An influence maximization method and device based only on node state observation results

Abstract

The application discloses a kind of influence maximization method and device based on only node state observation result, belong to information retrieval technical field.First, the matrix capable of representing the influence ability of node is calculated, then the probability that node is selected as seed node is used as parameter to construct quadratic programming problem to solve;Then the exact probability value set of each node obtained by solving is used as seed node Sampling obtains candidate seed node set;Finally, the influence ability of each candidate seed node set is calculated, and the most influential seed node set is returned.The application calculates the probability that node is selected as seed node based on the node infection state data that is easy to collect and relatively accurate, and uses the method to find the most influential node set with the aid of sampling, avoids the network structure and relatively difficult to collect information such as accurate infection time, and has more extensive application scenarios in real life.

Description

Technical Field

[0001] This invention belongs to the field of information retrieval technology, and in particular relates to a method and apparatus for maximizing the impact based solely on node state observation results. Background Technology

[0002] With the rapid iteration and development of information technology, communication methods among people have become more diverse, and interaction frequency has increased, creating an invisible information dissemination network centered on individuals, spreading opinions, information, and even diseases. Influence maximization aims to identify the most influential nodes (called seed nodes) within this network to maximize the reach and impact of information. This has significant real-world applications; for example, advertisers can target the most influential groups within a population for promotions, maximizing the effectiveness of limited marketing budgets. Similarly, disease control personnel can identify and manage the most infectious patients, minimizing the spread of infectious diseases.

[0003] Most existing impact maximization methods assume that the underlying propagation network structure is known, and then conduct impact maximization research based on a specific propagation model. However, in most practical applications, due to the exponential growth of networks and increasing user concerns about privacy, collecting the complete potential impact relationships contained in the propagation network is usually quite difficult, leading to limitations in most current methods that rely on prior knowledge of network structure for impact maximization research. Although some maximization studies that do not rely on propagation network structure analyze the infection time information of nodes during the propagation process, the cost of regularly monitoring the infection status of nodes to obtain the infection time may be prohibitive, and there may be an incubation period from infection to the appearance of symptoms, causing the collected time data to not accurately reflect the infection status of nodes, affecting the accuracy of the algorithm.

[0004] In summary, how to maximize the impact based solely on easily accessible data such as node state observations and identify the most influential nodes in the propagation network is a problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method and apparatus for maximizing the impact based solely on node state observation results. It constructs a matrix representing the node's influence based on the final infection state data of each node in the propagation network after the propagation process ends. The probability of a node being selected as a seed node is used as a parameter to be solved. The parameter is solved by constructing an optimization function that measures the influence range of the seed node set. Then, based on the solution results, sampling is performed to discover the most influential seed node set.

[0006] The technical solution adopted in this invention is:

[0007] Define the propagation network structure as G = {V, E}, where V = {v1, v2, ..., v...} n} represents n nodes in the propagation network, each node representing a user; E represents the set of directed edges in the propagation network representing influence relationships; the infection status observation data collected after β propagation processes are represented by S = {S 1 ,S 2 ,…,S β} indicates that, among which This represents the node infection status observation data after the end of the l-th transmission process. This indicates that node v has completed the l-th process. i The infection status of the node is marked as 1 if it is infected and 0 if it is not infected. "Infection" here means that the user status information corresponding to the node meets the expectations. For example, if the user has obtained certain information (speech / news / advertisement) or has contracted a certain infectious disease, the node is marked as infected; otherwise, the node is marked as uninfected.

[0008] Based on the above definition, the method for maximizing the impact solely based on node state observation results includes the following steps:

[0009] Step 1: Use the collected infection data to construct a matrix Q∈R representing the node's influence capability. n×n Q ij (i,j∈{1,2,…,n}) represents node v i and node v j The heterogeneity affecting ability is specifically calculated as follows:

[0010]

[0011]

[0012] Where n represents the number of nodes in the propagation network; β represents the number of information / disease transmission processes in the propagation network; Q ij Represents node v i and node v j Heterogeneity affecting ability; min(C) ik C jk ) represents C ik and C jk The smaller value in the middle; max(C ik C jk ) represents C ik and C jkThe larger of the values; I(·) is an indicator function that takes the value 1 when the condition in (·) is true and takes the value 0 when it is false; This indicates that node v has completed the l-th process. i The infection status, C ik Represents node v i and node v k The degree of correlation between infection states; s i This represents a value of either 0 or 1, therefore (s i ,s k There are four possible combinations: (0,0), (0,1), (1,0), and (1,1).

[0013] Step 2: Use matrix Q, which represents the influence of nodes, to construct an optimization function that measures the range of influence generated by the seed node set. And construct the following quadratic programming problem:

[0014]

[0015] stx i ∈[0,1],i=1,…,n

[0016]

[0017] Where, x i (i∈{1,…,n}) represents node v i The probability variable of being selected as a seed node; λ is a manually set penalty factor, λ>0; K is the number of seed nodes to be selected, which is manually set.

[0018] Step 3: Solve the quadratic programming problem in Step 2 to obtain the exact probability set P of each node as a seed node. x ={x′1,…,x′ n}, where x′ i Represents node v i The exact probability value of being a seed node.

[0019] Step 4: Determine the exact probability set P for each node as a seed node. x Perform m samplings to obtain m sets of candidate seed nodes CS = {CS1, ..., CS} m}, where CS i ={IS i1 ,…,IS in} represents the set of seed nodes obtained from the i-th sampling, IS ij ∈{0,1}(j=1,…,n), IS ij =1 indicates that node v in the i-th sampling jSelected as a seed node, IS ij =0 indicates that node v in the i-th sampling is... j It was not selected as a seed node.

[0020] Step 5: Use the optimization function f(x1,…,x) n To measure the seed node set CS in each sampling of the candidate seed node set CS i Scope of influence f(IS) i1 ,…,IS in The affected range f(IS) i1 ,…,IS in The largest set of seed nodes CS i Return as the final set of selected seed nodes.

[0021] Preferably, in step 4, the seed node set CS is obtained from the i-th sampling. i The value of can be obtained through the following method:

[0022] Step 4.1, initialize a set CS to indicate whether a node has been selected as a seed. i ={IS i1 ,…,IS in}, and set all elements to 0, i.e., IS ij =0,j=1,…,n.

[0023] Step 4.2, based on the exact probability set P of a node being selected as a seed. x Iterate through each node v in turn. j (j∈{1,2,…,n}), when traversing to v j Simultaneously generate a random number r between [0,1]. j If r j ≤x′ j Then node v j Selected as the seed node, i.e., IS ij The value of v is set to 1; otherwise, continue traversing to the next node v. j+1 When K seed nodes are selected during the traversal, the current CS is... i Return the sampled result. If no K seed nodes have been selected after all nodes have been traversed, return to step 4.1.

[0024] This invention solves the problem of selecting the most influential seed node set when the propagation network structure is unknown. Based on the final infection state data of nodes that are easy to collect during the propagation process, a matrix that can represent the influence of nodes is constructed. The probability of a node being a seed node is obtained by using a quadratic programming problem solving tool. Then, the most influential seed node set is obtained by sampling. This avoids using difficult-to-obtain knowledge such as network structure or the exact infection time of nodes, and has greater practical value. Attached Figure Description

[0025] Figure 1 : Flowchart of an embodiment of the present invention.

[0026] Figure 2 The following is a diagram showing the influence range of different numbers of seed nodes selected in the LFRNet artificial network and the Poster real network in this embodiment of the invention. Detailed Implementation

[0027] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0028] In this embodiment, an artificial network LFRNet generated by the LFR algorithm and a real-world collaborative network Poster representing scientists' research work are used as the propagation network. The number of nodes and edges in both networks are shown in Table 1. In the collaborative network Poster, each academic conference or journal paper inclusion is considered a propagation process. An author being "infected" (value 1) indicates that the author has a paper included, while not being "infected" (value 0) indicates that no paper has been included. Based on multiple inclusion records, the most influential authors can be identified, representing current popular research directions and providing insights into research trends.

[0029] In this embodiment, the infection status data of each node on the network is collected by randomly selecting 15% of the initial nodes according to the independent cascading propagation model and conducting multiple simulated propagation processes.

[0030] Table 1 Experimental Network

[0031] network Number of nodes Number of sides LFRNet 200 800 Poster 379 1602

[0032] Figure 1 The flowchart of an embodiment of the present invention is described below. The present invention provides a method for maximizing the impact based solely on node state observation results, defining the propagation network structure as G={V,E}, where V={v1,v2,...,v... n} represents the n nodes in the propagation network; E represents the set of directed edges in the propagation network representing influence relationships; the infection status observation data collected after β propagation processes are represented by S = {S 1 ,S 2 ,…,S β} indicates that, among which This represents the node infection status observation data after the end of the l-th transmission process. This indicates that node v has completed the l-th process. i The infection status is represented by a value of 1, which indicates that the person is infected, and a value of 0 indicates that the person is not infected.

[0033] Based on the above definition, the method includes the following steps:

[0034] Step 1: Use the collected infection data to construct a matrix Q∈R representing the node's influence capability. n×n Q ij (i,j∈{1,2,…,n}) represents node v i and node v j The heterogeneity affecting ability is specifically calculated as follows:

[0035]

[0036]

[0037] Where n represents the number of nodes in the propagation network; β represents the number of propagation processes; Q ij Represents node v i and node v j Heterogeneity affecting ability; min(C) ik C jk ) represents C ik and C jk The smaller value in the middle; max(C ik C jk ) represents C ik and C jk The larger of the values; I(·) is an indicator function that takes the value 1 when the condition in (·) is true and takes the value 0 when it is false; This indicates that node v has completed the l-th process. i The state of infection.

[0038] Step 2: Use matrix Q to construct an optimization function that measures the influence range of the seed node set. And construct the following quadratic programming problem:

[0039]

[0040] stx i∈[0,1],i=1,…,n

[0041]

[0042] Where x i (i∈{1,…,n}) represents node v i The probability variable of being selected as a seed node; the number of seed nodes K to be selected is set to 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 respectively.

[0043] Step 3: Use the cvxpy toolkit to solve the quadratic programming problem in Step 2 to obtain the exact probability set P of each node as a seed node. x ={x′1,…,x′ n}, where x′ i Represents node v i The probability of being a seed.

[0044] Step 4: Based on the exact probability set P of each node as a seed node x Perform 100 samplings to obtain 100 sets of candidate seed nodes CS = {CS1, ..., CS} 100}, where CS i ={IS i1 ,…,IS in} represents the set of seed nodes obtained from the i-th sampling, IS ij ∈{0,1}(j=1,…,n), IS ij =1 indicates that node v in the i-th sampling j Selected as a seed node, IS ij =0 indicates that node v in the i-th sampling is... j It was not selected as a seed node.

[0045] Step 5: Use the function f(x1,…,x) n To measure the set of seed nodes in each sample in CS. i Scope of influence f(IS) i1 ,…,IS in The affected range f(IS) i1 ,…,IS in The largest set of seed nodes CS i Return as the final set of selected seed nodes.

[0046] Please see Figure 2This diagram illustrates the influence range of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 seed nodes selected on the artificial network LFRNet generated by the LFR algorithm and the real network Poster, respectively, according to embodiments of this invention. When selecting the seed node set, improper distribution of the selected seed nodes may result in a larger number of seeds failing to produce the desired influence range. For example, if the selected seed nodes are too scattered, the limited influence capacity of individual nodes will prevent them from propagating for a longer period, thus limiting the influence range. Conversely, if a large number of seed nodes are selected but their influence ranges overlap significantly, the resulting influence range cannot cover more areas of the network, restricting the information propagation range within the network. The experimental results show that as the number of seeds increases, the influence range of the seed set selected in this invention also gradually increases, indicating that the seed distribution selected in this invention is reasonable and effective. Based on 200 propagation trajectory data generated on each network, the method provided by this invention is used to find the required number of seed node sets, and the influence of the seed node set found by this invention is measured by calculating the influence range of the selected seed nodes. The influence range is calculated by conducting 100 simulated propagations of the found seed node set on the experimental network, recording the number of all infected nodes in the network after each propagation process, and taking the average number of infected nodes in the 100 propagations as the influence range.

[0047] Besides the artificial network LFRNet and the cooperative relationship network Poster simulated in the above embodiments, this invention can also be applied to the fields of advertising and disease prevention. In advertising, the network of users registered on the advertising platform and the relationship network between users is used as the propagation network. Each advertisement placement is considered a round of propagation. It records whether the user has obtained the advertisement information in each round of propagation. If the user has obtained it, the propagation network node represented by the user is considered to be infected; if not, the propagation network node represented by the user is considered to be uninfected. Using the collected infection data, steps 1-4 above are executed. The returned set of seed nodes is the most influential group found from the propagation network. Advertisers can target this group for promotions, thereby maximizing the promotional effect with a limited marketing budget.

[0048] In disease control, the network of residents and their relationships in a certain area is used as a transmission network. The number of residents infected by infectious viruses in each outbreak is recorded. Steps 1-4 above are performed using the collected infection data. The returned set of seed nodes represents the most infectious residents found in the transmission network. By focusing on this group, the spread of infectious diseases can be minimized.

[0049] This invention proposes a method for maximizing the influence of nodes based solely on node state observations. This method constructs a matrix representing the influence of nodes based solely on the final infection state data of nodes after the propagation process ends. It constructs and solves a quadratic programming problem by using the probability of a node being selected as a seed as a parameter. Finally, it obtains the final set of seed nodes through sampling. With this invention, it is only necessary to collect the infection state data of nodes to find the set of the most influential nodes in the network.

[0050] Based on the same inventive concept, this invention also proposes an influence maximization device based solely on node state observation results, which is used to implement the above embodiments. The terms "module," "unit," etc., used below can refer to a combination of software and / or hardware that performs the intended function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible.

[0051] In this embodiment, an impact maximization device based solely on node state observation results includes:

[0052] A data acquisition module is used to acquire a propagation network that represents users and their relationships, collect user status information corresponding to each node after several propagation processes to obtain infection data, and mark the node as infected if the user status information meets the expectations, otherwise mark the node as uninfected.

[0053] The node influence matrix construction module is used to construct a matrix Q representing the node's influence capability using collected infection data;

[0054] The quadratic programming problem construction module is used to construct an optimization function f(x1,…,x) using matrix Q to measure the influence range of the seed node set. n And construct the following quadratic programming problem:

[0055]

[0056] stx i ∈[0,1],i=1,…,n

[0057]

[0058] Where, x i Represents node v i The probability variable for being selected as a seed node, where n represents the number of nodes in the propagation network; λ is the preset penalty factor; and K is the preset number of seed nodes to be selected.

[0059] The quadratic programming problem-solving module is used to solve the quadratic programming problem and obtain the exact probability set P of each node as a seed node.x ={x′1,…,x′ n}, where x′ i Represents node v i The probability of it being a seed;

[0060] The candidate seed set sampling module is used to sample the exact probability values ​​P of each node as a seed node. x Perform m samplings to obtain m sets of candidate seed nodes CS;

[0061] The candidate seed set selection module is used to optimize the set of seeds using the function f(x1,…,x). n To measure the seed node set CS in each sampling of m candidate seed node sets CS i The scope of influence is determined by the set of seed nodes CS that has the largest influence. i The final set of seed nodes is returned, and the users corresponding to the nodes in the seed node set are the selected target users whose impact is maximized.

[0062] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments, and the implementation methods of the remaining modules will not be repeated here. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this invention without creative effort. The embodiments of the device of the present invention can be applied to any device with data processing capabilities, such as a computer or other devices. The device embodiments can be implemented by software, hardware, or a combination of software and hardware. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device that it resides in reading the corresponding computer program instructions from the non-volatile memory into memory and running them.

[0063] It should be understood that all parts not described in detail in this specification belong to the prior art. The above description of the preferred embodiments is relatively detailed, but it should not be regarded as a limitation on the scope of protection of this invention. Those skilled in the art can make substitutions or modifications under the guidance of this invention without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for maximizing the impact based solely on node state observations, characterized in that, Includes the following steps: Step 1: Obtain the propagation network used to characterize authors and their relationships. The propagation network is a Poster network representing the collaborative relationships of scientists' research work. In the Poster network, the inclusion of a paper in an academic conference or journal is taken as a propagation process. The value of an author being infected is 1, indicating that the author has a paper included, and the value of not being infected is 0, indicating that no paper has been included. After collecting the author status information of each node after several propagation processes, infection data is obtained. If the author status information meets the expectations, the node is marked as infected; otherwise, the node is marked as uninfected. Step 2: Use the collected infection data to construct a matrix Q representing the node's influence capability, as shown in the following formula: ； ； Where β represents the number of propagation processes; Represents node v i and node v j Heterogeneity affecting capabilities; express and Small to medium values; express and The value of medium to large; It is an indicator function, when The value is 1 when the condition is true and 0 when the condition is false. Indicates the first After this process, node v i The infection status, Represents node v i and node v k The degree of correlation between infection status These represent a value of 0 or 1 respectively; Step 3: Use matrix Q to construct an optimization function to measure the influence range of the seed node set. And construct the following quadratic programming problem: ； ； ； ； in, Represents node v i The probability variable for being selected as a seed node, where n represents the number of nodes in the propagation network; K is the preset penalty factor; K is the preset number of seed nodes to be selected. Step 4: Solve the quadratic programming problem in Step 3 to obtain the exact probability set of each node as a seed node. ,in, Represents node v i The probability of it being a seed; Step 5: Based on the exact probability set of each node as a seed node Perform m samplings to obtain m sets of candidate seed nodes CS; Step 6: Use an optimization function to measure the impact range generated by the seed node set. To measure the seed node set in each sampling of the m candidate seed node set CS The scope of influence will be the set of seed nodes with the largest influence. The final set of seed nodes is returned, and the authors corresponding to the nodes in the seed node set are the target authors selected to maximize the impact. The target authors represent the most influential authors and represent the current popular research directions.

2. The method for maximizing the impact based solely on node state observation results according to claim 1, characterized in that, In step 5, the i-th sampling obtains the seed node set. The process of obtaining the value is as follows: Step 5.1: Initialize a set representing whether a node has been selected as a seed. And set all elements to 0, that is ; Step 5.2, based on the exact probability set of a node being selected as a seed. Iterate through each node in turn. When traversing to v j Simultaneously generate a random number r between [0,1]. j If r j Then node v j Selected as a seed node, i.e. The value of v is set to 1; otherwise, continue traversing to the next node v. j+1 When K seed nodes are selected during the traversal, the current... Return the sampled result; if K seed nodes have not been selected after all nodes have been traversed, return to step 5.

1.

3. A device for maximizing the impact based solely on node state observation results, characterized in that, include: The data acquisition module is used to acquire a propagation network that represents authors and their relationships. The propagation network is a Poster network representing the collaborative relationships of scientists' research work. In the Poster network, the inclusion of a paper in an academic conference or journal is taken as a propagation process. The value of an author being infected is 1, indicating that the author has a paper included, and the value of not being infected is 0, indicating that no paper has been included. After collecting the author status information of each node after several propagation processes, infection data is obtained. If the author status information meets the expectations, the node is marked as infected; otherwise, the node is marked as uninfected. The node influence matrix construction module is used to construct a matrix Q representing the node's influence capability using collected infection data. Specifically: ； ； Where β represents the number of propagation processes; Represents node v i and node v j Heterogeneity affecting capabilities; express and Small to medium values; express and The value of medium to large; It is an indicator function, when The value is 1 when the condition is true and 0 when the condition is false. Indicates the first After this process, node v i The infection status, Represents node v i and node v k The degree of correlation between infection status These represent a value of 0 or 1 respectively; The quadratic programming problem-building module is used to construct an optimization function using matrix Q to measure the influence range of the seed node set. And construct the following quadratic programming problem: ； ； ； ； in, Represents node v i The probability variable for being selected as a seed node, where n represents the number of nodes in the propagation network; K is the preset penalty factor; K is the preset number of seed nodes to be selected. The quadratic programming problem-solving module is used to solve the quadratic programming problem and obtain the exact probability set of each node as a seed node. ,in, Represents node v i The probability of it being a seed; The candidate seed set sampling module is used to sample the exact probability values ​​of each node as a seed node. Perform m samplings to obtain m sets of candidate seed nodes CS; The candidate seed set filtering module is used to filter the candidate seed set using an optimization function. To measure the seed node set in each sampling of the m candidate seed node set CS The scope of influence will be the set of seed nodes with the largest influence. The final set of seed nodes is returned, and the authors corresponding to the nodes in the seed node set are the target authors selected to maximize the impact. The target authors represent the most influential authors and represent the current popular research directions.

4. The device for maximizing the impact based solely on node state observation results according to claim 3, characterized in that, The sampling process in the candidate seed set sampling module is as follows: Initialize a set representing whether a node has been selected as a seed. And set all elements to 0, that is ; Based on the set of exact probability values ​​for a node to be selected as a seed Iterate through each node in turn. When traversing to v j Simultaneously generate a random number r between [0,1]. j If r j Then node v j Selected as a seed node, i.e. The value of v is set to 1; otherwise, continue traversing to the next node v. j+1 When K seed nodes are selected during the traversal, the current... The sampled result is returned; if no K seed nodes are selected after all nodes have been traversed, then resampling is performed.

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