case of the Com-LT model, what is the expected number of users adopting A at the end of diffusion? maximum; S3. Use the forward BFS algorithm to find all nodes that use propagation topic B; S4. Follow the opposite direction of the active edges to find users who can activate sampling nodes when serving as seeds for propagating topic A. Use node A.

2. The method for maximizing self-influence under the linear threshold model according to claim 1, characterized in that, In S2, the Com-LT model uses user complementarity parameters. and In the general case of taking any value, the expected number about It does not possess sub-modeling property; for In the special case where B is not affected by A, but B can affect A, the problem of maximizing its own influence has a submodal property.

3. The method for maximizing self-influence under the linear threshold model according to claim 2, characterized in that, In S2, for a given set of users Consider a given instance H and a seed set B. Consider two seed sets S⊆T⊆V, a user node u∈V\T, and another user node Due to monotonicity, there are According to the definition of v, there must be a path from some seed node A. Active path A to v ;in, In instance H, T and When the seed user sets are A and B respectively, the user node set of propagation topic A is used at the end of the diffusion process.

4. The method for maximizing self-influence under the linear threshold model according to claim 3, characterized in that, In S2, even It is the only A seed, represented as , in the path Each point on the graph will still use A to derive... Otherwise, then there is Because of the monotonicity of the model, it is concluded that... This contradicts the definition of v; ,so ;according to , yes The non-negative linear addition, therefore Also about It has sub-model properties.

5. The method for maximizing self-influence under the linear threshold model according to claim 4, characterized in that, In S3, a first-in-first-out queue Q is created, and all nodes in the seed set of user B are inserted into the queue and marked as B-adopted. Because... Therefore, topic A will not affect the diffusion process of topic B.

6. The method for maximizing self-influence under the linear threshold model according to claim 5, characterized in that, In S4, from the sampling node user Start by moving in the opposite direction of the active edges to find the ones that can be activated when seed A. Nodes that use A are added to the returned set R; and when traversing backwards from node u, edges are selected based on whether u used B. or Walking; among them, This indicates that user u's diffusion is related to A, and that A's active edge does not use B. This represents an active edge of A that is related to the diffusion of user u and A and has adopted B.

7. A device for maximizing self-influence under a linear threshold model, characterized in that, A method for maximizing self-influence under a linear threshold model as described in any one of claims 1 to 6, comprising: The sampling module is used to sample a deterministic instance in the Com-LT model; The abstract module is used in the Com-LT model to abstract the problem of maximizing one's own influence. The module is used to find all nodes that adopt the propagation topic B using the forward BFS algorithm; The reverse module is used to traverse the active edges in the opposite direction to find the edges that can be activated when serving as the seed for propagating topic A. Use node A.

8. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program is run on the computer, it causes the computer to execute the method for maximizing its own influence under the linear threshold model as described in any one of claims 1 to 6.

Images