Dynamic mixed rumor refuting method fusing user emotional characteristics and keyboard-driving behaviors

Abstract

The invention provides a dynamic mixed rumor refuting method fusing user emotional characteristics and keyboard-driving behaviors, and belongs to the field of propagation dynamics. The method comprises the following steps: 1) introducing parameters in combination with an actual scene, depicting the influence of each factor on rumor propagation, and constructing a differential power system to simulate a propagation process; 2) analyzing strategies of both parties, and quantifying income; 3) establishing a dynamic game model according to the game relationship of the two parties; 4) deriving and solving an optimality system of the game model by using a Pontryagin maximum / minimum principle; 5) designing a forward and backward scanning method to provide a numerical solution; and 6) verifying performance advantages through multi-dimensional comparison, and proposing an optimal rumor refuting strategy. According to the method, the influence of the user emotion and the behavior of the Keyaban is considered, the established dynamic model is more suitable for rumor propagation in an online social network, a rumor refuting party can obtain an optimal rumor refuting result according to a behavior adjustment strategy of the rumor refuting party, and real-time effective control over rumor propagation is achieved through the dynamic mixed rumor refuting method provided by the invention.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of propagation dynamics and relates to a dynamic hybrid rumor-busting method fusing user emotional features and keyboard warrior behavior. BACKGROUND

[0002] With the innovation of communication technology, the Internet will have multiple social connections between individuals or institutions, forming online social networks (OSNs), which have become the core carriers of information acquisition and dissemination, providing convenient communication services and real-time information services for users. In the fields of instant messaging, information diffusion and public opinion monitoring, OSNs have triggered extensive discussions in the industry and academia. The high openness and sharing characteristics of OSNs have also led to problems such as rumors, malicious comments and false information, causing economic losses, triggering social panic or triggering public opinion incidents, and posing a threat to network security and social stability. Therefore, analyzing the propagation mechanism of rumors in OSNs and exploring efficient rumor-busting strategies have become important issues to be addressed.

[0003] The propagation of rumors in the network is complex, and scholars at home and abroad have proposed many models to simulate the evolution of rumor diffusion. Most of these models draw on the theory of epidemiology, dividing the group state to study the propagation law of rumors. On this basis, some people combine the structure of social networks and user attribute characteristics, and existing researches mostly use homogeneous mixing networks or scale-free network models to model OSNs. However, actual OSNs have complex topological structures, and each user can send and receive information, so individual interaction and network environment will affect rumor propagation. The node-based modeling method describes the evolution of user state probability through differential dynamic system, which can be applied to the description of propagation process in any network structure, so a more adaptable dynamic model can better present the dynamic evolution of rumors in OSNs.

[0004] To address the problem of rumors in OSNs, measures need to be taken to reduce their impact. Currently, there are two main suppression strategies: blocking rumor propagation paths and publishing true information to debunk rumors. However, a single strategy is difficult to deal with complex scenarios such as network attacks and malicious slander. Some research attempts to implement multiple strategies in coordination, but existing hybrid debunking strategies are mostly developed from the perspective of the debunking party, ignoring the antagonistic interaction between rumor-mongering and debunking, which limits the effectiveness of the strategy. In fact, both parties will adjust their behavior according to the other party's strategy to pursue the optimal result, so it is necessary to study hybrid strategies based on the interaction mechanism of both parties.

[0005] In the research of rumor control mixed strategy, user emotion and keyboard warrior behavior are key factors. User emotion can exacerbate rumor spread, making the public spread rumors in an irrational state; keyboard warriors use network anonymity to publish extreme statements, malicious speculation, and even fabricate false content, further accelerating rumor spread and undermining the authenticity of information dissemination. The interweaving of the two leads to a double dilemma for rumor control: simple fact clarification is difficult to quickly guide public emotions and may even trigger a backlash; keyboard warriors' incendiary rhetoric can interfere with information dissemination paths and weaken the effectiveness of official rumor refutation. To build a complete strategy system, we need to cut off the rumor spread chain from user emotions and keyboard warrior behavior. In summary, for the problem of rumor control in online social networks, we should consider user emotions and keyboard warrior behavior, combine the dynamic confrontation process of rumor-making and rumor-refutation, and conduct research on mixed rumor-refutation strategies. SUMMARY

[0006] Therefore, the purpose of the present application is to provide a dynamic mixed rumor-refutation method that integrates user emotional characteristics and keyboard warrior behavior.

[0007] To achieve the above purpose, the present application provides the following technical solutions:

[0008] A dynamic mixed rumor-refutation method that integrates user emotional characteristics and keyboard warrior behavior, comprising the following steps:

[0009] Step 1: Introduce specific parameters in combination with actual application scenarios to depict the influence of various factors, including user emotions and keyboard warrior behavior, on rumor spread, and construct a differential dynamic system to simulate the rumor spread process in online social networks;

[0010] Step 2: Analyze the strategy methods of rumor-makers and rumor-refuters, and quantify the benefits of both parties;

[0011] Step 3: Establish a dynamic game model based on the game relationship between the two parties;

[0012] Step 4: Use the Pontryagin maximum / minimum principle to derive an optimality system for solving the game model;

[0013] Step 5: Use the forward-backward scanning method to design an algorithm to provide numerical solutions for the optimality system;

[0014] Step 6: Compare the proposed method in multiple dimensions to verify its performance advantages and propose the best rumor-refutation strategy accordingly.

[0015] Optionally, the specific process of step 1 includes: based on graph theory, taking an undirected graph G = {U, E} as a network topology structure representing a social network, a node set U = {u1, u2, L, u N} corresponding to a user group in the social network, and an edge set E used to depict the information interaction association between users, (u i ,j )∈E represents that user i and user j have the ability to interact with information through a social network platform. An adjacency matrix A=[a ij ] N×N Mathematical description of network structure, if (u i , u j )∈E, then a ij =1, indicating that there is a possibility of information interaction between users, and if a ij =0, then the opposite.

[0016] In the online social network scenario, combined with the rumor propagation dynamics analysis, each ordinary user can be divided into the following five typical states when facing rumors: uncertain state (D(t)):

[0017] The user has not yet contacted the rumor and has no cognition of the existence and content of the rumor. Neutral state (T(t)): the user neither believes the rumor nor believes the truth, and is in the state of believing the rumor. Believing the rumor shows positive forwarding state (B P (t)): the user believes the rumor information transmitted on the network and shows positive and propagates. Believing the rumor shows negative forwarding state (B N (t)): the user believes the rumor information transmitted on the network and shows negative and propagates. Rumor state (R(t)): the user does not believe the rumor information and will not spread the rumor.

[0018] For this group of people who publish fierce remarks through the keyboard, occupy the moral high ground to criticize others, regardless of the truth, scold others or maliciously speculate on others, it is believed that there is such a state:

[0019] Keyboard warrior state (E(t)): habit of being dominated by personal emotions or biases, lack of cognition of objective laws of things, and not considering the authenticity and consequences of rumors.

[0020] When the rumor-busting approach implements blocking measures against malicious remarks and their propagation behaviors, the user may present the following state:

[0021] Isolation and immunity rumor (Q(t)): when the user account has the behavior of spreading such rumors, it will face speech restriction; at the same time, the related posts involving rumors will also be deleted.

[0022] Let X i (t) = 0, X i (t) = 1, X i (t) = 2, X i (t) = 3, X i (t) = 4, X i (t) = 5, X i(t) = 6 respectively represent the states of user i being in uncertain, neutral, believing rumor with positive retweet, believing rumor with negative retweet, keyboard warrior, disbelief and isolated state. D i (t), T i (t), B Pi (t), B Ni (t), E i (t), R i (t) and Q i (t) respectively represent the probability of user i being in the corresponding state at time t, and D i (t) + T i (t) + B Pi (t) + B Ni (t) + E i (t) + R i (t) + Q i (t) = 1. Then the vector M(t) = {D1(t),..., D N (t), T1(t),..., T N (t), B P1 ,..., B PN , B N1 ,, B NN , E1(t),..., E N (t) R1(t),..., R N (t)} represents the network state at time t.

[0023] In combination with the rumor propagation in online social networks, the following parameters are introduced to characterize the influence of different factors on the rumor propagation process, and each state will be converted under the action of these factors:

[0024] (i) (corresponding ): the probability of an uncertain user being converted into a user believing rumor and showing positive (negative) retweet under the influence of a friend believing rumor and showing positive (negative) retweet.

[0025] (ii) (corresponding ): the probability of an uncertain user being converted into a user believing rumor and showing positive (negative) retweet under the influence of rumor supporting information. Obviously, and are monotonically increasing functions, let

[0026] (iii) (corresponding ) : the probability that a neutral user, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active (passive) forwarder. Obviously, and are monotone increasing functions, let

[0027] (iv) b D (S BP ) : the probability that an uncertain (neutral) user, influenced by rumor clarifying information, turns into a user who does not believe the rumor. Obviously, b T (S BP ) = 0, b D (0) = b T (0) = 0, b D and b T are monotone increasing functions, let b = (b D , b T ).

[0028] (v) (S ) : the probability that a user who believes the rumor and behaves as an active (passive) forwarder, influenced by rumor clarifying information, turns into a user who does not believe the rumor. Obviously, and are monotone increasing functions, let

[0029] (vi) (S ) : the probability that a user who does not believe the rumor, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active (passive) forwarder. Obviously, and q R are monotone increasing functions, let

[0030] (vii) ω ED (S ET or ) : the probability that an uncertain (neutral or believes the rumor and behaves as a passive forwarder) user, influenced by a keyboard warrior friend, turns into a user who believes the rumor and behaves as an active forwarder.

[0031] (viii) the probability that a user who believes the rumor and behaves as a passive forwarder, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active forwarder. Obviously, and q R are monotone increasing functions, let

[0032] (ix)h E (S BQ )(corresponding to h B (S BQ )) is the probability that a keyboard warrior (believing rumors and behaving as an active forwarder) turns into an isolated user due to the measures taken by the network regulator. Obviously, h B (0) = h E = (0), h B and h E are monotone increasing functions, let h = (h B , h E ).

[0033] (x)l ER (S BQ ): the probability that a keyboard warrior turns into a non-rumor-believing user due to the measures taken by the network regulator. Obviously, l ER (0) = 0, l ER is a monotone increasing function.

[0034] (xi) (corresponding to ): the probability that a neutral user turns into a rumor-believing and active forwarder (or a rumor-believing and passive forwarder) due to the rumor propagation and discussion in the network.

[0035] (xii)θ D (corresponding to θ T , ): the probability that an uncertain (neutral, rumor-believing and active forwarder, rumor-believing and passive forwarder) user turns into a non-rumor-believing user.

[0036] (xiii)ε: the probability that an isolated user turns into a non-rumor-believing user due to the influence of the change in attitude towards rumors.

[0037] (xiii)α (corresponding to ρ): the probability that an uncertain user turns into a neutral (keyboard warrior) user due to the influence of rumor propagation and discussion in the network.

[0038] Then the rumor propagation evolution in the network is subject to the following differential dynamic system:

[0039]

[0040] where M(0) = M0.

[0041] Optionally, in step two, the strategies of rumor-mongers and rumor-busters are analyzed, and the benefits of both sides are quantified: we can represent rumor-mongers and rumor-busters as A and B, respectively, and now we need to develop corresponding strategies for both sides.

[0042] The rumor-mongering strategies that the rumor-mongering party can take are:

[0043] wherein C A (t) denotes the cumulative cost of spreading rumor-supporting content in the range [0, t], denotes its upper bound, and PC[0, T] denotes the set of all piecewise continuous functions defined in the interval [0, T].

[0044] The rumor-busting strategies that the rumor-busting party can take are:

[0045] wherein C BP (t) denotes the cumulative cost of pushing rumor-clearing information (facts) in the range [0, t], C BQ (t) denotes the cumulative cost of implementing regulatory measures by the network regulatory department, and denote its upper bound, respectively, and the rumor-busting party's growth rate at time t is S B = (S BP , S BQ ), PC[0, T] denotes the set of all piecewise continuous functions defined in the interval [0, T].

[0046] To quantify the rumor-mongering party's expected net income and the rumor-busting party's expected total loss, the following assumptions are made: the income created by a user who believes in the rumor and behaves as an active forwarder (a user who believes in the rumor and behaves as a passive forwarder or a keyboard warrior) for the rumor-mongering party in unit time is ( or ), and the loss caused by a user who believes in the rumor and behaves as an active forwarder (a user who believes in the rumor and behaves as a passive forwarder or a keyboard warrior) for the rumor-busting party in unit time is ( or ). Among them, the rumor-mongering party continuously outputs rumor content at a rate of S A to support the spread of rumors, while the rumor-busting party publishes clarifying information (or implements regulatory measures) at a rate of S BP (S BQ ) to curb the spread of rumors.

[0047] The rumor-mongering party's net income is:

[0048] wherein is the income brought by a user who believes in the rumor and behaves as an active forwarder, is the income brought by a user who believes in the rumor and behaves as a passive forwarder, The benefits brought to keyboard warrior users, S A (t)dt is the cost of publishing rumor supporting information.

[0049] The total loss of the rumor refuting party can be expressed as:

[0050] Wherein, L is the loss caused by the user who believes the rumor and behaves as positive forwarding, L BP (t)dt represents the cost of publishing the truth, S BQ (t)dt is the cost of implementing regulatory measures.

[0051] Optionally, in step three, according to the game relationship between the two parties, a dynamic game model is established: during the process of rumor spreading in the network, rumor-making behavior and rumor-refuting behavior show an antagonistic situation, and the two behaviors interact with each other. The game parties can make corresponding adjustments to their own strategies according to the behavior of the other party and the change of the environment, aiming to pursue the most favorable result. Among them, the goal of the rumor-making party is to maximize its own interest L A (S A ,S B ), while the rumor-refuting party strives to minimize its own loss L B (S A ,S B ). In view of this, we model this problem into a differential game model, when any party in the game cannot improve its income by changing its own strategy alone, at this time the game reaches the Nash equilibrium state of maximizing the income of each party.

[0052] If the strategy combination satisfies the following conditions, it can be called the Nash equilibrium of the game:

[0053]

[0054] From the perspective of game strategy, when B continues to adopt the rumor-refuting strategy , A will inevitably choose the rumor-making strategy to maximize its own interests, and when A insists on adopting the rumor-making strategy , B cannot effectively reduce the expected loss even if it deviates from the strategy . In summary of the above two cases, the strategy combination is acceptable to both A and B.

[0055] Assuming that the goal of A is to maximize the income L A (SA S B ), B wants to minimize its expected loss L B (S A ,S B ), where (S A ,S B ) ∈ ℜ A × B . The objective is to find the Nash equilibrium, the game model under rumor-mongering and refutation confrontation can be represented by a 22-tuple:

[0056] Optionally, in the step four, the Pontryagin maximum / minimum principle is applied to derive the optimality system for solving the game model:

[0057] According to the differential game theory, to derive the necessary condition of the Nash equilibrium, the Hamiltonian functions of the rumor-mongering party and the refutation party need to be constructed, and the specific content is as follows:

[0058]

[0059]

[0060] where, is the adjoint vector of H A , and is the adjoint vector of H B .

[0061] According to the Pontryagin maximum / minimum principle, the optimality system for solving the game model can be derived:

[0062]

[0063]

[0064] where 0 ≤ t ≤ T, 1 ≤ i ≤ N.

[0065] The boundary conditions are:

[0066]

[0067] The optimality system is composed of the differential dynamic system and the above equations, and by solving the system, the optimal rumor-mongering and refutation strategies can be obtained.

[0068] Optionally, in the step five, the forward-backward scanning method is used to design an algorithm to provide a numerical solution for the optimality system, which specifically includes:

[0069]

[0070] Optionally, in step six, the proposed method is compared in multiple dimensions to verify its performance advantage, and accordingly the best rumor-busting strategy is proposed: we implemented the proposed algorithm in the three real social network architectures of Facebook, Twitter and YouTube, and solved the optimality system to obtain the best rumor-busting strategy, thereby verifying the effectiveness of the method.

[0071] The beneficial effects of the present application are: the present application proposes a dynamic hybrid rumor-busting method that fuses user emotional characteristics and keyboard warrior behavior, including: 1) a node-based rumor propagation model is constructed, which fully considers the influence of user emotional characteristics and keyboard warrior behavior on rumor propagation, the dynamic evolution process of the model can reflect the competitive propagation of rumors and truth and the comprehensive effect of the regulatory department, and can be applied to any network architecture; 2) the process of rumor-making and rumor-busting is analyzed with the help of game theory, and a dynamic game model is constructed; 3) according to the Pontryagin maximum / minimum principle, the optimality system for solving the game model is derived, and an algorithm is designed to provide a numerical solution for the optimality system; 4) the effectiveness of the proposed method is proved by comparative experiments, and the best dynamic hybrid rumor-busting method can effectively reduce the loss of the rumor-busting party and improve the rumor suppression effect.

[0072] Other advantages, objects, and features of the present application will be apparent to those skilled in the art from the following specification, and it is intended to be covered by the following claims, insofar as is not inconsistent with the prior art. The objects and other advantages of the present application can be realized and attained by the embodiments particularly pointed out in the specification. BRIEF DESCRIPTION OF DRAWINGS

[0073] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings, in which:

[0074] Fig. 1 The process of dynamic hybrid rumor-busting in a social network considering user emotional characteristics and keyboard warrior behavior;

[0075] Fig. 2 Application scenario diagram of rumor propagation in a social network;

[0076] Fig. 3 Rumor propagation state transition diagram; DETAILED DESCRIPTION

[0077] The present application is illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar, but not necessarily identical, elements. The principles described herein can be employed in any of the embodiments or examples without departing from the spirit of the present application and the scope of the appended claims. The figures of the accompanying drawings in which like numbers refer to like components, unless otherwise specified, are as follows in which:

[0078] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:

[0079] The same or similar components in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only for illustrative purposes, and cannot be understood as a limitation of the present application, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0080] Referring to Figs. 1-3 The present application provides a dynamic mixed rumor-busting method fusing user emotional characteristics and keyboard warrior behavior, Fig. 1 To realize the flow chart.

[0081] Fig. 2 The application scenario of the present application is shown in the figure. The following description is made in conjunction with the drawings, including the following steps:

[0082] Optionally, step one specifically includes: according to the attitude difference of the user to the rumor, the state is divided, with the help of graph theory related theory, the user account is regarded as node, the friendship association in social network is regarded as edge, and relevant parameters are introduced to reflect the effect of actual factors on rumor transmission. Then the model is built, and the differential dynamic system is obtained, so as to realize the simulation of rumor transmission process in social network.

[0083] Fig. 2This is a diagram of the application scenario of rumor spread on social networks. In the online social network scenario, combined with the analysis of rumor propagation dynamics, each ordinary user can be divided into the following five typical states when facing rumors:

[0084] Uncertain state (D(t)): The user has not yet been exposed to the rumor and has no knowledge of the existence and content of the rumor.

[0085] Neutral state (T(t)): The user neither believes the rumor nor the truth and is in a neutral state.

[0086] Believing in rumors is reflected in the active forwarding state (B P (t)): Users believe in the rumor information spread on the Internet and spread it actively.

[0087] Believing in rumors is reflected in a passive forwarding state (B N (t)): The user believes the rumor information spread on the network and behaves negatively and spreads it. The state of not believing the rumor (R(t)): The user does not believe the rumor information and does not spread the rumor.

[0088] Regarding the group of people who make fierce remarks through keyboards, occupy the moral high ground to criticize others, and insult others or make malicious speculations about others regardless of the truth, we believe that there is a state: the keyboard warrior state (E(t)):

[0089] They are accustomed to letting personal emotions or prejudices dominate their opinions, lack the understanding of the objective laws of things, and do not consider the authenticity and consequences of rumors.

[0090] When rumor-busting agencies implement measures to block malicious speech and its spread, they often take measures such as deleting posts and banning users. At this time, users may appear in the following states:

[0091] Isolation immunity rumors (Q(t)): When a user account spreads such rumors, it will face a ban; at the same time, related posts involving the rumors will also be deleted.

[0092] Considering the spread of rumors in online social networks, we introduce the following parameters to characterize the impact of different factors on the rumor propagation process. Each state will change under the influence of these factors:

[0093] (i) (correspond ): The probability that an uncertain user is influenced by a friend who believes the rumor and actively forwards it (passively forwards it) and turns into a user who believes the rumor and actively forwards it (passively forwards it).

[0094] (ii) (correspond ) : the probability that an uncertain user, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active (passive) forwarder. Obviously, and are monotone increasing functions, let

[0095] (iii) (corresponding to ) : the probability that a neutral user, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active (passive) forwarder. Obviously, and are monotone increasing functions, let

[0096] (iv) b D (S BP ) (corresponding to b T (S BP )) : the probability that an uncertain (neutral) user, influenced by rumor clarifying information, turns into a user who does not believe the rumor. Obviously, b D (0) = b T (0) = 0, b D and b T are monotone increasing functions, let b = (b D , b T ).

[0097] (v) (corresponding to ) : the probability that a user who believes the rumor and behaves as an active (passive) forwarder, influenced by rumor clarifying information, turns into a user who does not believe the rumor. Obviously, and are monotone increasing functions, let

[0098] (vi) (corresponding to ) : the probability that a user who does not believe the rumor, influenced by rumor supporting information, turns into a user who believes the rumor and behaves as an active (passive) forwarder. Obviously, and q R are monotone increasing functions, let

[0099] (vii) ω ED (corresponding to ω ET or ): The probability that an uncertain user (neutral or believing the rumor and passively forwarding it) is influenced by a keyboard warrior friend and becomes a believer in the rumor and actively forwarding it.

[0100] (viii) The probability that a user who believes in a rumor and forwards it passively will be influenced by the rumor's supporting information and then become a user who believes in the rumor and forwards it actively. and q R is a monotonically increasing function, let

[0101] (ix)h E (S BQ )(corresponding to h B (S BQ )):The probability that a user who behaves as a keyboard warrior (believes rumors and actively forwards them) will be turned into an isolated user due to the measures taken by the Internet regulatory authorities. B (0) = h E =(0),h B and h E is a monotonically increasing function, let h=(h B ,h E ).

[0102] (x)l ER (S BQ ): The probability that a user who behaves like a keyboard warrior will turn into a user who does not believe in rumors due to the measures taken by the Internet regulatory authorities. ER (0)=0,l ER is a monotonically increasing function.

[0103] (xi) (correspond ) is the probability that a neutral user will be influenced by the spread and discussion of rumors on the network and become a rumor believer and actively forward (passively forward) the rumor.

[0104] (xii)θ D (corresponding to θ T , ): The probability that an uncertain (neutral, believing the rumor and actively forwarding it, believing the rumor and passively forwarding it) user will turn into a user who does not believe the rumor.

[0105] (xiii)ε: The probability that an isolated user becomes a user who does not believe the rumor due to the change in attitude towards the rumor.

[0106] (xiii) α (corresponding to ρ): The probability that an uncertain user is influenced by the spread of rumors and discussions on the network and turns into a neutral (keyboard warrior) user.

[0107] Fig. 3 The state transition graph corresponding to the rumor propagation model is shown in the following differential dynamic system:

[0108]

[0109] Optionally, step two specifically includes: analyzing the strategy of the rumor maker and the rumor refuter, quantifying the benefits of both parties, and establishing a dynamic game model according to the game relationship between the two parties.

[0110] The rumor-making strategy that a rumor maker can adopt is:

[0111] Wherein C A (t) represents the cumulative cost of spreading rumor content in the range of [0, t], PC[0, T] represents the set of all piecewise continuous functions defined in the interval [0, T].

[0112] The rumor refuting strategy that a rumor refuter can adopt is:

[0113] Wherein, C BP (t) represents the cumulative cost of pushing rumor clarification information (facts) in the range of [0, t], C BQ (t) represents the cumulative cost of implementing regulatory measures by the network regulatory department, and respectively represent the upper bounds, and the growth rate of the rumor refuter at time t is S B = (S BP , S BQ ), PC[0, T] represents the set of all piecewise continuous functions defined in the interval [0, T].

[0114] To quantify the expected net benefit of the rumor maker and the expected total loss of the rumor refuter, the following assumptions are made: a user who believes the rumor and behaves as an active forwarder (believes the rumor and behaves as a negative forwarder or keyboard warrior) creates a benefit of ( or ) for the rumor maker per unit time, and a user who believes the rumor and behaves as an active forwarder (believes the rumor and behaves as a negative forwarder or keyboard warrior) causes a loss of ( or ) for the rumor refuter per unit time. Wherein, the rumor maker continuously outputs rumor content at a rate of S A to support rumor propagation, and the rumor refuter pushes rumor clarification information (facts) at a rate of SBP (S BQ ) of the rate of release of clarifying information (or implementation of regulatory initiatives) to curb the spread of rumors.

[0115] The net benefit of the rumor-mongers is:

[0116] Where, is the benefit of believing the rumor and acting as an active retweeting user, is the benefit of believing the rumor and acting as a passive retweeting user, is the benefit of the keyboard warrior user, S A (t)dt is the cost of releasing rumor-supporting information.

[0117] The total loss of the rumor-busters can be expressed as:

[0118] Where, is the loss of believing the rumor and acting as an active retweeting user, is the loss of believing the rumor and acting as a passive retweeting user, is the loss of the keyboard warrior user, S BP (t)dt represents the cost of releasing the truth, S BQ (t)dt is the cost of implementing regulatory measures.

[0119] During the spread of rumors on the network, rumor-mongering and rumor-busting behaviors present an antagonistic situation, and the two interact with each other. Both parties can adjust their own strategies according to the behavior of the other party and the changes in the environment, in order to pursue the most favorable results. Among them, the goal of the rumor-mongers is to maximize their own benefits L A (S A ,S B ), while the rumor-busters strive to minimize their own losses L B (S A ,S B ). In view of this, we model this problem as a differential game model, when any party in the game cannot improve its own benefits by changing its own strategy alone, at this time the game reaches the Nash equilibrium state of maximizing the benefits of all parties.

[0120] If the strategy combination satisfies the following conditions, it can be called the Nash equilibrium of the game:

[0121]

[0122] From the perspective of game strategy, when B continues to adopt the rumor-busting strategy At this time, A will choose rumor strategy to maximize its own interests When A insists on rumor strategy , B can not effectively reduce the expected loss even if deviating from the strategy Combining the above two cases, the strategy combination is acceptable to both A and B.

[0123] Assume that A's goal is to maximize the revenue L A (S A ,S B ), and B wants to minimize its expected loss L B (S A ,S B ), where (S A ,S B ) ∈ Ù A × B . The purpose is to find the Nash equilibrium, and the game model under rumor and rumor confrontation can be represented by a 22-tuple:

[0124] Optionally, step three specifically includes: using the Pontryagin maximum / minimum principle, deriving the optimality system for solving the game model, using the forward-backward scanning method, and designing an algorithm to provide numerical solutions for the optimality system.

[0125] According to the Pontryagin maximum / minimum principle, the optimality system for solving the game model can be derived:

[0126]

[0127]

[0128] Its boundary conditions are:

[0129]

[0130] The optimality system is composed of the differential dynamic system and the above equations. By solving this system, the optimal rumor and rumor strategy can be obtained.

[0131] Further, an algorithm is designed to solve the optimality system, i.e., to find the Nash equilibrium.

[0132]

[0133] Optionally, step four specifically includes: multi-dimensional comparison of the proposed method, verifying its performance advantage, and accordingly proposing the best rumor-busting strategy: we implemented the proposed algorithm in the three real social network architectures of Facebook, Twitter and YouTube, solved the optimality system to obtain the best rumor-busting strategy, thereby verifying the effectiveness of the method.

[0134] After the above steps are completed, a dynamic hybrid rumor-busting method fusing user emotional features and keyboard warrior behavior is provided. When rumors are widely spread in social networks, the rumor-busting party can consider the influence of user emotions and keyboard warrior behavior on rumor spreading, and adopt truth spreading and rumor blocking methods to control rumors.

[0135] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and all should be covered in the scope of the claims of the present application.

Claims

1. A dynamic hybrid rumor-busting method that integrates user emotional characteristics and keyboard warrior behavior, characterized by: The method comprises the following steps: Step 1: Introduce specific parameters based on actual application scenarios to characterize the impact of various factors, including user emotions and keyboard warrior behavior, on rumor propagation, and construct a differential dynamic system to simulate the rumor propagation process in online social networks; Step 2: Analyze the strategies and methods of rumor-mongers and rumor-debunkers, and quantify the benefits for both parties; Step 3: Establish a dynamic game model based on the game relationship between the two parties; Step 4: Use Pontryagin's maximum / minimum principle to derive the optimality system for solving the game model; Step 5: Use the forward and backward scanning method to design an algorithm to provide a numerical solution for the optimal system; Step 6: Compare the proposed methods in multiple dimensions to verify their performance advantages and propose the best rumor-busting strategy accordingly.

2. A dynamic hybrid rumor-refuting method that integrates user emotional characteristics and keyboard warrior behavior according to claim 1, characterized in that: The specific process of step 1 includes: based on graph theory, taking the undirected graph G = {U, E} as the network topology structure to represent the social network, and the node set U = {u1, u2, L, u N } corresponds to the user group in the social network, and the edge set E is used to characterize the information interaction between users. i ,u j )∈E indicates that user i and user j have the ability to exchange information through the social network platform. Using the adjacency matrix A=[a ij ] N×N Mathematically describe the network structure. If (u i ,u j )∈E, then a ij =1, indicating the possibility of information interaction between users. If a ij =0, the opposite is true. In online social network scenarios, combined with analysis of rumor propagation dynamics, each ordinary user can be divided into the following five typical states when faced with rumors: Uncertain state (D(t)): The user has not yet been exposed to the rumor and has no knowledge of the existence and content of the rumor. Neutral state (T(t)): The user neither believes the rumor nor the truth and is in a neutral state. Believing in rumors is reflected in the active forwarding state (B P (t)): Users believe in the rumor information spread on the Internet and spread it actively. Believing in rumors is reflected in a passive forwarding state (B N (t)): Users believe the rumor information spread on the Internet and behave negatively and spread it. Rumor-disbelief state (R(t)): The user does not believe the rumor information and will not spread the rumor. Regarding the group of people who make fierce remarks through keyboards, occupy the moral high ground to criticize others, insult others or make malicious speculations about others regardless of the facts, I believe that this situation exists: Keyboard warrior status (E(t)): They are accustomed to letting personal emotions or prejudices dominate their opinions, lack the understanding of the objective laws of things, and do not consider the authenticity and consequences of rumors. When rumor-busting agencies implement measures to block malicious speech and its spread, they often take measures such as deleting posts and banning users. At this time, users may appear in the following states: Isolation immunity rumors (Q(t)): When a user account spreads such rumors, it will face a ban; at the same time, related posts involving the rumors will also be deleted. Let X i (t) = 0, X i (t) = 1, X i (t) = 2, X i (t) = 3, X i (t) = 4, X i (t) = 5, X i (t) = 6 indicates that user i is in the uncertain, neutral, believing rumors and actively forwarding, believing rumors and passively forwarding, keyboard warrior, not believing, and isolated states. i (t), T i (t), B Pi (t), B Ni (t), E i (t), R i (t) and Q i (t) represent the probability that user i is in the corresponding state at time t, and D i (t)+T i (t)+B Pi (t)+B Ni (t)+E i (t)+R i (t)+Q i (t)=1. Then the vector M(t)={D1(t),…,D N (t),T1(t),…,T N (t),B P1 ,…,B PN ,B N1 ,…,B NN ,E1(t),…,E N (t)R1(t),…,R N (t)} represents the network status at time t. Considering the spread of rumors in online social networks, we introduce the following parameters to characterize the impact of different factors on the rumor propagation process. Each state will change under the influence of these factors: (i) (correspond ): The probability that an uncertain user is influenced by a friend who believes the rumor and actively forwards it (passively forwards it) and turns into a user who believes the rumor and actively forwards it (passively forwards it). (ii) (correspond ): The probability that an uncertain user is influenced by the rumor supporting information and becomes a believer in the rumor and actively forwards (or passively forwards) the rumor. Obviously, and is a monotonically increasing function, let (iii) (correspond ): The probability that a neutral user is influenced by the rumor-supporting information and becomes a user who believes the rumor and actively forwards (or passively forwards). Obviously, and is a monotonically increasing function, let (iv)b D (S BP )(corresponding to b T (S BP )):The probability that an uncertain (neutral) user will be influenced by the rumor clarification information and become a user who does not believe the rumor. Obviously, b D (0) = b T (0) = 0, b D and b T is a monotonically increasing function, let b=(b D ,b T ). (v) (correspond ): The probability that a user who believes in a rumor and actively forwards it (or passively forwards it) is influenced by the rumor clarification information and becomes a user who does not believe the rumor. Obviously, and is a monotonically increasing function, let (vi) (correspond ): The probability that a user who does not believe the rumor is influenced by the information supporting the rumor and becomes a user who believes the rumor and actively forwards (or passively forwards). Obviously, and q R is a monotonically increasing function, let (vii)ω ED (corresponding to ω ET or ): The probability that an uncertain user (neutral or believing the rumor and passively forwarding it) is influenced by a keyboard warrior friend and becomes a believer in the rumor and actively forwarding it. (viii) The probability that a user who believes in a rumor and forwards it passively will be influenced by the rumor's supporting information and then become a user who believes in the rumor and forwards it actively. and q R is a monotonically increasing function, let (ix)h E (S BQ )(corresponding to h B (S BQ )):The probability that a user who behaves as a keyboard warrior (believes rumors and actively forwards them) will be turned into an isolated user due to the measures taken by the Internet regulatory authorities. B (0) = h E =(0),h B and h E is a monotonically increasing function, let h=(h B ,h E ). (x)l ER (S BQ ): The probability that a user who behaves like a keyboard warrior will turn into a user who does not believe in rumors due to the measures taken by the Internet regulatory authorities. ER (0)=0,l ER is a monotonically increasing function. (xi) (correspond ) is the probability that a neutral user will be influenced by the spread and discussion of rumors on the network and become a rumor believer and actively forward (passively forward) the rumor. (xii)θ D (correspond ): The probability that an uncertain (neutral, believing the rumor and actively forwarding it, believing the rumor and passively forwarding it) user will turn into a user who does not believe the rumor. (xiii)ε: The probability that an isolated user becomes a user who does not believe the rumor due to the change in attitude towards the rumor. (xiii) α (corresponding to ρ): The probability that an uncertain user is influenced by the spread of rumors and discussions on the network and turns into a neutral (keyboard warrior) user. The evolution of rumor propagation on the Internet obeys the following differential dynamic system: Where M(0)=M0.

3. The dynamic hybrid rumor-refuting method that integrates user emotional characteristics and keyboard warrior behavior according to claim 2 is characterized by: In the second step, we can represent the rumor-mongering party and the rumor-refuting party as A and B respectively. Now we need to formulate corresponding strategies for both parties. The rumor-mongering strategies that a party may adopt are: in C A (t) refers to the cumulative cost of spreading rumor-supporting content in the range [0, t], Represents its upper bound, PC[0,T] represents the set of all piecewise continuous functions defined in the interval [0,T]. The rumor-refuting strategies adopted by participants are: in, C BP (t) refers to the cumulative cost of pushing rumor-clarification information (facts) within the range [0, t], C BQ (t) refers to the cumulative cost of regulatory measures implemented by network regulatory authorities, and They represent their upper bounds respectively, and the growth rate of the rumor-refuting party at time t is S B =(S BP ,S BQ ), PC[0,T] represents the set of all piecewise continuous functions defined in the interval [0,T]. In order to quantify the expected net profit of the rumor-monger and the expected total loss of the rumor-refuting party, the following assumption is made: the profit created by a user who believes the rumor and actively forwards it (believes the rumor and passively forwards it or acts as a keyboard warrior) for the rumor-monger in unit time is The loss caused to the rumor-refuting party by a user who believes the rumor and actively forwards it (believes the rumor and passively forwards it or acts as a keyboard warrior) per unit time is Among them, the rumor-mongering party used S A The rumor content is continuously output at a rate of S to support the spread of rumors, while the rumor refutation party responds at a rate of S BP (S BQ ) to release clarifying information (or implement regulatory measures) at a reasonable rate to curb the spread of rumors. The net profit of the rumormonger is: in, To believe the rumor and actively forward it to the user, For those who believe the rumors and behave passively in forwarding the users, Benefits brought to keyboard warrior users, S A (t)dt is the cost of publishing information supporting the rumor. The total loss of the rumor-refuting party can be expressed as: in, Losses caused by users who believed in rumors and actively forwarded them. Losses caused by users who believed rumors and passively forwarded them. For the losses caused by keyboard warrior users, S BP (t)dt represents the cost of publishing the truth, S BQ (t)dt is the cost of implementing regulatory measures.

4. The intelligent hybrid rumor-refuting method based on rumor-mongering and rumor-refuting confrontation according to claim 3 is characterized by: In step 3, a dynamic game model is established based on the game relationship between the rumor-mongering party and the rumor-refuting party: during the spread of rumors on the Internet, rumor-mongering and rumor-refuting behaviors present a confrontational situation, and the two interact with each other. The two parties in the game can adjust their own strategies according to the other party's behavior and changes in the environment, aiming to achieve the most favorable results. Among them, the goal of the rumor-monger is to achieve its own interests. A (S A ,S B ) is maximized, while the rumor-refuting party strives to make its own losses B (S A ,S B ) is minimized. Therefore, we model this problem as a differential game model. When neither party in the game can improve its profit by changing its own strategy alone, the game reaches a Nash equilibrium state where all parties maximize their profits. If the strategy combination If the following conditions are met, it can be called the Nash equilibrium of the game: From the perspective of game strategy, when B continues to adopt the rumor-refuting strategy In order to maximize its own interests, A will inevitably choose the rumor-mongering strategy. And when A insists on using the rumor-mongering strategy Even if B deviates from the strategy It is also impossible to effectively reduce the expected loss. Combining the above two situations, the strategy combination It is acceptable to both A and B. Assume that A's goal is to maximize the profit L A (S A ,S B ), B hopes to minimize its expected loss L B (S A ,S B ), where (S A ,S B )∈ゥ A × B The goal is to find the Nash equilibrium. The game model under the confrontation between rumor-mongering and rumor-refuting can be represented by a 22-tuple:

5. The dynamic hybrid rumor-refuting method that integrates user emotional characteristics and keyboard warrior behavior according to claim 4 is characterized by: In step 4, the Pontryagin maximum / minimum principle is used to derive the optimality system for solving the game model. According to differential game theory, in order to derive the necessary conditions for Nash equilibrium, it is necessary to construct the Hamiltonian functions of the rumor-mongering party and the rumor-refuting party: in, It is H A The adjoint vector of It is H B The adjoint vector of . Based on differential game theory, the optimality system provides a method for finding Nash equilibrium, which gives the necessary conditions for the Nash equilibrium of the proposed model. By utilizing this system, the solution to the game problem can be found. According to Pontryagin's maximum / minimum principle, we can obtain the optimal system for solving the game model: Its boundary conditions are: The optimality system is composed of the differential dynamics system and the above equations.

6. The dynamic hybrid rumor-refuting method that integrates user emotional characteristics and keyboard warrior behavior according to claim 5 is characterized by: In step five, a forward-backward scanning method is used to design an algorithm to provide a numerical solution for the optimal system, thereby obtaining the best rumor-mongering and rumor-refuting strategies.

7. The dynamic hybrid rumor-refuting method that integrates user emotional characteristics and keyboard warrior behavior according to claim 6 is characterized by: In step six, we conduct a multi-dimensional comparison of the proposed method to verify its performance advantages and propose an optimal rumor-debunking strategy based on this. We implement the proposed algorithm on three real social network architectures: Facebook, Twitter, and YouTube. By solving the optimality system to obtain the optimal rumor-debunking strategy, we verify the effectiveness of the method.

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