A heuristic method and system for maximizing influence with budget constraints

Abstract

The present invention discloses a heuristic method and system for maximizing influence considering budget constraints. The method steps are as follows: Step 1. Set the S of any node u to u The value is initialized to 1, F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values; Step 2. In each iteration, find the nodes that meet the current remaining budget as candidate nodes, find the node k with the largest marginal influence per unit cost among the candidate nodes as the seed node, and accordingly increase the S of the current seed node k Value and F k Set the value to 0; Step 3. When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly; Update the S of node v at time t v value; Step 4. Update F of all nodes w value; the F value #imgabs0# of node w at time t is the expected first-order influence of node w; step 5. Repeat steps 2‑4 until all budgets are used up or there are no candidate nodes that meet the budget conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of information dissemination in social networks, and in particular relates to a heuristic method and system for maximizing influence considering budget constraints. Background Art

[0002] In today's world, the media ecology and communication pattern of information dissemination are undergoing profound changes. Information is emerging all the time and in all directions, and the Internet has become the main channel for people to obtain information. As the main carrier of Internet information dissemination, online social networks are the distribution center for various types of information release and the main battlefield for information dissemination. Unlike traditional communication media, information dissemination on online social networks has the characteristics of fast dissemination speed, low dissemination cost, large influence range, and good dissemination effect. Therefore, a new marketing model - viral marketing came into being.

[0003] Viral marketing refers to a method whereby a company uses some incentives to attract a portion of users (seed nodes) in a social network to publish marketing information about its products, and then spreads word of mouth among individuals so that word of mouth spreads rapidly in the network like a virus, thus achieving the effect of product promotion. Maximizing influence is the core algorithmic problem in viral marketing, which is to find a set of seed nodes under a given information dissemination model so that the coverage of marketing information disseminated through these nodes is maximized.

[0004] Generally, the influence maximization algorithm aims to find the top 50 nodes that can maximize the spread of information. But in fact, the cost of activating a node as a seed node varies depending on the node's position in the network and the node's own characteristics. Under budget constraints, the cost of activating the seed nodes found by the traditional influence maximization method may exceed the enterprise's budget, so it is necessary to design a new heuristic technology solution to efficiently mine the seed node set under budget constraints. Summary of the invention

[0005] In view of the above-mentioned defects in the prior art, the present invention provides a heuristic method and system for maximizing influence considering budget constraints. The present invention is based on the degree centrality of nodes, considers the homogeneity of nodes and information, and the activation cost of nodes, and approximates the global influence of nodes with the first-order influence of nodes. Each time, the point with the largest marginal influence per unit cost is selected as the seed node until all budgets are used up or there are no candidate nodes that meet the budget conditions.

[0006] To avoid overlap in the influence coverage of seed nodes, the present invention iteratively adjusts the first-order influence of nodes in each round: if a node u is selected as a seed node, its out-degree neighbor v may be activated by this node, so the marginal benefit that neighbor v can bring after being selected as a seed node will be reduced accordingly. At the same time, the first-order influence of all nodes that can pass information to u or v will also be reduced accordingly.

[0007] The specific technical solutions of the present invention are as follows:

[0008] A heuristic method for maximizing influence with budget constraints. Assume that the information to be disseminated is i, the maximum budget that can be provided is B, and the network structure of the social platform to be disseminated is G, where G is a directed graph, the nodes in the graph are users in the network, and the edges are the paths of information dissemination in the network. If there is an edge from node u to node v, it means that the information sent by user u can be disseminated to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i is disseminated from u to v; Assume that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u It represents the contribution value of node u to itself after being activated, that is, the probability value that node u is still not activated. u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u. If the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is:

[0009]

[0010] Where m is the power index, preferably between 0.4 and 0.8. The more professional the field to which node u belongs, the larger the value of m.

[0011] The specific steps are as follows:

[0012] Step 1. Set S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values, that is:

[0013]

[0014] Where O(u) represents the set of out-degree neighbors of u.

[0015] Step 2. In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes. The remaining budget value for the next round is modified to:

[0016] B t+1 =B t -C k

[0017] Among them B t is the remaining budget at time t, C k is the activation cost of node k.

[0018] If a node F k t If the value is 0, then set

[0019] Step 3. Update S of the out-degree neighbor v of the current seed node v When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly. v The value is updated to:

[0020]

[0021] in is the S value of node v at time t.

[0022] Step 4. Update the F value of all nodes. Since the F value only involves first-order neighbors, we only need to update the F of u and O(u) in-degree neighbors w (ignoring seed nodes). w Value (that is, for any w, if there exists v∈O(u),v∈O(w), or u∈O(w), then update its F w value). Because ①u and w both point to v, if v has been activated by u, then v should be ignored when calculating the expected influence of w, so the expected first-order influence of w will be reduced accordingly. ②w points to u, u has been activated, and the expected influence of w should be reduced accordingly.

[0023] The F value of node w at time t is the expected first-order influence of node w.

[0024]

[0025] Step 5. Repeat steps 2-4 until all budgets are used up or there are no candidate nodes that meet the budget conditions.

[0026] The present invention also discloses an influence maximization heuristic system considering budget constraints, assuming that the information to be disseminated is i, the maximum budget that can be provided is B, and the network structure G of the social platform to be disseminated is G, wherein G is a directed graph, the nodes in the graph are users in the network, and the edges are paths for information dissemination in the network; if there is an edge from node u to node v, it means that the information sent by user u can be disseminated to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i is disseminated from u to v; assuming that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u represents the contribution value of node u to itself after being activated, that is, the probability value that node u is still not activated; F u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u; if the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is:

[0027]

[0028] Wherein, m is a power index, preferably between 0.4 and 0.8;

[0029] Includes the following modules:

[0030] Expected first-order influence F u Acquisition module: Get the S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values, that is:

[0031]

[0032] Among them, O(u) represents the set of out-degree neighbors of u;

[0033] Seed node search module: In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes; the remaining budget value for the next round is modified to:

[0034] B t+1 =B t -C k

[0035] Among them, B t is the remaining budget at time t, C k is the activation cost of node k;

[0036] If a node If the value is 0, then set

[0037] Contribution value S v Update module: When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly; the S of node v at time t v The value is updated to:

[0038]

[0039] in, is the S value of node v at time t;

[0040] The expected first-order influence acquisition module of node w: Update u and O(u) non-seed node in-degree neighbors w of F w Value; F value of node w at time t is the expected first-order influence of node w:

[0041]

[0042] Iteration module: Repeat the execution of seed node search module and contribution value S v The update module and the expected first-order influence acquisition module of node w operate until all budgets are used up or there are no candidate nodes that meet the budget conditions.

[0043] The present invention can efficiently find a group of seed nodes that meet a given budget constraint in a social network to spread given information, so that the information spread through these seed nodes can affect as many social network users as possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is an example graph of the relationship between nodes u, v, and w.

[0045] Figure 2 4 is a diagram of the first stage of processing involved in the influence maximization heuristic method considering budget constraints in the preferred embodiment.

[0046] Figure 3 4 is a diagram of the second stage processing involved in the influence maximization heuristic method considering the budget constraint in the preferred embodiment.

[0047] Figure 4 4 is a block diagram of the influence maximization heuristic system considering budget constraints of the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with preferred embodiments, but the following examples are by no means intended to limit the present invention in any way.

[0049] This embodiment is a heuristic method for maximizing influence with consideration of budget constraints. Assume that the information to be disseminated is i, the maximum budget that the enterprise can provide is B, and the network structure of the social platform to be disseminated is G, where G is a directed graph, the nodes in the graph are users in the network, and the edges are paths for information dissemination in the network. If there is an edge from node u to node v, it means that the information sent by user u can be propagated to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i propagates from u to v. This propagation probability can be obtained through the existing information propagation model that considers the characteristics of information content. Assume that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u It represents the contribution value of node u to itself after being activated, that is, the probability value that node u is still not activated. u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u. If the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is:

[0050]

[0051] Among them, m is the power index, which ranges from 0.4 to 0.8. The more professional the field to which node u belongs, the larger the value of m.

[0052] Step 1. Set S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values. That is:

[0053]

[0054] Where O(u) represents the set of out-degree neighbors of u.

[0055] Step 2. In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes. The remaining budget value for the next round is modified to:

[0056] B t+1 =B t -C k

[0057] Among them B t is the remaining budget at time t, C k is the activation cost of node k.

[0058] If a node If the value is 0, then set

[0059] Step 3. Update S of the out-degree neighbor v of the current seed node v When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly. v The value is updated to:

[0060]

[0061] in is the S value of node v at time t.

[0062] Specific as Figure 1 The relationship between nodes u, v, and w is shown in the example.

[0063] Step 4. Update the F value of all nodes. Since the F value only involves first-order neighbors, we only need to update the F of u and O(u) in-degree neighbors w (ignoring seed nodes). w Value (that is, for any w, if there exists v∈O(u),v∈O(w), or u∈O(w), then update its F w value). Because ①u and w both point to v, if v has been activated by u, then v should be ignored when calculating the expected influence of w, so the expected first-order influence of w will be reduced accordingly. ②w points to u, u has been activated, and the expected influence of w should be reduced accordingly.

[0064] The F value of node w at time t is the expected first-order influence of node w.

[0065]

[0066] Step 5. Repeat steps 2-4 until all budgets are used up or there are no candidate nodes that meet the budget conditions.

[0067] The above embodiment is further described in detail below with reference to a specific application case.

[0068] Assume the network structure is as follows Figure 2 As shown, the budget B = 4, the activation cost exponent m = 0.6, and the propagation probability of a given information i are given. The S value of each node is 1 at the initial moment. The F value is calculated as follows:

[0069]

[0070]

[0071] The C value is calculated as follows:

[0072]

[0073] In the first iteration, any node u as follows Figure 2 As shown:

[0074] In the first round of iteration, all nodes meet the budget requirements, and the unit cost marginal influence of each node is as follows:

[0075]

[0076] Select node 3 as the current seed node, set S3 = 0 and F3 = 0, and modify the remaining budget value for the next round to:

[0077] B 2 =B 1 -C3=4-2.3=1.7

[0078] Update the S values ​​of the out-degree neighbors 1, 2, 4, and 5 of the current seed node 3:

[0079] Neighbor 1:

[0080] Neighbor 2:

[0081] Neighbor 4:

[0082] Neighbor 5:

[0083] The S values ​​of other nodes remain unchanged.

[0084] The current seed nodes and their out-degree neighbors are 1, 2, 3, 4, 5, and their non-seed node in-degree neighbors are 1, 2, 8, 4. Update the F values ​​of these nodes:

[0085]

[0086] The F values ​​of other nodes remain unchanged.

[0087] In the second iteration, any node u like Figure 3 As shown:

[0088] In the second iteration, node 4 does not meet the budget requirements. The unit cost marginal impact of each node that meets the budget requirements is as follows:

[0089]

[0090] Select node 2 as the current seed node, set S2 = 0 and F2 = 0, and modify the remaining budget value for the next round to:

[0091] B 3 =B 2 -C2=1.7-1=0.7

[0092] There are no candidate nodes that meet the budget conditions, and the algorithm terminates. The final seed node set is {3, 2}.

[0093] like Figure 4 As shown, this embodiment discloses an influence maximization heuristic system considering budget constraints. Assume that the information to be disseminated is i, the maximum budget that can be provided is B, and the network structure G of the social platform to be disseminated is G, where G is a directed graph, the nodes in the graph are users in the network, and the edges are paths for information dissemination in the network; if there is an edge from node u to node v, it means that the information sent by user u can be disseminated to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i is disseminated from u to v; Assume that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u represents the contribution value of node u to itself after being activated, that is, the probability value that node u is still not activated; F u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u; if the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is:

[0094]

[0095] Wherein, m is a power index, preferably between 0.4 and 0.8;

[0096] Includes the following modules:

[0097] Expected first-order influence F u Acquisition module: Get the S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values, that is:

[0098]

[0099] Among them, O(u) represents the set of out-degree neighbors of u;

[0100] Seed node search module: In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes; the remaining budget value for the next round is modified to:

[0101] B t+1 =B t -C k

[0102] Among them, B t is the remaining budget at time t, C k is the activation cost of node k;

[0103] If a node If the value is 0, then set

[0104] Contribution value S v Update module: When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly; the S of node v at time t v The value is updated to:

[0105]

[0106] in, is the S value of node v at time t;

[0107] The expected first-order influence acquisition module of node w: Update u and O(u) non-seed node in-degree neighbors w of F w Value; F value of node w at time t is the expected first-order influence of node w:

[0108]

[0109] Iteration module: Repeat the execution of seed node search module and contribution value S v The update module and the expected first-order influence acquisition module of node w operate until all budgets are used up or there are no candidate nodes that meet the budget conditions.

[0110] The above description is only the specific implementation method and principle of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A heuristic method for maximizing influence with budget constraints, characterized by: Assume that the information to be transmitted is i, the maximum budget that can be provided is B, and the network structure of the social platform to transmit information is G, where G is a directed graph, the nodes in the graph are users in the network, and the edges are the paths of information transmission in the network; if there is an edge from node u to node v, it means that the information sent by user u can be transmitted to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i is transmitted from u to v; Assume that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u Indicates the probability value that node u has not been activated; F u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u; if the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is: Where m is the power index; Here are the steps: Step 1. Set S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values, that is: Among them, O(u) represents the set of out-degree neighbors of u; Step 2. In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes; the remaining budget value for the next round is modified to: B t+1 =B t -C k Among them, B t is the remaining budget at time t, C k is the activation cost of node k; If a node If the value is 0, then set Step 3. When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly; the S of node v at time t v The value is updated to: in, is the S value of node v at time t; Step 4. Update F of u and O(u) non-seed node in-degree neighbors w w value; The F value of node w at time t is the expected first-order influence of node w: Step 5. Repeat steps 2-4 until all budgets are used up or there are no candidate nodes that meet the budget conditions.

2. The heuristic method for maximizing influence with consideration of budget constraints as claimed in claim 1, characterized in that: The value of m is between 0.4 and 0.

8.

3. A heuristic system for maximizing influence with budget constraints, characterized by: Assume that the information to be transmitted is i, the maximum budget that can be provided is B, and the network structure of the social platform to transmit information is G, where G is a directed graph, the nodes in the graph are users in the network, and the edges are the paths of information transmission in the network; if there is an edge from node u to node v, it means that the information sent by user u can be transmitted to user v, and the weight of the edge (u, v) is the probability p(u, v) that information i is transmitted from u to v; Assume that each node u corresponds to a three-dimensional vector (S u ,F u ,C u ), S u Indicates the probability value that node u has not been activated; F u represents the expected first-order influence of node u after being activated, C u represents the activation cost of node u; if the activation cost of each node is known, then C u Take the true value, otherwise assume C u The out-degree of node u The relationship is: Where m is the power index; Includes the following modules: Expected first-order influence F u Acquisition module: Get the S of any node u u The value is initialized to F u The value is the weight p(u,v) of all out-degree edges (u,v) of node u and S of out-degree neighbor v. v The sum of the products of the values, that is: Among them, O(u) represents the set of out-degree neighbors of u; Seed node search module: In each iteration, find the node that meets the current remaining budget as the candidate node, and find the node with the largest marginal influence per unit cost among the candidate nodes, that is, The node k with the largest value is the seed node, and the S of the current seed node is changed accordingly. k Value and F k The value is set to 0 so that it no longer participates in the selection of subsequent seed nodes; the remaining budget value for the next round is modified to: B t+1 =B t -C k Among them, B t is the remaining budget at time t, C k is the activation cost of node k; If a node If the value is 0, then set Contribution value S v Update module: When a node u is selected as a seed node at time t-1, its out-degree neighbor v may be activated, and the probability that v is still not activated will decrease accordingly; the S of node v at time t v The value is updated to: in, is the S value of node v at time t; The expected first-order influence acquisition module of node w: Update u and O(u) non-seed node in-degree neighbors w of F w Value; F value of node w at time t is the expected first-order influence of node w: Iteration module: Repeat the execution of seed node search module and contribution value S v The update module and the expected first-order influence acquisition module of node w operate until all budgets are used up or there are no candidate nodes that meet the budget conditions.

4. The influence maximization heuristic system considering budget constraints as claimed in claim 3, characterized in that: The value of m is between 0.4 and 0.8.

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