CN108960979A - A kind of method that initial user is chosen in product distribution on line - Google Patents

Abstract

The invention discloses a method for selecting initial users for online product promotion. First, process the data set of online products to obtain the real topology graph G(V,E), then calculate the t-order neighbors of all nodes in G, and use each node as the initial user to independently cascade the model to its neighbors Propagate, calculate the influence of the node, and then select the best t'-order neighbor for the node, and select the most influential one from the t'-order neighbor of the node as the initial user. The present invention reduces the time complexity by selecting the initial user in the t-order neighbors of the node.

Description

A method for selecting initial users for online product promotion

technical field

The invention belongs to the field of complex networks, in particular to a method for selecting initial users for online product promotion.

Background technique

The goal of influence maximization is to select a group of users in an online social network. A seed set with maximum influence, i.e., in information dissemination, the expected number of affected users passing through the seed set is maximized. A well-known application of influence maximization is viral marketing, where a company may wish to spread the adoption of a new product away from a few initially selected adopters through social links between users. Since influence maximization is an NP-hard problem, existing work focuses on approximate solutions, whereas these influence maximization algorithm studies focus on a greedy framework. We review the greedy framework and propose a taxonomy of existing simulation-based methods, agent-based and sketch methods, based on their algorithmic design to achieve different desired goals.

The greedy algorithm puts the current most influential node as a candidate node into the seed set at each step, and then iterates continuously until all the seed nodes are selected. However, the local optimum strategy of this algorithm cannot guarantee the global optimum of the final result, and the efficiency of the algorithm is relatively low, and the time complexity is high, so it is not suitable for large-scale actual networks. On this basis, Tsai et al. improved the greedy algorithm and proposed the GNG algorithm (Genetic New Greedy, GNG). Experiments show that this algorithm can improve the performance of greedy algorithm by about 10% after combining some characteristics of genetic algorithm. In order to solve the dilemma of the accuracy and scalability of the influence maximization algorithm, Cheng et al. proposed a heuristic SG algorithm (StaticGreedy, SG). The algorithm uses the submodel characteristic of the influence maximization objective function to select the most influential node at present, so as to reduce the time spent on candidate node selection. Gong et al. proposed the Probability Transfer Matrix Algorithm (PTMA) based on the probability transfer matrix. This algorithm obtains the influence probability between nodes at a certain moment by matrix product method, without calculating all nodes at each moment. The marginal benefits of inactive nodes to improve the efficiency of algorithm runtime. Cao et al. proposed a heuristic algorithm based on core number hierarchical features and influence radius - Core Covering Algorithm CCA (Core Covering Algorithm, CCA). The algorithm firstly introduces the concept of K-core, calculates the number of cores of each node based on K-core decomposition, then introduces the influence radius parameter of the node according to the hierarchy of the distribution of the number of cores, and finally combines the two attributes of the number of cores and the degree to find A set of influential nodes. Chen Hao et al. proposed a concept of potential influence node number PIN based on the threshold, by considering the initial activation threshold of the node itself, the influence of the node's activated incoming neighbors on it, and the influence of the node on its neighbor nodes. In the first stage, the one with the largest PIN is selected as the seed node, and in the second stage, the seed node is selected through a greedy algorithm, which has a small complexity and a wide range of influence. The algorithm design of this kind of influence maximization is based on model-driven, and based on the given influence propagation model, heuristic method is used to select the seed nodes.

The traditional selection of initial users for product promotion is through manual selection. Due to the consumption of human resources and the existence of a certain one-sidedness, the manual selection method cannot be selected according to the characteristics of products and objects, resulting in the effect of selecting initial users is not considerable.

Contents of the invention

Purpose of the invention: To address the above problems, the present invention provides a method for selecting initial users for online product promotion that saves time and labor costs and reduces time complexity.

Technical solution: The present invention proposes a method for selecting initial users for online product promotion, including the following steps:

Step 1: Process the data set of online products to obtain the real topology graph G(V,E); where V represents the set of nodes in G, E represents the set of edges in G, and the input P, P is In the independent cascading model, the probability that an activated node v activates its inactive outgoing neighbor nodes, input S, S is the number of selected seed nodes, the specific method is:

Step 1.1: Delete the self-loops existing in the data set of online products to obtain the real topology graph G(V,E), where G is the adjacency matrix;

Step 1.2: The potential of a node is how many nodes there are in G, the potential of an edge is how many edges there are in G, and the potential m of a node and the potential n of an edge are obtained;

Step 1.3: Independent cascading is a probabilistic model. When a node v is activated, it will try to activate its inactive outbound neighbor node w with probability P. This attempt is only made once, and between these attempts are independent of each other, that is, the activation of v on w will not be affected by other nodes. The probability P is defined at the beginning of the experiment, so in selecting the initial nodes to maximize influence based on the user's neighbors in the social network, P=1/degree. degree is the degree of the node, and the sum of each row of the adjacency matrix G is calculated as the matrix Degree, which is the degree corresponding to the node.

Step 2: Calculate the t-order neighbors of each node, and put the obtained t-order neighbors of each node in a large set SubList, t=1, 2, 3, 4, 5, 6, 7, 8, 9 , 10, the specific method is:

Step 2.1: Number the rows/columns of the adjacency matrix G in step 1.1, the first row/column is 1, the second row/column is 2... and numbered in turn;

Step 2.2: Find the first-order neighbors of node i, and set an empty matrix D with m rows and m columns, where m is the potential of the node obtained in step 1.2. Change the 0 in the i-th row and the i-column of the matrix D to 1, calculate the matrix D*G, and obtain the subgraph of the first-order neighbor of the node i, which is defined as J ₁ ;

Step 2.3: Find the second-order neighbors of node i, take the i-th row of the adjacency matrix G, set it as matrix A, change the i-th number of matrix A to 1, and generate a matrix B, the diagonal is matrix A, and the rest Both are 0; calculate the matrix B*G, and obtain the subgraph of the second-order neighbor of node i, which is defined as J ₂ ;

Step 2.4: To find the third-order neighbors of node i, first calculate G+G*G, record it as matrix F1, set all the numbers in matrix F1 that are not 0 to 1, and set all the numbers on the diagonal to 0; Take the i-th row of matrix F1, set it as matrix C1, change the i-th number of matrix C1 to 1, generate a matrix E1, the diagonal line is matrix C1, and the rest are all 0; calculate matrix E1*G, find The obtained subgraph is the third-order neighbor of node i, which is defined as J ₃ ;

Step 2.5: To find the fourth-order neighbor of node i, first calculate G+G ² +G ³ , set it as matrix F2, set all the numbers in matrix F2 that are not 0 to 1, and set all the numbers on the diagonal to is 0; take the i-th row of matrix F2, set it as matrix C2, change the i-th number of matrix C2 to 1, and generate a matrix E2, the diagonal is matrix C2, and the rest are 0; calculate matrix E2* G, what is obtained is the subgraph of the 4th order neighbor of node i, defined as J ₄ ;

Step 2.6: To find the fifth-order neighbors of node i, first calculate G+G ² +G ³ +G ⁴ , set it as matrix F3, set all the numbers in matrix F3 that are not 0 to 1, and set All numbers are set to 0; take the i-th row of matrix F3, set it as matrix C3, change the i-th number of matrix C3 to 1, and generate a matrix E3, the diagonal line is matrix C3, and the rest of the numbers are all 0; calculate The matrix E3*G obtains the subgraph of the fifth-order neighbor of node i, which is defined as J ₅ ;

Step 2.7: Find the 6th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ , set it as matrix F4, set all the numbers in matrix F4 that are not 0 to 1, and set the diagonal The numbers on the line are all set to 0; take the i-th row of matrix F4, set it as matrix C4, change the i-th number of matrix C4 to 1, and generate a matrix E4, the diagonal line is matrix C4, and the rest of the numbers are 0; calculate the matrix E4*G, and obtain the subgraph of the 6th order neighbor of node i, which is defined as J ₆ ;

Step 2.8: To find the 7th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ , set it as matrix F5, set all the numbers in matrix F5 that are not 0 to 1, and Set all the numbers on the diagonal to 0; take the i-th row of matrix F5, set it as matrix C5, change the i-th number of matrix C5 to 1, and generate a matrix E5, the diagonal is matrix C5, and the rest The numbers are all 0; the calculation matrix E5*G obtains the subgraph of the 7th order neighbor of node i, which is defined as J ₇ ;

Step 2.9: To find the 8th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ , set it as matrix F6, and set all the numbers in matrix F6 that are not 0 to 1, and set all the numbers on the diagonal to 0; take the i-th row of matrix F6, set it as matrix C6, change the i-th number of matrix C6 to 1, and generate a matrix E6, and the diagonal is a matrix C6, the remaining numbers are all 0; calculate the matrix E6*G, obtain the subgraph of the 8th order neighbor of node i, defined as J ₈ ;

Step 2.10: Find the 9th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ +G ⁸ , set it as matrix F7, and set the number in matrix F7 that is not 0 Set all to 1, and set all numbers on the diagonal to 0; take the i-th row of matrix F7, set it as matrix C7, change the i-th number of matrix C7 to 1, and generate a matrix E7, diagonal The line is the matrix C7, and the remaining numbers are all 0; the calculation matrix E7*G obtains the subgraph of the 9th order neighbor of node i, which is defined as J ₉ ;

Step 2.11: To find the 10th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ +G ⁸ +G ⁹ and set it as matrix F8, and set the matrix F8 not to 0 Set all the numbers to 1, and set all the numbers on the diagonal to 0; take the i-th row of matrix F8, set it as matrix C8, change the i-th number of matrix C8 to 1, and generate a matrix E8, The diagonal line is the matrix C8, and the rest are all 0; the calculation matrix E8*G obtains the subgraph of the 10th order neighbor of node i, which is defined as J ₁₀ .

Step 2.12: All the subgraphs of nodes i∈V’s order ₁ nodes are in J1, all the subgraphs of nodes i∈V’s order ₂ nodes are in J2, and all the subgraphs of nodes i∈V’s order 3 nodes The graphs are all in J3, the subgraphs of all nodes i∈V’s order ₄ nodes are in J4, all the subgraphs of nodes i∈V’s order ₅ nodes are in J5, and all the nodes i∈V’s ₆ The subgraphs of order nodes are all in J ₆ , the subgraphs of all nodes i ∈ V of order 7 are in J ₇ , the subgraphs of all nodes i ∈ V of order 8 are in J ₈ , and all nodes i The subgraphs of nodes of order 9 of ∈V are all in J ₉ , the subgraphs of nodes of order 10 of all nodes i∈V are in J ₁₀ , put J ₁ , J ₂ , J ₃ , J ₄ , J ₅ , J ₆ , J ₇ , J ₈ , J ₉ , J ₁₀ are placed in the matrix SubList.

Step 3: Treat each node as an initial user, regard each node's t-order neighbors as a network, and let each node perform R independent cascade model propagation on its t-order neighbors, and R is defined by itself Positive integer, calculate the average influence of each node on its t-order neighbors, t=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, the specific method is:

Step 3.1: Define a positive integer R and an empty matrix In;

Step 3.2: Calculate the sum of each row of the matrix G, and put it in the matrix degree, which stores the degree of each node; define the loop variable m,m∈[1,R];

Step 3.3: If m≤R, go to step 3.4, otherwise go to step 3.10;

Step 3.4: Treat node i as an active node, and have an impact on its neighbor node v, so that the probability of v activation is p, and the chance is only once; p=1/degree, degree is the degree of node i obtained in step 302 ; v belongs to the t-order neighbor of node i, t=1,2,3,4,5,6,7,8,9,10;

Step 3.5: If node v is successfully activated, then node v becomes active, which will affect its adjacent inactive nodes; otherwise, node v will not change;

Step 3.6: Repeat steps 3.3 and 3.4 until no new nodes can be activated and the propagation process ends;

Step 3.7: The number of nodes activated by each node in the t-order neighbors is its influence;

Step 3.8: The influence of each node in its first-order neighbors exists in the matrix In1, the influence in its second-order neighbors exists in the matrix In2, and the influence in its third-order neighbors exists in the matrix In3 , the influence in its 4th-order neighbor exists in the matrix In4, the influence in its 5th-order neighbor exists in the matrix In5, the influence in its 6th-order neighbor exists in the matrix In6, in its 7 The influence of its neighbors of order 9 exists in the matrix In7, the influence of its neighbors of order 8 exists in matrix In8, the influence of its neighbors of order 9 exists in matrix In9, and the influence of its neighbors of order 10 exists The force exists in the matrix In10;

Step 3.9: m=m+1;

Step 3.10: Add up the influence obtained R times, and then divide it by R to find the average influence of each node in its t-order neighbors, and put it in the matrix In.

Step 4: Sort the t-order neighbors of nodes according to their influence from large to small, and select 50 nodes with the greatest influence among each-order neighbors. Through comparison, it is found that the t'-order neighbors of nodes have the greatest influence, t=1, 2 , 3, 4, 5, 6, 7, 8, 9, 10, and t'∈t, the specific method is:

Step 4.1: Sort the values in the matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, In10 from large to small;

Step 4.2: Select the first 50 values in the matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, In10, and place them in the matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, In Z8, Z9, Z10;

Step 4.3: Draw a graph, the horizontal axis is 1 to 10, which are 10 numbers, and the vertical axis is the numbers in the matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, found at t=t' When , the number on the vertical axis is the largest, that is, the t' neighbor of the node has the greatest influence;

Step 5: Carry out K independent cascade model propagation for all nodes in the order neighbors of the node in the entire network, t' is the value obtained in step 5, K is a positive integer defined by yourself, and at the t' order of the node Select the largest S nodes in the neighborhood as initial users, the specific method is:

Step 5.1: Define a positive integer M, take out the matrix SubList from step 2.12, and take out the matrix J _t' from the matrix SubList, t'∈[1,10];

Step 5.2: Define the cyclic variable n,n∈[1,M], calculate the sum of each row of the matrix J _t' , and record it as the matrix De, which stores the degree of neighbors of the node t'order;

Step 5.3: If n≤M, then go to step 5.4, otherwise go to step 5.9;

Step 5.4: Take the node in the matrix J _t' as an active node, and have an impact on its neighbor node w, so that the probability of w activation is p, and there is only one chance; p=1/degree, degree is obtained in step 5.2 The number in the matrix De;

Step 5.5: If the node w is successfully activated, then the node w becomes active, which will affect its adjacent inactive nodes; otherwise, the node w does not change;

Step 5.6: Repeat steps 5.4 and 5.5 until no new nodes can be activated and the propagation process ends;

Step 5.7: The number of nodes activated by each node in the data set of online products is its influence, which is recorded as matrix IN;

Step 5.8: n=n+1;

Step 5.9: Add up the influence obtained M times, and then divide by M to find the average influence of each node in the entire network, and put them all in the matrix LIN;

Step 5.10: Sort the values in the matrix LIN, select S with the largest value, and the corresponding node is the initial user.

The present invention adopts the above-mentioned technical scheme, and has the following beneficial effects: the present invention proposes a method for quickly selecting seed nodes based on the t-order neighbors of nodes for the problem of influence maximization, by calculating the t-order neighbors of nodes, (t=1,2...n ) to calculate the influence of a node in its neighbor subgraph, and select the one with higher influence and better effect through comparison. After being determined, select the node with the greatest overall influence as the seed node among the first-order neighbors of the node. This method can greatly reduce the calculation overhead and storage overhead, so that the time for selecting seed nodes is greatly reduced, and the time complexity is reduced.

Description of drawings

Fig. 1 is the overall flow chart of the present invention

Fig. 2 is a specific flowchart of processing online product data sets in Fig. 1;

Fig. 3 is the concrete flow chart of calculating node t order neighbor in Fig. 1;

Figure 4 is a specific flow chart for calculating the average influence of nodes in Figure 1;

Fig. 5 is the concrete flow chart of selecting optimal node t ' order neighbor among Fig. 1;

Fig. 6 is a specific flow chart of selecting the most influential online product promotion initial user in Fig. 1;

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

As shown in Figures 1-6, a method for selecting an initial user for online product promotion according to the present invention, the specific steps are as follows:

Step 1: Process the data set of online products to obtain the real topology graph G(V,E); where V represents the set of nodes in G, E represents the set of edges in G, and the input P, P is In the independent cascading model, the probability that an activated node v activates its unactivated outgoing neighbor nodes, input S, S is the number of selected seed nodes, as shown in Figure 2:

Step 1.1: Delete the self-loops existing in the data set of online products to obtain the real topology graph G(V,E), where G is the adjacency matrix;

Step 1.2: The potential of a node is how many nodes there are in G, the potential of an edge is how many edges there are in G, and the potential m of a node is obtained;

Step 1.3: Independent cascading is a probabilistic model. When a node v is activated, it will try to activate its inactive outbound neighbor node w with probability P. This attempt is only made once, and between these attempts are independent of each other, that is, the activation of v on w will not be affected by other nodes. The probability P is defined at the beginning of the experiment, so in the selection of the initial nodes to maximize influence based on the user's neighbors in the social network, =1/degree. degree is the degree of the node, and the sum of each row of the adjacency matrix G is calculated as the matrix Degree, which is the degree corresponding to the node.

Step 2: Calculate the t-order neighbors of each node, and put the obtained t-order neighbors of each node in a large set SubList, t=1, 2, 3, 4, 5, 6, 7, 8, 9 , 10, specifically as shown in Figure 3:

Step 2.1: Number the rows/columns of the adjacency matrix G in step 1.1, the first row/column is 1, the second row/column is 2... and numbered in turn;

Step 2.2: Find the first-order neighbors of node i, and set an empty matrix D with m rows and m columns, where m is the potential of the node obtained in step 1.2. Change the 0 in the i-th row and the i-column of the matrix D to 1, calculate the matrix D*G, and obtain the subgraph of the first-order neighbor of the node i, which is defined as J ₁ ;

Step 2.3: Find the second-order neighbors of node i, take the i-th row of the adjacency matrix G, set it as matrix A, change the i-th number of matrix A to 1, and generate a matrix B, the diagonal is matrix A, and the rest Both are 0; calculate the matrix B*G, and obtain the subgraph of the second-order neighbor of node i, which is defined as J ₂ ;

Step 2.4: To find the third-order neighbors of node i, first calculate G+G*G, record it as matrix F1, set all the numbers in matrix F1 that are not 0 to 1, and set all the numbers on the diagonal to 0; Take the i-th row of matrix F1, set it as matrix C1, change the i-th number of matrix C1 to 1, generate a matrix E1, the diagonal line is matrix C1, and the rest are all 0; calculate matrix E1*G, find The obtained subgraph is the third-order neighbor of node i, which is defined as J ₃ ;

Step 2.5: To find the fourth-order neighbor of node i, first calculate G+G ² +G ³ , set it as matrix F2, set all the numbers in matrix F2 that are not 0 to 1, and set all the numbers on the diagonal to is 0; take the i-th row of matrix F2, set it as matrix C2, change the i-th number of matrix C2 to 1, and generate a matrix E2, the diagonal is matrix C2, and the rest are 0; calculate matrix E2* G, what is obtained is the subgraph of the 4th order neighbor of node i, defined as J ₄ ;

Step 2.6: To find the fifth-order neighbors of node i, first calculate G+G ² +G ³ +G ⁴ , set it as matrix F3, set all the numbers in matrix F3 that are not 0 to 1, and set All numbers are set to 0; take the i-th row of matrix F3, set it as matrix C3, change the i-th number of matrix C3 to 1, and generate a matrix E3, the diagonal line is matrix C3, and the rest of the numbers are all 0; calculate The matrix E3*G obtains the subgraph of the fifth-order neighbor of node i, which is defined as J ₅ ;

Step 2.7: Find the 6th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ , set it as matrix F4, set all the numbers in matrix F4 that are not 0 to 1, and set the diagonal The numbers on the line are all set to 0; take the i-th row of matrix F4, set it as matrix C4, change the i-th number of matrix C4 to 1, and generate a matrix E4, the diagonal line is matrix C4, and the rest of the numbers are 0; calculate the matrix E4*G, and obtain the subgraph of the 6th order neighbor of node i, which is defined as J ₆ ;

Step 2.8: To find the 7th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ , set it as matrix F5, set all the numbers in matrix F5 that are not 0 to 1, and Set all the numbers on the diagonal to 0; take the i-th row of matrix F5, set it as matrix C5, change the i-th number of matrix C5 to 1, and generate a matrix E5, the diagonal is matrix C5, and the rest The numbers are all 0; the calculation matrix E5*G obtains the subgraph of the 7th order neighbor of node i, which is defined as J ₇ ;

Step 2.9: To find the 8th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ , set it as matrix F6, and set all the numbers in matrix F6 that are not 0 to 1, and set all the numbers on the diagonal to 0; take the i-th row of matrix F6, set it as matrix C6, change the i-th number of matrix C6 to 1, and generate a matrix E6, and the diagonal is a matrix C6, the remaining numbers are all 0; calculate the matrix E6*G, obtain the subgraph of the 8th order neighbor of node i, defined as J ₈ ;

Step 2.10: Find the 9th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ +G ⁸ , set it as matrix F7, and set the number in matrix F7 that is not 0 Set all to 1, and set all numbers on the diagonal to 0; take the i-th row of matrix F7, set it as matrix C7, change the i-th number of matrix C7 to 1, and generate a matrix E7, diagonal The line is the matrix C7, and the remaining numbers are all 0; the calculation matrix E7*G obtains the subgraph of the 9th order neighbor of node i, which is defined as J ₉ ;

Step 2.11: To find the 10th-order neighbor of node i, first calculate G+G ² +G ³ +G ⁴ +G ⁵ +G ⁶ +G ⁷ +G ⁸ +G ⁹ and set it as matrix F8, and set the matrix F8 not to 0 Set all the numbers to 1, and set all the numbers on the diagonal to 0; take the i-th row of matrix F8, set it as matrix C8, change the i-th number of matrix C8 to 1, and generate a matrix E8, The diagonal line is the matrix C8, and the remaining numbers are all 0; the calculation matrix E8*G obtains the subgraph of the 10th order neighbor of node i, which is defined as J ₁₀ ;

Step 2.12: All the subgraphs of nodes i∈V’s order ₁ nodes are in J1, all the subgraphs of nodes i∈V’s order ₂ nodes are in J2, and all the subgraphs of nodes i∈V’s order 3 nodes The graphs are all in J3, the subgraphs of all nodes i∈V’s order ₄ nodes are in J4, all the subgraphs of nodes i∈V’s order ₅ nodes are in J5, and all the nodes i∈V’s ₆ The subgraphs of order nodes are all in J ₆ , the subgraphs of all nodes i ∈ V of order 7 are in J ₇ , the subgraphs of all nodes i ∈ V of order 8 are in J ₈ , and all nodes i The subgraphs of nodes of order 9 of ∈V are all in J ₉ , the subgraphs of nodes of order 10 of all nodes i∈V are in J ₁₀ , and J ₁ , J ₂ , J ₃ , J ₄ , J ₅ , J ₆ , J ₇ , J ₈ , J ₉ , J ₁₀ are placed in the matrix SubList.

Step 3: Treat each node as an initial user, regard each node's t-order neighbors as a network, and let each node perform R independent cascade model propagation on its t-order neighbors, and R is defined by itself Positive integer, calculate the average influence of each node on its t-order neighbors, t=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, as shown in Figure 4:

Step 3.1: Define a positive integer R and an empty matrix In;

Step 3.2: Calculate the sum of each row of the matrix G, and put it in the matrix degree, which stores the degree of each node; define the loop variable m,m∈[1,R];

Step 3.3: If m≤R, go to step 3.4, otherwise go to step 3.10;

Step 3.4: Treat node i as an active node, and have an impact on its neighbor node v, so that the probability of v activation is p, and the chance is only once; p=1/degree, degree is the degree of node i obtained in step 302 ; v belongs to the t-order neighbor of node i, t=1,2,3,4,5,6,7,8,9,10;

Step 3.5: If node v is successfully activated, then node v becomes active, which will affect its adjacent inactive nodes; otherwise, node v will not change;

Step 3.6: Repeat steps 3.3 and 3.4 until no new nodes can be activated and the propagation process ends;

Step 3.7: The number of nodes activated by each node in the t-order neighbors is its influence;

Step 3.8: The influence of each node in its first-order neighbors exists in the matrix In1, the influence in its second-order neighbors exists in the matrix In2, and the influence in its third-order neighbors exists in the matrix In3 , the influence in its 4th-order neighbor exists in the matrix In4, the influence in its 5th-order neighbor exists in the matrix In5, the influence in its 6th-order neighbor exists in the matrix In6, in its 7 The influence of its neighbors of order 9 exists in the matrix In7, the influence of its neighbors of order 8 exists in matrix In8, the influence of its neighbors of order 9 exists in matrix In9, and the influence of its neighbors of order 10 exists The force exists in the matrix In10;

Step 3.9: m=m+1;

Step 3.10: Add up the influence obtained R times, and then divide it by R to find the average influence of each node in its t-order neighbors, and put it in the matrix In.

Step 4: Sort the t-order neighbors of nodes according to their influence from large to small, and select 50 nodes with the greatest influence among each-order neighbors. Through comparison, it is found that the t'-order neighbors of nodes have the greatest influence, t=1, 2 , 3, 4, 5, 6, 7, 8, 9, 10, and t'∈t, specifically as shown in Figure 5:

Step 4.1: Sort the values in the matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, In10 from large to small;

Step 4.2: Select the first 50 values in the matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, In10, and place them in the matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, In Z8, Z9, Z10;

Step 4.3: Draw a graph, the horizontal axis is 1 to 10, which are 10 numbers, and the vertical axis is the numbers in the matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10, found at t=t' When , the number on the vertical axis is the largest, that is, the t' neighbors of the node have the greatest influence.

Step 5: Carry out K independent cascade model propagation for all nodes in the order neighbors of the node in the entire network, t' is the value obtained in step 5, K is a positive integer defined by yourself, and at the t' order of the node Select the largest S nodes in the neighborhood as initial users, as shown in Figure 6:

Step 5.1: Define a positive integer M, take out the matrix SubList from step 2.12, and take out the matrix J _t' from the matrix SubList, t'∈[1,10];

Step 5.2: Define the cyclic variable n,n∈[1,M], calculate the sum of each row of the matrix J _t' , and record it as the matrix De, which stores the degree of neighbors of the node t'order;

Step 5.3: If n≤M, then go to step 5.4, otherwise go to step 5.9;

Step 5.4: Take the node in the matrix J _t' as an active node, and have an impact on its neighbor node w, so that the probability of w activation is p, and there is only one chance; p=1/degree, degree is obtained in step 5.2 The number in the matrix De;

Step 5.5: If the node w is successfully activated, then the node w becomes active, which will affect its adjacent inactive nodes; otherwise, the node w does not change;

Step 5.6: Repeat steps 5.4 and 5.5 until no new nodes can be activated and the propagation process ends;

Step 5.7: The number of nodes activated by each node in the data set of online products is its influence, which is recorded as matrix IN;

Step 5.8: n=n+1;

Step 5.9: Add up the influence obtained M times, and then divide by M to find the average influence of each node in the entire network, and put them all in the matrix LIN;

Step 5.10: Sort the values in the matrix LIN, select S with the largest value, and the corresponding node is the initial user.

By calculating the t-order neighbors of nodes in 10 online product data sets, and then calculating the influence of nodes in t-order neighbors, taking 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 as horizontal The axis represents the neighbors of the node from order 1 to order 10; the influence corresponding to each order neighbor is used as the vertical axis for drawing comparison. It can be found that each data set has an optimal value, most of which are 3. Therefore, the third-order neighbors of the node are used as seed nodes, the influence of each node is calculated, and the largest S among them is selected as the initial user. It reduces the time complexity and calculation overhead of the algorithm, and the effect is also very good.

Claims (6)

1. a kind of method that initial user is chosen in product distribution on line, which comprises the steps of:

(1) data set of product on line is handled, obtains true topology diagram G (V, E)；Wherein, V indicates to produce on line Node set in product G, E indicate the set on the side on line in product G, seek the gesture on node and side；P is inputted, P is separate stage gang mould The node v that is activated activates the probability of its unactivated out-degree neighbor node in type, inputs S, and S is that selected seed node is i.e. first The number of beginning user；

(2) the t rank neighbours of each node acquired, are placed on a big collection SubList by the t rank neighbours for calculating each node In, t=1,2,3,4,5,6,7,8,9,10；

(3) each node is treated as initial user, it is a network that the t rank neighbours of each node, which are treated as, allows each section Point carries out R independent cascade model to his t rank neighbours and propagates, and R is the positive integer of oneself definition, calculates each node to his The average influence of t rank neighbours, t=1,2,3,4,5,6,7,8,9,10；

(4) node t rank neighbours are ranked up from big to small according to influence power, choose maximum 50 of influence power in every rank neighbours Node finds that the t' rank neighbours influence power of node is maximum by comparing, t=1,2,3, and 4,5,6,7,8,9,10, and t' ∈ t；

(5) it carries out K independent cascade model in the entire network to node all in the rank neighbours of node to propagate, t' is step 5 values asked, K are the positive integers of oneself definition, and maximum S node is chosen in the t' rank neighbours of node and is used as initial Family.

2. the method that initial user is chosen in product distribution on a kind of line according to claim 1, which is characterized in that the step Suddenly handled the data set of product on line that specific step is as follows in (1):

(1.1) on strikethrough present in the data set of product from ring, obtain true topology diagram G (V, E), G is adjacent Matrix；

(1.2) gesture of node is exactly how many node in G, while gesture be exactly in G how many while, acquire node gesture m and The gesture n on side；

(1.3) independent cascade is a kind of probabilistic model, and when a node v is activated, it can be unactivated out to it with probability P Side neighbor node w attempts activation, and this trial only carries out once, and is independent from each other between these trials, i.e., v is to w Activation not will receive the influences of other nodes；Probability P is tested to be defined at the beginning, therefore according to user in social networks Neighbours choose in maximizing influence start node, P=1/degree；Degree is the degree of node, calculates the every of adjacency matrix G The sum of a line is denoted as matrix D egree, is the corresponding degree of node.

3. the method that initial user is chosen in product distribution on a kind of line according to claim 2, which is characterized in that the step Suddenly specific step is as follows by calculate node t rank neighbours in (2):

(2.1) row/column of the adjacency matrix G in step (1.1) is numbered, the first row/column is 1, and the second row/column is 2 ... Successively label；

(2.2) the 1 rank neighbours for seeking node i, the empty matrix D, m for setting m row m column are the nodes acquired in step (1.2) Gesture；0 that the i-th row i-th of matrix D is arranged is changed to 1, calculating matrix D*G, and what is acquired is the subgraph of 1 rank neighbours of node i, definition For J₁；

(2.3) the 2 rank neighbours for seeking node i, take the i-th row of adjacency matrix G, are set as matrix A, and i-th of number of matrix A is changed to 1, A matrix B is generated, diagonal line is matrix A, remaining is all 0；Calculating matrix B*G, what is acquired is the son of 2 rank neighbours of node i Figure, is defined as J₂；

(2.4) 3 rank neighbours of node i, first calculating G+G*G are asked, matrix F 1 is denoted as, the number in matrix F 1 not being 0 is all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 1, is set as Matrix C 1, and i-th of number of Matrix C 1 is changed to 1, a matrix E1 is generated, diagonal line is Matrix C 1, and remainder is all 0；Calculating matrix E1*G, that acquire is the 3 ranks neighbour of node i The subgraph in residence, is defined as J₃；

(2.5) 4 rank neighbours of node i, first calculating G+G are asked²+G³, it is set as matrix F 2, the number in matrix F 2 not being 0 is all set It is 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 2, is set as Matrix C 2, and i-th of number of Matrix C 2 is changed It is 1, generates a matrix E2, diagonal line is Matrix C 2, and remainder is all 0；Calculating matrix E2*G, what is acquired is 4 ranks of node i The subgraph of neighbours, is defined as J₄；

(2.6) 5 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴, it is set as matrix F 3, the number in matrix F 3 not being 0 It is all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 3, is set as Matrix C 3, i-th of Matrix C 3 Number is changed to 1, generates a matrix E3, diagonal line is Matrix C 3, and remainder is all 0；Calculating matrix E3*G, what is acquired is node i 5 rank neighbours subgraph, be defined as J₅；

(2.7) 6 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴+G⁵, it is set as matrix F 4, not being 0 in matrix F 4 Number is all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 4, is set as Matrix C 4, the i-th of Matrix C 4 Number is changed to 1, generates a matrix E4, and diagonal line is Matrix C 4, and remainder is all 0；Calculating matrix E4*G, what is acquired is node The subgraph of the 6 rank neighbours of i, is defined as J₆；

(2.8) 7 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴+G⁵+G⁶, it is set as matrix F 5, not being 0 in matrix F 5 Number be all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 5, is set as Matrix C 5, the of Matrix C 5 I number is changed to 1, generates a matrix E5, and diagonal line is Matrix C 5, and remainder is all 0；Calculating matrix E5*G, what is acquired is section The subgraph of the 7 rank neighbours of point i, is defined as J₇；

(2.9) 8 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴+G⁵+G⁶+G⁷, be set as matrix F 6, in matrix F 6 not It is that 0 number is all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 6, is set as Matrix C 6, Matrix C 6 I-th of number be changed to 1, generate a matrix E6, diagonal line is Matrix C 6, and remainder is all 0；Calculating matrix E6*G, is acquired It is the subgraph of 8 rank neighbours of node i, is defined as J₈；

(2.10) 9 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴+G⁵+G⁶+G⁷+G⁸, it is set as matrix F 7, matrix F 7 In be not that 0 number is all set to 1, and the number on diagonal line is all set to 0；The i-th row for taking matrix F 7, is set as Matrix C 7, square I-th of number of battle array C7 is changed to 1, generates a matrix E7, diagonal line is Matrix C 7, and remainder is all 0；Calculating matrix E7*G, is asked What is obtained is the subgraph of 9 rank neighbours of node i, is defined as J₉；

(2.11) 10 rank neighbours of node i, first calculating G+G are asked²+G³+G⁴+G⁵+G⁶+G⁷+G⁸+G⁹It is set as matrix F 8, matrix It is not that 0 number is all set to 1, and the number on diagonal line is all set to 0 in F8；The i-th row for taking matrix F 8, is set as Matrix C 8, I-th of number of Matrix C 8 is changed to 1, generates a matrix E8, and diagonal line is Matrix C 8, and remainder is all 0；Calculating matrix E8*G, What is acquired is the subgraph of 10 rank neighbours of node i, is defined as J₁₀；

(2.12) subgraph of the 1 rank node of all node i ∈ V is all in J₁In, the subgraph of the 2 rank nodes of all node i ∈ V all exists J₂In, the subgraph of the 3 rank nodes of all node i ∈ V is all in J₃In, the subgraph of the 4 rank nodes of all node i ∈ V is all in J₄In, The subgraph of the 5 rank nodes of all node i ∈ V is all in J₅In, the subgraph of the 6 rank nodes of all node i ∈ V is all in J₆In, Suo Youjie The subgraph of the 7 rank nodes of point i ∈ V is all in J₇In, the subgraph of the 8 rank nodes of all node i ∈ V is all in J₈In, all node i ∈ V 9 rank nodes subgraph all in J₉In, the subgraph of the 10 rank nodes of all node i ∈ V is all in J₁₀In, J₁、J₂、J₃、J₄、J₅、 J₆、J₇、J₈、J₉、J₁₀It is placed in matrix SubList.

4. the method that initial user is chosen in product distribution on a kind of line according to claim 3, which is characterized in that the step Suddenly specific step is as follows for calculate node average influence in (3):

(3.1) a positive integer R, empty matrix In are defined；

(3.2) sum of every a line of calculating matrix G, is placed in matrix degree, and what is stored in matrix degree is each node Degree；Define cyclic variable m, m ∈ [1, R]；

(3.3) if m≤R, step (3.4) are jumped to, not so jump to step (3.10)；

(3.4) node i is treated as live-vertex, its neighbor node v is had an impact, the probability for activating v is p, and chance Only once；P=1/degree, degree are the degree of the node i acquired in step 302；V belongs to the t rank neighbours of node i, t= 1,2,3,4,5,6,7,8,9,10；

(3.5) success if node v is activated, node v switch to active state, and inactive node will be abutted to it and generates shadow It rings；Otherwise, node v does not change；

(3.6) step (3.3) and (3.4) are repeated, until being unable to the new node of reactivation, communication process terminates；

(3.7) number for the node that each node activates in t rank neighbours is exactly its influence power；

(3.8) there are the influence powers in matrix In1, in its 2 rank neighbours for influence power of each node in its 1 rank neighbours There are in matrix In2, the influence power in its 3 rank neighbours there are in matrix In3, deposit by the influence power in its 4 rank neighbours In matrix In4, there are in matrix In5, the influence power in its 6 rank neighbours exists the influence power in its 5 rank neighbours In matrix In6, the influence power in its 7 rank neighbours is there are in matrix In7, and there are squares for the influence power in its 8 rank neighbours In battle array In8, the influence power in its 9 rank neighbours is there are in matrix In9, and there are matrixes for the influence power in its 10 rank neighbours In In10；

(3.9) m=m+1；

(3.10) influence power that R times is acquired is added up, then divided by R, seeks average shadow of each node in its t rank neighbour It rings, is placed in matrix In.

5. the method that initial user is chosen in product distribution on a kind of line according to claim 4, which is characterized in that the step Suddenly optimal node t ' rank neighbours being chosen in (4), specific step is as follows:

(4.1) to matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, the value inside In10 arranged from big to small Sequence；

(4.2) matrix In1, In2, In3, In4, In5, In6, In7, In8, In9, preceding 50 numerical value in In10, by suitable are chosen Sequence is placed on matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, in Z10；

(4.3) it draws, it is 10 numbers that horizontal axis, which is 1 to 10, and the longitudinal axis is matrix Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, in Z10 Number, find in t=t', the number on the longitudinal axis is maximum, that is, t' neighbours' influence power of node is maximum.

6. the method that initial user is chosen in product distribution on a kind of line according to claim 5, which is characterized in that the step Suddenly initial user being chosen in (5), specific step is as follows:

(5.1) a positive integer M is defined, from taking-up matrix SubList in step (2.12), and is taken out from matrix SubList Matrix J_t', t' ∈ [1,10]；

(5.2) cyclic variable n, n ∈ [1, M], calculating matrix J are defined_t'The sum of every a line is denoted as matrix D e, stores in matrix D e Be node t' rank neighbours degree；

(5.3) if n≤M, step (5.4) are jumped to, not so jump to step (5.9)；

(5.4) matrix J_t'In node treat as live-vertex, its neighbor node w is had an impact, make w activate probability be P, and chance is once；P=1/degree, degree are the numbers in the matrix D e acquired in step (5.2)；

(5.5) success if node w is activated, node w switch to active state, and inactive node will be abutted to it and generates shadow It rings；Otherwise, node w does not change；

(5.6) step (5.4) and (5.5) are repeated, until being unable to the new node of reactivation, communication process terminates；

(5.7) number for the node that each node activates in the data set of product on line is exactly its influence power, is denoted as matrix IN；

(5.8) n=n+1；

(5.9) influence power that M times is acquired is added up, then divided by M, seeks the average shadow of each node in the entire network It rings, is all placed in matrix L IN；

(5.10) value in matrix L IN is ranked up, selected value maximum S, corresponding node is initial user.