Neural network-based social network opinion competition model construction method and system

Abstract

The invention discloses a social network opinion competition model construction method and system based on a neural network, and relates to the technical field of big data analysis, and the method comprises the steps: describing a social network through an undirected graph; evaluating the opinion dynamic state of each node in the social network based on a distributed consensus protocol; integrating a distributed consensus protocol into the k-WTA model and obtaining model output; obtaining an MGNN model and carrying out opinion dynamic evolution to obtain a social network opinion competition model; theoretical analysis and simulation verification are carried out; the method aims to clarify the dynamic state of opinion competition behaviors in the social network, and the development mechanism of various viewpoints and the influence of the social environment on the evolution of the opinion competition behaviors are captured through the opinion competition model; the method successfully simulates public opinion competition and evolution behaviors, provides a new perspective for understanding and predicting the competition phenomenon, can be widely applied to various fields of social networks, and provides a new perspective and mode for understanding and predicting the competition phenomenon in a complex social system.

Description

Technical Field

[0001] The present invention belongs to the technical field of big data analysis, and in particular relates to a method and system for constructing a social network opinion competition model based on a neural network. Background Art

[0002] In recent years, the study of opinion dynamics in social networks has attracted widespread attention. On the one hand, the development of new media technologies, such as social media platforms such as Douyin and Xiaohongshu, has introduced many social factors that directly affect public opinion; in addition, these technologies are profoundly changing the structure of social networks, thereby changing the mechanism of opinion evolution. On the other hand, opinion dynamics have a wide range of applications in various fields, such as marketing activities. In order to study and explain opinion dynamics on social networks, researchers have proposed several models to simulate the consensus problem, where consensus represents the agreement between agents on the variables of interest. Freemanet et al. studied the efficiency of two algorithms for the average consensus problem, in which each agent must estimate the average input of all agents. In the related literature, the joint influence of the dynamic characteristics of individual agents and their interaction topology on opinion dynamics is studied, which may lead to polarity, consensus, or neutrality. In addition, a continuous-time model with a signature model is introduced for the consensus problem in leader-follower competitive interactions, and the convergence and stability of the model under different leader states are analyzed. In addition, in order to capture influential cognitive connections, a multi-dimensional learning model is designed for opinion dynamics, and its effectiveness is successfully verified through extensive subjective simulations. The above studies have examined opinion dynamics models under different conditions. However, these studies focus more on the collaboration between agents' opinions.

[0003] Competition is also a common phenomenon in public opinion dynamics, which drives the evolution of public opinion. Therefore, further studying the characteristics of public opinion competition will help us better model and analyze public opinion dynamics. In real life, individuals (agents) in social networks have specific views on a topic / target in the initial stage, such as evaluations of goods / events, favorability towards online celebrities, feelings towards events, etc. Then, agents can communicate with their friends, family members, and even strangers through social networks; after dissemination and interaction, those opinions with advantageous positions (close to social norms, more dissemination channels, and support from opinion leaders) will be amplified and adopted by more and more agents.

[0004] In this context, a popular competition model: the k-winner-take-all (k-WTA) model is often used for consensus problems. In the k-WTA model, it can be divided into two types: centralized model and distributed model. In the relevant literature, the k-WTA model is transformed into a quadratic programming under certain conditions, so that the scheme originally designed to solve the quadratic programming can be used to solve the k-WTA problem. In addition, a new k-WTA model is designed, whose coefficient k is implicitly determined by the initial state of the neuron instead of being given directly; although these models have been proven to be effective, their centralized structure may have problems such as poor scalability, uncertainty, and privacy leakage. In addition, the existing technology rarely uses the distributed k-WTA model to simulate the competitive behavior of opinions in social networks. Summary of the invention

[0005] The purpose of the present invention is to provide a method and system for constructing a social network opinion competition model based on a neural network, which can be achieved through the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a method for constructing a social network opinion competition model based on a neural network, comprising the following steps:

[0007] S1, using undirected graphs to describe the topological structure of social networks;

[0008] S2, evaluating the opinion dynamics of each node in the social network based on a distributed consensus protocol;

[0009] S3, integrating the distributed consensus protocol into the k-WTA model and obtaining the output of the k-WTA model;

[0010] S4, defining the opinion matching error and obtaining the MGNN model, and using the MGNN model to evolve the opinion dynamics and thereby obtain a social network opinion competition model;

[0011] S5, performing theoretical analysis and simulation verification based on the social network opinion competition model.

[0012] Preferably, the social network opinion competition model is expressed as:

[0013]

[0014] In formula (1), represents the opinion held by the i-th node in the MGNN model; q i (t) is an auxiliary variable in the k-WTA model; v i (t) is the input of the k-WTA model, and its error degree of agreement with the opinion is e i (t) related, e i (t) is larger, the larger vi The larger the (t) is, the larger the θ(t) is; θ(t) represents the adaptive coefficient in the MGNN model, which is used to improve the accuracy of the MGNN model; Φ Ω represents the output equation function; λ represents the input correlation coefficient; T represents the transposition operation of the vector; Indicates O i The transpose of (t);

[0015] In formula (2), γ is the first convergence coefficient, which is used to adjust the convergence speed of the k-WTA model; i (t) represents the estimation of the social network consensus by the i-th node; k represents the number of winners in the k-WTA model;

[0016] In formula (3), Yes i The derivative of (t) represents the opinion dynamics of the ith node on the social network consensus estimate; α is a positive adjustment coefficient; m i,j represents the adjacency matrix of the social network; u i (t) represents external input; y j (t) represents the jth node’s estimate of the social network consensus; Represents a state scalar of the i-th node; Represents a state scalar of the jth node;

[0017] In formula (4), Represents the derivative of a state scalar of the i-th node.

[0018] Preferably, in step S1, the undirected graph is represented as: G = (A, E, M);

[0019] Where A=(a1,a2,...,a n ) represents the set of nodes in the social network, with a total of n nodes; E represents the edge set; M = [m i,j ] represents the adjacency matrix of a social network;

[0020] Furthermore, if any two nodes a of a social network i and a j If there is a connection between them, then node a i and node a j is an adjacent node, and there is a node with a weight of w i,j The undirected edge (a i ,a j )∈E;

[0021] In addition, the undirected graph does not have self-loop connections, that is, there is no connection between nodes themselves, which is expressed as: m i,i =0.

[0022] Preferably, the adjacency matrix M of the social network specifically includes:

[0023] For the i-th node in the social network, define a neighbor node set N j ={j,((a i ,a j )∈E)}, which contains all neighbor nodes of node i;

[0024] Based on this, the expression of the adjacency matrix M is:

[0025]

[0026] Among them, w i,j represents the weight between the i-th node and the j-th node, which is used to represent the influence degree between two adjacent nodes; and w is obtained according to the undirected graph G i,j =w j,i ;

[0027] In addition, the adjacency matrix M is used to represent the connection status of each node in the social network.

[0028] Preferably, the step S2 is specifically:

[0029] The distributed consensus protocol is used to represent the opinion dynamics of the social network consensus estimate of the i-th node, and its expression is:

[0030]

[0031] Among them, y i (t) represents the estimation of the social network consensus by the i-th node;

[0032] Yes i The derivative of (t) represents the opinion dynamics of the i-th node on the social network consensus estimate;

[0033] u i (t) represents external input;

[0034] Represents the neighbor node set N j Neighboring nodes in the network estimate the consensus of the social network.

[0035] Preferably, opinion dynamics Further expressed as:

[0036]

[0037] Among them, α represents the adjustment coefficient, which is a positive number;

[0038] yj (t) represents the jth node’s estimate of the social network consensus;

[0039] Represents a state scalar of the i-th node;

[0040] Represents a state scalar of the jth node;

[0041] Represents the derivative of a state scalar of the i-th node.

[0042] Preferably, the integration of the distributed consensus protocol into the k-WTA model is specifically as follows:

[0043] The external input u in the opinion dynamic expression i (t) as the output of the k-WTA model;

[0044] External input u i (t) is expressed as:

[0045]

[0046] Among them, v i (t) is the input of the k-WTA model and is expressed as: e i (t) is the error of opinion fit.

[0047] Preferably, obtaining the output of the k-WTA model comprises:

[0048] The auxiliary variables are obtained by the state equation, which is expressed as:

[0049]

[0050] Among them, q i (t) is an auxiliary variable; n represents the number of all nodes in the social network; k represents the number of winners in the k-WTA model; γ represents the first convergence parameter, which is a positive real number used to adjust the convergence speed of the k-WTA model;

[0051] Based on the auxiliary variables, the output of the k-WTA model is obtained through the output equation, and the output equation is expressed as:

[0052]

[0053] Among them, Φ Ω Represents the output equation function, and Ω=[0,1], defined as:

[0054]

[0055] λ represents the input correlation coefficient and satisfies in, and They represent the kth and k+1th large inputs respectively.

[0056] Preferably, the definition of the opinion fit error degree includes:

[0057] The expected opinions on the target social issue are defined as O e (t);

[0058] The subject opinions related to the social environment are defined as O i (t);

[0059] A mapping function is used to transform the expected opinion O e (t) and subject opinion O i (t) is defined as e(O i (t)-O e (t)), that is: e i (t);

[0060] The MGNN model is obtained as follows:

[0061] Let the opinion fit error e i (t) converges to zero, and the MGNN model is obtained based on the traditional GNN model, then the MGNN model is expressed as:

[0062]

[0063] Where T represents the transpose operation of the vector; Indicates O i The transpose of (t);

[0064] θ(t) represents an adaptive coefficient, and the expression of θ(t) is:

[0065] β>2; β represents the second convergence coefficient, which is used to adjust the convergence speed of the MGNN model.

[0066] In a second aspect, an embodiment of the present application provides a social network opinion competition model construction system based on a neural network, including:

[0067] at least one processor;

[0068] at least one memory for storing at least one program;

[0069] When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0070] The beneficial effects of the present invention are:

[0071] (1) The present invention provides an improved new distributed competition model, which aims to illustrate the dynamics of opinion competition behavior in social networks. The model captures the development mechanism of various opinions, their appeal to individuals, and the influence of the social environment on their evolution. The model shows that a subset of opinions eventually prevails and is adopted. The key elements of social networks are quantified as parameters, and the changes in parameters represent the dynamics of opinions. On this basis, an improved gradient-based neural network (MGNN model) is designed as the evolution law of opinions, and its stability and convergence are verified through theoretical analysis. In addition, the real-world competition scenario is simulated experimentally to demonstrate the practical application of the model, specifically: the behavior of public opinion competition and evolution is successfully simulated; a new perspective is provided for understanding and predicting competition phenomena, etc. In addition, the model can be widely used in various fields of social networks, such as marketing, public opinion supervision, and election prediction, etc., providing a new perspective and method for understanding and predicting competition phenomena in complex social systems.

[0072] (2) The present invention studies the distributed opinion competition behavior in social networks. First, an undirected graph is used to describe the topological structure of the social network. Specifically, an undirected graph and algebraic topology are used to represent the connection between the social network and the intelligent agent, and the undirected graph is not fully connected. Then, the opinion dynamics of each node in the social network are evaluated based on a distributed consensus protocol. Specifically, a distributed consensus protocol is used to evaluate the interaction between adjacent nodes. Next, the distributed consensus protocol is integrated into a k-WTA model and the output of the k-WTA model is obtained. Specifically, a distributed consensus protocol and a k-WTA model are integrated. The TA model incorporates the competition mechanism into the k-WTA model. More specifically, for those opinions in the k most advantageous positions and the top k opinions with the largest investment in the k-WTA model, they will continue to evolve and may converge to a consensus. On the contrary, the remaining opinions may become invalid and stop evolving. In this competition mechanism, the position of opinions is associated with the social environment, making this k-WTA model closer to the real world. In addition, in order to ensure the convergence of the k-WTA model, an improved MGNN model is used to drive the evolution of opinions. Finally, theoretical analysis and simulation verification are also carried out based on the social network opinion competition model. So far, a distributed opinion competition model in social networks has been established. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] For better understanding and implementation, the technical solution of the present application is described in detail below with reference to the accompanying drawings.

[0074] Figure 1 A flowchart of a method for constructing a social network opinion competition model based on a neural network provided in an embodiment of the present application;

[0075] Figure 2 A structural diagram of a social network opinion competition model construction system based on a neural network provided in an embodiment of the present application. DETAILED DESCRIPTION

[0076] In order to further explain the technical means and effects taken by the present invention to achieve the predetermined invention purpose, exemplary embodiments will be described in detail here, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are only examples of methods and systems consistent with some aspects of the present application as detailed in the attached claims.

[0077] The terms used in this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in this article refers to any or all possible combinations of one or more associated listed items.

[0078] The specific implementation methods, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0079] See also Figure 1 The present application embodiment provides a method for constructing a social network opinion competition model based on a neural network, comprising the following steps:

[0080] S1, using undirected graphs to describe the topological structure of social networks;

[0081] S2, evaluating the opinion dynamics of each node in the social network based on a distributed consensus protocol;

[0082] S3, integrating the distributed consensus protocol into the k-WTA model and obtaining the output of the k-WTA model;

[0083] S4, defining the opinion matching error and obtaining the MGNN model, and using the MGNN model to evolve the opinion dynamics and thereby obtain a social network opinion competition model;

[0084] S5, performing theoretical analysis and simulation verification based on the social network opinion competition model.

[0085] Specifically, since the distributed k-WTA model is rarely used in the prior art to simulate the competitive behavior of opinions in social networks, this application studies the distributed competitive behavior of opinions in social networks to address this problem. First, an undirected graph is used to describe the topological structure of the social network, specifically: an undirected graph and algebraic topology are used to represent the connection between the social network and the intelligent agent (the intelligent agent represents an intelligent device that can provide social network nodes), and the above undirected graph is not fully connected; then, the opinion dynamics of each node in the social network are evaluated based on a distributed consensus protocol, specifically: a distributed consensus protocol is used to evaluate the interaction between adjacent nodes; then, the distributed consensus protocol is integrated into the k-WTA model and the output of the k-WTA model is obtained, specifically: a distributed consensus protocol and k-WTA are integrated. The model incorporates the competition mechanism into the k-WTA model. More specifically, for those opinions in the k most advantageous positions and the top k opinions with the largest investment in the k-WTA model, they will continue to evolve and may converge to a consensus. On the contrary, the remaining opinions may become invalid and stop evolving. In this competition mechanism, the position of opinions is associated with the social environment, making this k-WTA model closer to the real world. In addition, in order to ensure the convergence of the k-WTA model, an improved MGNN model is used to drive the evolution of opinions. Finally, theoretical analysis and simulation verification are also carried out based on the social network opinion competition model. So far, a distributed opinion competition model in social networks has been established.

[0086] In summary, this application provides an improved new distributed competition model, which aims to illustrate the dynamics of opinion competition behavior in social networks. The model captures the development mechanism of various opinions, their appeal to individuals, and the influence of the social environment on their evolution. The model shows that a subset of opinions eventually prevails and is adopted. The key elements of social networks are quantified as parameters, and the changes in parameters represent the dynamics of opinions. On this basis, an improved gradient-based neural network (MGNN model) is designed as the evolution law of opinions, and its stability and convergence are verified through theoretical analysis. In addition, the real-world competition scenario is simulated experimentally to demonstrate the practical application of the model, specifically: the behavior of public opinion competition and evolution is successfully simulated; new perspectives are provided for understanding and predicting competition phenomena, etc. And the model can be widely used in various fields of social networks, such as marketing, public opinion supervision, and election prediction, etc., providing new perspectives and methods for understanding and predicting competition phenomena in complex social systems.

[0087] It should be noted that the MGNN model (Modified Gradient Neural Network) is a recursive neural network model. This type of recursive neural network model is widely used in solving time-varying problems. Its core idea is to solve time-varying problems in real time based on the information of input parameters, and can solve them with high precision. In the present invention, the accuracy of the MGNN model is improved by carefully designing the adaptive coefficient θ(t), and it has the effect of rapid convergence.

[0088] In an embodiment provided in the present application, in step S1, the undirected graph is represented as:

[0089] G = (A, E, M);

[0090] Where A=(a1,a2,...,a n ) represents the set of nodes in the social network, with a total of n nodes; E represents the edge set; M = [m i,j ] represents the adjacency matrix of a social network;

[0091] Furthermore, if any two nodes a of a social network i and a j If there is a connection between them, then node a i and node a j is an adjacent node, and there is a node with a weight of w i,j The undirected edge (a i ,a j )∈E;

[0092] In addition, the undirected graph does not have self-loop connections, that is, there is no connection between nodes themselves, which is expressed as: m i,i =0.

[0093] In an embodiment provided in the present application, the adjacency matrix M of the social network specifically includes:

[0094] For the i-th node in the social network, define a neighbor node set N j ={j,((a i ,a j )∈E)}, which contains all neighbor nodes of node i;

[0095] Based on this, the expression of the adjacency matrix M is:

[0096]

[0097] Among them, w i,j represents the weight between the i-th node and the j-th node, which is used to represent the influence degree between two adjacent nodes; and w is obtained according to the undirected graph Gi,j =w j,i ;

[0098] In addition, the adjacency matrix M is used to represent the connection status of each node in the social network.

[0099] Specifically, the topological structure of the social network is described by using an undirected graph in step S1, which specifically includes the following contents: without loss of generality, the topological structure of the social network is described by using an undirected graph G = (A, E, M), where A = (a1, a2, ..., a n ) represents the set of nodes in the real social network, with a total of n nodes; E represents the edge set; M = [m i,j ] represents the adjacency matrix of a social network. If any two nodes a of a social network are connected i and a j If there is a connection, then the two nodes are called adjacent nodes, and there is a weight w i,j The undirected edge (a i ,a j )∈E. In addition, this application does not consider the self-efficacy in social networks, that is, the undirected graph G does not have self-loop connections, and the nodes are not connected to themselves, that is, m i,i =0.

[0100] In addition, for the i-th node in the social network, a neighbor node set N is defined for it j ={j,((a i ,a j )∈E)}, which includes all neighbor nodes of the node. Based on this, the expression of the adjacency matrix M of the social network is:

[0101]

[0102] Among them, w i,j represents the weight between the i-th node and the j-th node, representing the influence between two adjacent nodes; and, because G is an undirected graph, w i,j =w j,i The adjacency matrix M is used to represent the connection status of each node in the social network.

[0103] In an embodiment provided in the present application, the step S2 is specifically as follows:

[0104] The distributed consensus protocol is used to represent the opinion dynamics of the social network consensus estimate of the i-th node, and its expression is:

[0105]

[0106] Among them, y i(t) represents the estimation of the social network consensus by the i-th node;

[0107] Yes i The derivative of (t) represents the opinion dynamics of the i-th node on the social network consensus estimate;

[0108] u i (t) represents external input;

[0109] Represents the neighbor node set N j Neighboring nodes in the network estimate the consensus of the social network.

[0110] In one embodiment provided in this application, the opinion dynamics Further expressed as:

[0111]

[0112] Among them, α represents the adjustment coefficient, which is a positive number;

[0113] y j (t) represents the jth node’s estimate of the social network consensus;

[0114] Represents a state scalar of the i-th node;

[0115] Represents a state scalar of the jth node;

[0116] Represents the derivative of a state scalar of the i-th node.

[0117] Specifically, in order to study how the opinions of various nodes in a social network compete and reach a consensus, this application uses a distributed consensus protocol to process and express the estimation of the social network consensus of the i-th node as:

[0118]

[0119] where y i (t) represents the estimation of the social network consensus by the i-th node; Yes i The derivative of (t) represents the opinion dynamics of the ith node on the social network consensus estimate; u i (t) represents external input; Represents the neighbor node set N j The neighboring nodes in the network estimate the consensus of the social network. From the above formula, we can see that y i(t) is only affected by the opinions of neighboring nodes and not by the opinions of all nodes in the network, thus proving the distributed nature of the distributed consensus protocol. More specifically, Further expressed as:

[0120]

[0121] Where α is a positive adjustment coefficient. From the above formula, we can see that in the expression If you want to obtain , then the above Do the integral processing, that is, for m i,j (y i (t)-y j (t)), so the integral from time 0 to the current time is related to the historical difference between the two. Therefore, It is not only related to the difference between the opinions of the i-th node and its neighboring nodes in the current state, but also to the historical difference between the two; and It can also be used to filter out noise from the input signal.

[0122] In an embodiment provided in the present application, the integration of the distributed consensus protocol into the k-WTA model is specifically as follows:

[0123] The external input u in the opinion dynamic expression i (t) as the output of the k-WTA model;

[0124] External input u i (t) is expressed as:

[0125]

[0126] Among them, v i (t) is the input of the k-WTA model and is expressed as: e i (t) is the error of opinion fit.

[0127] In an embodiment provided in the present application, obtaining the output of the k-WTA model includes:

[0128] The auxiliary variables are obtained by the state equation, which is expressed as:

[0129]

[0130] Among them, q i(t) is an auxiliary variable; n represents the number of all nodes in the social network; k represents the number of winners in the k-WTA model; γ represents the first convergence parameter, which is a positive real number used to adjust the convergence speed of the k-WTA model;

[0131] Based on the auxiliary variables, the output of the k-WTA model is obtained through the output equation, and the output equation is expressed as:

[0132]

[0133] Among them, Φ Ω Represents the output equation function, and Ω=[0,1], defined as:

[0134]

[0135] λ represents the input correlation coefficient and satisfies in, and They represent the kth and k+1th large inputs respectively.

[0136] Specifically, in the field of opinion evolution in social networks, the WTA model (winner-takes-all concept) stands out. Social media platforms amplify content that gains initial traction, thereby increasing its visibility and influence. Consider a scenario where many conflicting opinions emerge on a controversial topic, and because the algorithm favors engagement and popularity, an opinion that gains an early advantage, perhaps due to timing, high emotional state, resonance with a subset of users, or even strategic promotion, can quickly dominate the discourse. As more users encounter and interact with this opinion, it gains additional attention, reinforcing its prominence through a feedback loop of visibility and validation. For example, the WTA phenomenon has been found in electronic word-of-mouth systems in the digital tourism sector, where a small number of influential microblogs dominate tourism discussions. However, due to the complexity of the competitive process and environment, there will be several winners in many cases, resulting in a k-WTA model. In the k-WTA model, the output of the first k largest inputs out of the total input of the model is 1, and the output of the other inputs is 0.

[0137] In order to introduce the influence of social environment and competition in the distributed consensus protocol, this embodiment will i (t) is defined as the output of the k-WTA model, where the k winners are the top k opinions with the highest fitness. In addition, in order to maximize the input of the opinion with the highest fitness to the k-WTA model, the model input v is defined as i (t) is Therefore, u i (t) is expressed mathematically as:

[0138]

[0139] Furthermore, the output of the k-WTA model can be obtained using the following equation:

[0140] (1) Equation of state:

[0141]

[0142] Among them, γ represents the first convergence coefficient, which is a positive real number used to adjust the convergence speed of the k-WTA model, q i (t) is an auxiliary variable.

[0143] (2) Output equation:

[0144]

[0145] Among them, Φ Ω is a function related to the output equation, so this application names it as the output equation function, Ω=[0,1],Φ Ω is defined as:

[0146]

[0147] λ is a function related to the output equation and used to limit v i (t) is a coefficient of the range of values, so this application names it as the input correlation coefficient. To ensure that the solution of the state equation and the output equation is equal to u i (t) expression, then λ should satisfy in, and are the kth and k+1th largest inputs respectively.

[0148] In an embodiment provided in the present application, the definition of the opinion matching error degree includes:

[0149] The expected opinions on the target social issue are defined as O e (t);

[0150] The subject opinions related to the social environment are defined as O i (t);

[0151] A mapping function is used to transform the expected opinion O e (t) and subject opinion O i (t) is defined as e(O i (t)-O e (t)), that is: e i (t).

[0152] Specifically, the opinions of individuals (nodes) are related to the social environment, and the dynamics of opinions are significantly affected by social factors, including social norms, communication channels, and other factors. Opinions that conform to mainstream norms, gain support from influential figures, or resonate with public sentiment are more likely to spread and be accepted, benefiting from the positive feedback mechanism. In contrast, opinions that deviate from norms, lack influential support, or face resistance from social factors tend to get into trouble and may lose their appeal. Therefore, this application defines the expected opinions on the target social issue as O e (t), defining the subject opinions related to the social environment as O i (t), and O i (t) and O e The fitting error between (t) can be defined as a mapping function e(O i (t)-O e (t)), for simplicity, referred to as e i (t).

[0153] In an embodiment provided in the present application, the obtaining of the MGNN model is specifically as follows:

[0154] Let the opinion fit error e i (t) converges to zero, and the MGNN model is obtained based on the traditional GNN model, then the MGNN model is expressed as:

[0155]

[0156] Where T represents the transpose operation of the vector; Indicates O i The transpose of (t);

[0157] θ(t) represents an adaptive coefficient, and the expression of θ(t) is:

[0158] β>2; β represents the second convergence coefficient, which is used to adjust the convergence speed of the MGNN model.

[0159] Specifically, according to the above analysis on the error degree of opinion fit, the subject opinion O i (t) should evolve gradually to accommodate society's expected opinions on the event. e (t). In other words, the error of opinion fit e i The expected value of (t) should be zero. Therefore, the opinion evolution problem becomes a time-varying zero-finding problem.

[0160] In recent years, massive neural networks represented by ordinary differential equations have been studied for their outstanding performance in solving time-varying problems. Among these neural networks, zeroing neural networks and gradient-based neural networks are two popular models. However, since the zeroing neural network model contains an inverse matrix, the calculation is large and cannot be solved. Therefore, this embodiment adopts a gradient-based neural network. Define a non-negative scalar Then the traditional GNN model for solving opinion dynamics can be expressed as:

[0161]

[0162] Among them, ρ is a positive stability coefficient.

[0163] In order to make i (t) converges to zero. Based on the traditional GNN model, a MGNN model is designed as the opinion evolution law. The MGNN model is expressed as:

[0164]

[0165] in,

[0166] Compared with the traditional GNN model, the MGNN model uses a variable θ(t) to replace the above-mentioned stability coefficient ρ.

[0167] In an embodiment provided in the present application, the social network opinion competition model is expressed as:

[0168]

[0169] In formula (1), represents the opinion held by the i-th node in the MGNN model; q i (t) is an auxiliary variable in the k-WTA model; v i (t) is the input of the k-WTA model, and its error degree of agreement with the opinion is e i (t) related, e i (t) is larger, the larger v i The larger the (t) is, the larger the θ(t) is; θ(t) represents the adaptive coefficient in the MGNN model, which is used to improve the accuracy of the MGNN model; φ Ω represents the output equation function; λ represents the input correlation coefficient; T represents the transposition operation of the vector; Indicates O i The transpose of (t);

[0170] In formula (2), γ is the first convergence coefficient, which is used to adjust the convergence speed of the k-WTA model; i (t) represents the estimation of the social network consensus by the i-th node; k represents the number of winners in the k-WTA model;

[0171] In formula (3), Yes i The derivative of (t) represents the opinion dynamics of the ith node on the social network consensus estimate; α is a positive adjustment coefficient; m i,j represents the adjacency matrix of the social network; u i (t) represents external input; y j (t) represents the jth node’s estimate of the social network consensus; Represents a state scalar of the i-th node; Represents a state scalar of the jth node;

[0172] In formula (4), Represents the derivative of a state scalar of the i-th node.

[0173] Specifically, as analyzed above, only those opinions that are won will evolve. Therefore, combining the output equation and state equation of the k-WTA model in the above embodiment, and the MGNN model, the opinion dynamics model is improved as follows:

[0174]

[0175] in addition, The item needs to know the status of all nodes in the entire social network, which is unrealistic for individuals. Therefore, combined with the distributed consensus protocol, the above opinion dynamic model is further improved to obtain a distributed opinion competition model, that is, the social network opinion competition model of this embodiment, which is expressed as:

[0176]

[0177] In an embodiment provided in the present application, the theoretical analysis based on the social network opinion competition model is specifically: proving the convergence of the MGNN model, and the proof process is as follows:

[0178] S5-1, define a non-negative Lyapunov operator, expressed as: in Indicates e i The transpose of (t);

[0179] S5-2, find the derivative of the Lyapunov operator, expressed as:

[0180]

[0181] S5-3, substituting the MGNN model into the derivative expression, we get:

[0182]

[0183] S5-4, after formula rearrangement, we get:

[0184]

[0185] S5-5, substituting the expression of θ(t) into the equation, we get:

[0186]

[0187] because therefore

[0188] S5-6, according to the Lyapunov stability criterion, if the MGNN model is asymptotically stable, then the opinion fit error e i (t) converges to 0;

[0189] S5-7, proof completed.

[0190] Specifically, according to the MGNN model proposed in this application, the opinion fit error degree e i (t) will eventually converge to 0. In other words, the node’s opinion O i (t) will converge to the expected opinion O that society expects e (t), therefore, this example uses the above proof method to prove the convergence of the MGNN model.

[0191] See also Figure 2 The embodiment of the present application provides a social network opinion competition model construction system based on a neural network, including:

[0192] at least one processor;

[0193] at least one memory for storing at least one program;

[0194] When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0195] It can be seen that the contents of the above method embodiments are all applicable to the present system embodiments, the functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0196] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0197] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0198] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0199] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technical personnel in this field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for constructing a social network opinion competition model based on a neural network, characterized by: The steps include: S1, using undirected graphs to describe the topological structure of social networks; S2, evaluating the opinion dynamics of each node in the social network based on a distributed consensus protocol; S3, integrating the distributed consensus protocol into the k-WTA model and obtaining the output of the k-WTA model; S4, defining the opinion matching error and obtaining the MGNN model, and using the MGNN model to evolve the opinion dynamics and thereby obtain a social network opinion competition model; S5, performing theoretical analysis and simulation verification based on the social network opinion competition model.

2. The method for constructing a social network opinion competition model based on a neural network according to claim 1, characterized in that: The social network opinion competition model is expressed as: In formula (1), represents the opinion held by the i-th node in the MGNN model; q i (t) is an auxiliary variable in the k-WTA model; v i (t) is the input of the k-WTA model, and its error degree of agreement with the opinion is e i (t) related, e i (t) is larger, the larger v i The larger the (t) is, the larger the θ(t) is; θ(t) represents the adaptive coefficient in the MGNN model, which is used to improve the accuracy of the MGNN model; Φ Ω represents the output equation function; λ represents the input correlation coefficient; T represents the transposition operation of the vector; Indicates O i The transpose of (t); In formula (2), γ is the first convergence coefficient, which is used to adjust the convergence speed of the k-WTA model; i (t) represents the estimation of the social network consensus by the i-th node; k represents the number of winners in the k-WTA model; In formula (3), Yes i The derivative of (t) represents the opinion dynamics of the ith node on the social network consensus estimate; α is a positive adjustment coefficient; m i,j represents the adjacency matrix of the social network; u i (t) represents external input; y j (t) represents the jth node’s estimate of the social network consensus; Represents a state scalar of the i-th node; Represents a state scalar of the jth node; In formula (4), Represents the derivative of a state scalar of the i-th node.

3. The method for constructing a social network opinion competition model based on a neural network according to claim 1, characterized in that: In step S1, the undirected graph is represented as: G = (A, E, M); Where A=(a1,a2,...,a n ) represents the set of nodes in the social network, with a total of n nodes; E represents the edge set; M = [m i,j ] represents the adjacency matrix of a social network; If any two nodes a of a social network i and a j If there is a connection between them, then node a i and node a j is an adjacent node, and there is a node with a weight of w i,j The undirected edge (a i ,a j )∈E; The undirected graph does not have self-loop connections, that is, there is no connection between nodes themselves, which is expressed as: m i,i =0.

4. The method for constructing a social network opinion competition model based on a neural network according to claim 3, characterized in that: Regarding the adjacency matrix M of the social network, it specifically includes: For the i-th node in the social network, define a neighbor node set N j ={j,((a i ,a j )∈E)}, which contains all neighbor nodes of node i; Based on this, the expression of the adjacency matrix M is: Among them, w i,j represents the weight between the i-th node and the j-th node, which is used to represent the influence degree between two adjacent nodes; and w is obtained according to the undirected graph G i,j =w j,i ; The adjacency matrix M is used to represent the connection status of each node in the social network.

5. The method for constructing a social network opinion competition model based on a neural network according to claim 1, characterized in that: The step S2 is specifically as follows: The distributed consensus protocol is used to represent the opinion dynamics of the social network consensus estimate of the i-th node, and its expression is: Among them, y i (t) represents the estimation of the social network consensus by the i-th node; Yes i The derivative of (t) represents the opinion dynamics of the i-th node on the social network consensus estimate; u i (t) represents external input; Represents the neighbor node set N j Neighboring nodes in the network estimate the consensus of the social network.

6. The method for constructing a social network opinion competition model based on a neural network according to claim 5, characterized in that: Opinion News Further expressed as: Among them, α represents the adjustment coefficient, which is a positive number; y j (t) represents the jth node’s estimate of the social network consensus; Represents a state scalar of the i-th node; Represents a state scalar of the jth node; Represents the derivative of a state scalar of the i-th node.

7. The method for constructing a social network opinion competition model based on a neural network according to claim 1, characterized in that: The integration of the distributed consensus protocol into the k-WTA model is specifically as follows: The external input u in the opinion dynamic expression i (t) as the output of the k-WTA model; External input u i (t) is expressed as: Among them, v i (t) is the input of the k-WTA model and is expressed as: e i (t) is the error of opinion fit.

8. The method for constructing a social network opinion competition model based on a neural network according to claim 7, characterized in that: The obtaining the output of the k-WTA model comprises: The auxiliary variables are obtained by the state equation, which is expressed as: Among them, q i (t) is an auxiliary variable; n represents the number of all nodes in the social network; k represents the number of winners in the k-WTA model; γ represents the first convergence parameter, which is a positive real number used to adjust the convergence speed of the k-WTA model; Based on the auxiliary variables, the output of the k-WTA model is obtained through the output equation, and the output equation is expressed as: Among them, Φ Ω Represents the output equation function, and Ω=[0,1], defined as: λ represents the input correlation coefficient and satisfies in, and They represent the kth and k+1th large inputs respectively.

9. The method for constructing a social network opinion competition model based on a neural network according to claim 1, characterized in that: The definition of the opinion fit error includes: The expected opinions on the target social issue are defined as O e (t); The subject opinions related to the social environment are defined as O i (t); A mapping function is used to transform the expected opinion O e (t) and subject opinion O i (t) is defined as e(O i (t)-O e (t)), that is: e i (t); The MGNN model is obtained as follows: Let the opinion fit error e i (t) converges to zero, and the MGNN model is obtained based on the traditional GNN model, then the MGNN model is expressed as: Where T represents the transpose operation of the vector; Indicates O i The transpose of (t); θ(t) represents an adaptive coefficient, and the expression of θ(t) is: β represents the second convergence coefficient, which is used to adjust the convergence speed of the MGNN model.

10. A social network opinion competition model construction system based on neural network, characterized by: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1 to 9.

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