Methods for predicting the spread of intentional topics

Abstract

This invention relates to a method for predicting the spread of intentional topics. The method includes: acquiring topic data online in real-time from social networks; preprocessing this data to obtain basic user information, user historical behavior, and basic topic information; extracting factors influencing the spread of intentional topics; constructing the message influence of the intentional topic based on these factors; combining the message influence with a Bayesian linear regression model to dynamically quantify users' emotional states towards the topic, obtaining the proportion of users exhibiting different emotional states; combining the message influence with an Ising model to predict the transitions between different emotional states of users towards the topic, obtaining the probability of these transitions; and constructing a dynamic equation based on this probability, combined with an SVICR model; solving the dynamic equation to obtain the set of users' emotional states towards the topic at different times during the spread of the intentional topic, from which the spread trend of the intentional topic is obtained. This invention can accurately predict the spread trend of intentional topics.

Description

Technical Field

[0001] This invention belongs to the field of Internet application technology, and in particular relates to a method for predicting the spread of intentional topics. Background Technology

[0002] Topics play a crucial role in communication, helping people connect, exchange ideas, share information, and establish shared interests. With the rapid development of the internet, numerous topics have spread quickly online, and users have posted a wide variety of topics, including intentional topics. Intentional topics are specific topics designed to guide and influence users' thinking, attitudes, and behaviors. On social media and online platforms, the spread of intentional topics can have a wide-ranging impact, including shaping public opinion, influencing social dynamics, and driving business goals. Therefore, researching how to control and guide the spread of intentional topics has significant theoretical and practical value. In recent years, academic experts have increasingly used social psychology to study topic dissemination.

[0003] Current research on this topic mainly focuses on two major directions: First, based on the classic infectious disease dynamics model, the model is improved by further segmenting user states to study the spread of the topic on social networks. Second, machine learning or deep learning is used to extract information data from social networks to effectively model and predict the spread of the topic.

[0004] In recent years, researchers have studied different psychological states of users and their characteristics on social networks, primarily based on traditional infectious disease models, proposing improvements for different states. Users' trust levels are a factor worth considering. Urena R, Kou G, Dong Y, et al. (A review on trust propagation and opinion dynamics in social networks and group decision making frameworks[J]. Information Sciences, 2019, 478:461-475) found a close relationship between trust, reputation, and influence, and categorized trust levels into trust, distrust, hesitation, and conflict. In social networks, users establish various explicit or implicit social relationships, using the network as a platform to disseminate and share their information, opinions, and suggestions. In these scenarios, the dissemination of information relies on the level of trust and influence among users. Summary of the Invention

[0005] To address the above challenges, this invention proposes a method for predicting the spread of intentional topics, which includes:

[0006] S1: Obtain topic data online in real time from social networks, and after preprocessing, obtain basic user information, user historical behavior and basic topic information;

[0007] S2: Extract factors that influence the spread of intentional topics from user basic information, user historical behavior and topic basic information, and construct the message influence of intentional topics based on the factors;

[0008] S3: Combine the influence of the message with a Bayesian linear regression model to dynamically quantify users' emotional state towards the topic and obtain the proportion of users who present different emotional states towards the topic.

[0009] S4: Combine the message influence with the Ising model to predict the user's different emotional state transitions on the topic, and obtain the probability of the user's different emotional state transitions on the topic.

[0010] S5: Based on the proportion of users exhibiting different emotional states towards a topic, the probability of users switching between different emotional states towards a topic, and the SVICR model, construct dynamic equations;

[0011] S6: Solve the dynamic equation to obtain the set of user sentiment states towards the topic at different times during the dissemination of the intentional topic, and obtain the dissemination trend of the intentional topic based on the set of sentiment states.

[0012] The beneficial effects of this invention are as follows: This invention focuses on the relationship between users and between users and topics. By combining user characteristics, information about the topic itself, and the dissemination capabilities of the topic network, it can accurately simulate the dissemination trend of intentional topics in social networks, as well as the changes in the dissemination trend of intentional topics after control measures are implemented. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the steps of an embodiment of the present invention;

[0014] Figure 2 This is a schematic diagram illustrating the process of spreading intentional topics in this invention;

[0015] Figure 3 This is a schematic diagram of the user emotional response mechanism in this invention;

[0016] Figure 4 This is a schematic diagram of user emotion transformation in this invention;

[0017] Figure 5 This is a schematic diagram illustrating the optimized control of intentional topic propagation in this invention. Detailed Implementation

[0018] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate; this is merely a way of distinguishing objects with the same attributes in the embodiments of this application.

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In studying the spread of intentional topics, an interesting phenomenon was discovered: Initially, each user has their own thoughts and behaviors. However, due to the influence of friends and the topic itself, as well as psychological biases and distrust mechanisms, users may become distrustful of the topic and seek verification. During the spread of the topic, users may become disseminators because they discover the information is true after their friends' involvement and verification; conversely, they may become users who inhibit the topic because they discover it carries false information. Although many scholars, both Chinese and foreign, have conducted a series of studies on topic spread models and the control of topic spread, the research on intentional topics still faces the following challenges:

[0021] 1. The diversity and dynamism of user states. In social networks, when users encounter information on intentional topics, they make different choices based on their individual emotions towards the topic, resulting in different user states. Furthermore, user states change constantly during the dissemination of the topic, making the dynamic quantification of user states a challenge.

[0022] 2. User trust issues. Intentional topics are purposeful, and users may have trust issues with such topics, leading to skepticism and a need to verify the information. Traditional information dissemination models are not well-suited to describe these types of topics, making it challenging to incorporate appropriate states into the dissemination model.

[0023] 3. Uncertainty of positive and negative feedback in intentional topics. The impact of intentional topics after dissemination is uncertain, requiring dynamic control strategies for optimization. Controlling the impact of topics with optimal control costs presents challenges.

[0024] This invention proposes a method for predicting the spread of intentional topics, the method comprising:

[0025] S1: Obtain topic data online in real time from social networks, and after preprocessing, obtain basic user information, user historical behavior, and basic topic information.

[0026] Specifically, raw topic data is obtained from publicly available datasets on platforms such as Weibo and Twitter. This topic data is unstructured and cannot be directly used for data analysis. Data preprocessing (such as simple data cleaning) can structure most of this unstructured data. Data preprocessing includes removing duplicate data and cleaning up invalid information.

[0027] The user's basic information includes the number of followers and the number of friends.

[0028] The user's historical behavior includes the user's historical participation in the dissemination of topics (such as liking, saving, forwarding, blocking, etc.) as well as the user's own behavior of posting topics.

[0029] The basic information of the topic includes the topic's content focus, keywords, source, and popularity (such as number of likes, shares, and favorites).

[0030] In social networks, user behavior during topic dissemination is influenced by various factors, such as user sentiment compatibility, the influence of relevant users, and the topic's popularity. Based on this, this invention extracts factors influencing user behavior from both user and topic perspectives.

[0031] S2: Extract factors that influence the spread of intentional topics from user basic information, user historical behavior and topic basic information, and construct the message influence of intentional topics based on the factors.

[0032] Furthermore, the factors influencing the spread of intentional topics include user factors and topic factors. The user factors include user sentiment matching degree (Fit(U)). i User activity (Positivity) i User influence (U) i ) and user credibility (U i The topic factors include Popularity(t) and Origin(t).

[0033] The extraction of user factors specifically includes:

[0034] S211: Calculate the user's emotional compatibility Fit(U) i )

[0035] User sentiment matching reflects whether a user has an initial emotional connection to a topic. During topic dissemination, user participation is influenced by this initial emotion. User loyalty reflects their level of trust and satisfaction with the e-commerce platform. The higher the degree of matching between a user's sentiment and the sentiment conveyed by the current topic information, the greater the probability of the user participating in topic dissemination. By extracting user sentiment tags and keywords from the topic content, the Jaccard similarity coefficient is used to measure the matching degree between user sentiment and topic tags, defining user sentiment matching Fit(U i )for:

[0036]

[0037] Here, Label(Ui) represents the high-frequency words used in the user's historical behavior, and Words(msg) represents the set of keywords in the intent topic.

[0038] S212: Calculate user activity (U i )

[0039] User engagement includes the number of tweets a user posts and the number of tweets they retweet on social networks, which to some extent influences the probability of a user participating in topic dissemination. Generally, the likelihood of a user participating in the dissemination of an intentional topic is directly proportional to their engagement, defined as Positivity(U). i )for:

[0040] Positivity (U i )=α*Num[orig(U i )]+Num[forw(U i (2)

[0041] Among them, Positivity (U i ) represents the level of engagement of the i-th user in the topic, Num[orig(U i )] represents user U i The number of Weibo posts published before the topic appeared, Num[forw(U i )] represents user U i The number of Weibo posts forwarded before the topic appeared. Since users who frequently forward Weibo posts are more likely to forward topics, and the number of original Weibo posts from ordinary users is far less than the number of forwarded Weibo posts, a weakening factor α is defined before the original Weibo posts to reduce the influence of original Weibo posts on this feature, where α∈[0,1].

[0042] S213: Calculating User Influence (U i )

[0043] User influence refers to the degree to which a user's participation in a topic affects their friends' participation in that topic. The greater a user's influence, the higher the likelihood that they will influence their friends to participate in and spread the topic. User influence includes the average number of retweets and likes on a user's original Weibo posts. User influence (Influence) is defined as... i )for:

[0044]

[0045] Among them, Influence (U i ) represents the i-th user U i The influence of participating in this topic This represents the average number of reposts of the i-th user's original Weibo post. This represents the average number of likes for the i-th user's original Weibo post.

[0046] S214: Calculate user credibility (U i )

[0047] Social networks often have fake followers and paid trolls, which need to be identified. A user's credibility can be judged by whether it's an official account, the level of their followers, and their interactions with friends.

[0048] Define user credibility (Credibility) i )for:

[0049]

[0050] Among them, Credibility(U i ) represents the i-th user U i The credibility of participating in this topic, baseCre represents the base credibility of all users, baseCre∈(0,1), s authGra(U i ) represents the user's official account level, fansGra(U i ) represents the user's fan level, and α represents the decay factor; Num[Interact(U i ] represents the i-th user U i The total number of interactions (including likes, favorites, shares, and blocks) with messages posted by their friends, Num[Interacted(U i ] represents the i-th user U i The total number of times a posted message is interacted with by friends (including likes, favorites, shares, and blocks), where β represents the first decay coefficient and γ represents the second decay coefficient, β and γ ∈ (0, 1). The smaller the values ​​of β and γ, the better the interaction for the i-th user U. iThe less credible something is, the less effective it is in spreading the topic; conversely, the more credible it is, the greater its influence.

[0051] The emotional attitude of high-quality topic commenters is crucial for identifying intentional topics, and high-quality users often represent official or celebrity accounts, but official accounts generally have higher credibility than celebrity accounts. Therefore, a decay factor α∈[0,1] is used to weaken the impact of celebrity accounts on the overall credibility of users.

[0052] The topic factors include Popularity(t) and Origin(t).

[0053] S221: Calculate the topic popularity(t)

[0054] Topic popularity is defined as the amount of traffic a topic receives, that is, its popularity online. Any topic, after being published, will reach a peak in dissemination and then decline over time, eventually reaching a low level. This decline process is similar to the half-life of physical elements; therefore, this invention introduces a half-life function to describe the decline process of topic popularity.

[0055] The topic popularity(t) is defined as:

[0056]

[0057] Where t represents the current moment of the topic's popularity decay process, t0 represents the start moment of the topic's popularity decay process, and w represents the regularization factor, which is set to 100.

[0058] S222: Topic source: Origin(t)

[0059] The source of a topic refers to the event, action, message, opinion, or other factor that initially raises or triggers the topic. Topic sources can be diverse, including media reports, social media, public discussions, or personal opinions. Among these sources, the more professional and authoritative the topic initiator, the greater their influence on users.

[0060] Define the topic source Origin(t) as:

[0061] Origin(t) = {M, S, D, P} (6)

[0062] Where t represents the current moment in the process of the topic's popularity waning, M represents media reports, S represents social media, D represents public discussion, and P represents personal opinions.

[0063] Intentional topic message influence refers to the ability of a topic to spread on social networks and the degree of its impact on users.

[0064] When a topic spreads, the factors that determine the impact of an intentional topic message include topic factors and user factors. Topic factors include the topic's popularity and its source, while user factors include the relevance of user emotions to the topic, user engagement, user influence, and user credibility.

[0065] The message influence of intentional topics is constructed based on the extracted factors that influence the spread of intentional topics.

[0066] The message influence of intentional topics is defined as:

[0067]

[0068] Among them, fac topic This refers to the topic factor in the influence of a message, fac user This represents the user factor in the message's influence, where Popularity(t) represents the topic's popularity, Origin(t) represents the topic's source, and Fit(U) represents the user factor. i ) represents user sentiment matching degree, Positivity (U i ) represents user engagement, Influence (U i ) represents user influence and Credibility (U i This indicates the user's credibility.

[0069] Figure 3 This is a schematic diagram of the user emotional response mechanism in this invention.

[0070] S3: Combine the influence of the message with a Bayesian linear regression model to dynamically quantify users' emotional state towards the topic and obtain the proportion of users who present different emotional states towards the topic.

[0071] Reference Figure 3 As shown, considering that the Bayesian linear regression model can more flexibly handle situations with incomplete data or high noise levels, and combining user factors and topic factors, the calculation formula for dynamically quantifying user sentiment is as follows:

[0072] ERM(U i )=ω1*fac topic +ω2*fac user +ε (8)

[0073] Where ERM(Ui) represents the emotional response effect of the i-th user to the intended topic, ω1 represents the first weight coefficient obtained by training and fitting the Bayesian linear regression model, and fac topic Indicates topic factors, fac userLet ω1 represent the user factor, ω2 represent the first weight coefficient obtained by training and fitting the Bayesian linear regression model, and ε be the error term. In the prior parameter settings, the prior distribution of the weight coefficients ω1 and ω2 in this invention is a Gaussian distribution ω~N(0,σ). 2 ), σ 2 This represents the variance of the weighting coefficients.

[0074] After encountering a message with an intentional topic, the user will decide whether to spread the intentional topic according to formula (8). The user will be in one of five states: users who have not yet encountered the topic information are in a susceptible state (S); users who have encountered the topic and seek verification of the topic due to the doubt mechanism are in a verification state (V); users who believe the topic information and spread it are in an infected state (I); users who seek verification of the topic and do not trust the topic and inhibit its spread are in a constrained state (C); and users who are immune to this type of information after being exposed to too much information are in an immune state (R).

[0075] The SIR (Susceptible-Infected-Recovered Model) is a classic infectious disease model and an abstract description of the information transmission process. In the SIR model, the population is divided into three categories: susceptible (S), infected (I), and recovered (R).

[0076] In this invention, during the dissemination of intentional topics, based on the SIR model and the psychological mechanism of doubt, an optimized intentional topic dissemination control dynamics model, SVICR, is constructed by introducing the Verify (V) and Constraint (C) states arising from questioning. This model is then applied to predict the dissemination trend of intentional topics. In the SVICR model, users exhibit five states: susceptible (S), verify (Q), infected (I), inhibited (C), and immune (R).

[0077] Figure 4 This is a schematic diagram of user emotion transformation in this invention.

[0078] S4: Combine the aforementioned message influence with the Ising model to predict the user's different emotional state transitions towards the topic, and obtain the probability of the user's different emotional state transitions towards the topic.

[0079] Considering the mutual influence of emotional state changes between adjacent users and the updating of states over time, this invention introduces the Ising model from statistical physics to simulate user state transitions and constructs a user state transition mechanism.

[0080] Reference Figure 4 As shown, the process of user state transition using the user state transition mechanism specifically includes:

[0081] S401: Define the state space: Define the user's emotional state toward the topic as a state space, which includes the vulnerable state (S), the seeking state (Q), the infected state (I), the inhibited state (C), and the immune state (R).

[0082] Based on the idea of ​​the Ising model, an energy value is assigned to each state, and the energy value reflects the stability of the user in that state.

[0083] S402: Define the energy function as follows:

[0084] E(state) = w1 * ERM S +w2*ERM V +w3*ERM I +w4*ERM C +w5*ERM R (9)

[0085] Where E (state) represents emotional state energy, ERM S ERM represents the energy level at which a user is susceptible to topic-related information. V ERM represents the energy value indicating a user's desire for verification regarding topic information. I ERM represents the energy value indicating a user's state of infection with topic information. C ERM represents the energy value indicating a user's suppressed attitude towards topic information. R The energy value represents the user's immune state to the topic information. w1 represents the weight corresponding to the susceptible state energy, w2 represents the weight corresponding to the verification state energy, w3 represents the weight corresponding to the infected state energy, w4 represents the weight corresponding to the inhibited state energy, and w5 represents the weight corresponding to the immune state energy.

[0086] According to the characteristics of the Ising model, the transition of users between different states is probabilistically driven by energy differences.

[0087] S403: Based on the energy function, define the transition probability of a user moving from the current state to other states, which can be expressed using the Boltzmann distribution:

[0088]

[0089] Where P represents the probability of a user's attitude towards the topic information shifting from the current state to a new state, state_current represents the user's current state regarding the topic information, state_new represents the user's new state regarding the topic information, E(state_new) represents the energy corresponding to the user's new state regarding the topic information, E(state_current) represents the energy corresponding to the user's current state regarding the topic information, and T represents the temperature parameter, used to control the randomness of the transition; to make the model more deterministic, the initial value of the temperature parameter T in this invention is set to 1.0.

[0090] S404: Perform state transition: Based on the defined transition probabilities, use random sampling to perform state transitions and obtain the probability of the user's emotional state transitioning to different topics.

[0091] At each time step, a new state is randomly selected as the user's next state based on the current state and transition probabilities. In the Ising model, each user can be viewed as a spin, capable of being in different states. Interactions between users can be represented by the energy between neighboring users. This energy can be defined based on social network relationships or other factors. The Ising model considers the mutual influence between users. When a user's state changes, it may be influenced by the states of neighboring users.

[0092] An annealing cooling algorithm is introduced to improve the propagation and recovery probabilities during topic propagation. An optimal control problem is established, and an optimized intentional topic propagation control dynamics model, SVICR, is proposed.

[0093] The SVICR model is constructed based on the following assumptions:

[0094] 1. Since the spread of topics is characterized by explosiveness and time-limitedness, this invention assumes that the number of user nodes in the social network will always remain constant at any time during the spread of topics. Therefore, the sum of the state ratios in the model at any time is S+V+I+C+R=1.

[0095] 2. In social networks, the spread of topic information is a special kind of infectious disease transmission. Therefore, users in different states will have a certain probability of infection after contact. When susceptible users come into contact with infected users or users seeking verification, there is a risk of infection.

[0096] 3. During the dissemination process, the popularity of information will gradually decrease over time, and users will gradually forget about the topic and become immune users. Therefore, infected users and users seeking verification have a certain recovery rate and become immune users.

[0097] Based on the above assumptions, the rules for the dissemination of intentional topics in social networks according to this invention are as follows:

[0098] 1. During the spread of a topic, susceptible nodes will become infection nodes with a probability of α, verification nodes with a probability of β, or inhibition nodes with a probability of γ.

[0099] 2. As time goes on, the node to be verified will become an infected node with a probability of δ, an immune node with a probability of ε, or a suppressed node with a probability of Ф. At the same time, due to the influence of various factors, the infected node will become an immune node with a probability of η.

[0100] 3. Under certain circumstances, an immune node can also become a suppressor node with a probability of θ.

[0101] S5: Based on the proportion of users exhibiting different emotional states towards a topic, the probability of users transitioning between different emotional states towards a topic, and the SVICR model, a dynamic equation is constructed. This dynamic equation satisfies the propagation rules of intentional topics in social networks.

[0102] The specific dynamic equation is as follows:

[0103]

[0104] Where I(t) represents the proportion of users in infected state I at any time t during the topic's spread, S(t) represents the proportion of users in susceptible state S at any time t during the topic's spread, V(t) represents the proportion of users in seeking verification state V at any time t during the topic's spread, C(t) represents the proportion of users in inhibited state C at any time t during the topic's spread, R(t) represents the proportion of users in immune state R at any time t during the topic's spread, α represents the probability that a user changes from susceptible state S to infected state I during the topic's spread, and β represents the probability that a user changes from susceptible state S to infected state I during the topic's spread. The probability of a user transitioning from a susceptible state S to a verification state V during topic dissemination is given by: γ representing the probability of a user transitioning from a susceptible state S to an inhibited state C during topic dissemination; δ representing the probability of a user transitioning from a verification state V to an infected state I during topic dissemination; η representing the probability of a user transitioning from an infected state I to an immune state R during topic dissemination; φ representing the probability of a user transitioning from a verification state V to an inhibited state C during topic dissemination; ε representing the probability of a user transitioning from a verification state V to an immune state R during topic dissemination; and θ representing the probability of a user transitioning from an immune state R to an inhibited state C during topic dissemination.

[0105] Figure 5 This is a schematic diagram illustrating the optimized control of intentional topic propagation in this invention.

[0106] S6: Solve the dynamic equation to obtain the set of user sentiment states towards the topic at different times during the dissemination of the intentional topic, and obtain the dissemination trend of the intentional topic based on the set of sentiment states.

[0107] Since the spread of intentional misinformation can have negative impacts on social networks and the real world, and the propagation probability P' and recovery probability R' are important indicators for measuring the degree of impact of rumor propagation, a higher propagation probability P' means that the information is more easily spread widely; a lower recovery probability R' means that the information has a more lasting impact on the audience. Therefore, certain measures need to be taken to control the spread of intentional topics. This invention adjusts the propagation probability and recovery probability based on an annealing strategy, such as... Figure 5 As shown. Figure 5 In this context, Natural propagation represents natural propagation, propagation with control represents controlled propagation, optimization represents optimization, propagation probability represents propagation probability, and recovery probability represents recovery probability. S represents a user's susceptible state to the topic, Q represents a user's seeking confirmation of the topic, I represents a user's infected state to the topic, C represents a user's inhibited state to the topic, and R represents a user's immune state to the topic. The annealing strategy allows for a certain degree of state change while reaching the global optimum, thus avoiding getting trapped in local optima. After implementing the annealing strategy, users in the infected state will, to some extent, become immune or inhibited users, represented by the variable V1(t); while users in the susceptible state will, to some extent, become immune users, represented by the variable V2(t).

[0108] To achieve optimal control performance while considering control costs and consequences, this invention defines a system loss function when implementing an annealing strategy, thereby establishing an optimal control problem. Implementing a control strategy inevitably leads to user churn. Therefore, the loss in this invention is divided into two parts: the user component and the cost component of implementing the control strategy. The system loss function is defined as follows:

[0109]

[0110] Where L represents the system loss during the state transition process, V1(t) represents the cost of converting an infected user to an immune user or an inhibited user at different times t, V2(t) represents the cost of converting a susceptible user to an immune user at different times t, c1 represents the first weight of the cost component and the user churn component, c2 represents the second weight of the cost component and the user churn component, c3 represents the third weight of the cost component and the user churn component, and I(t) represents the proportion of users in the infected state I at any time t during the topic propagation process.

[0111] Furthermore, based on the annealing strategy, introducing control variables into the kinetic equations yields the following:

[0112]

[0113] Where V1 = m + n. Therefore, there exists an optimal control V1. * (t),V2 * (t) and the corresponding solution S * I * V * C * R * To minimize L, the optimal solution is L(V1,V2)={L ... * (t),V2 * (t))}, and at this time V1 and V2 reach their minimum values.

[0114] To solve the optimal control problem, we first construct the Lagrangian function L for the problem and then derive the optimal solution:

[0115] L=c1V1 2 (t)+c2V2 2 (t)+c3I(t) (14)

[0116] Define the Hamiltonian function H for this problem as:

[0117]

[0118] In the formula, λ S (t) represents the accompanying variable of the susceptible state S, λ I (t) represents the accompanying variable of infection state I, λ V (t) represents the accompanying variable of the state V to be proved, λ C (t) represents the accompanying variable of the suppressed state C, λ R (t) represents the accompanying variable of immune status R.

[0119] The final state of this system is not fixed, and therefore is subject to the following constraints:

[0120] S(0)≥0,I(0)≥0,V(0)≥0,C(0)≥0,R(0)≥0

[0121] S(t n ),I(t n ),V(t n ),C(t n ),R(t n Final state free

[0122] Taking the partial derivative of the Hamiltonian function with respect to the state variables, we can obtain the adjoint function as follows:

[0123]

[0124] The ultimate goal of this optimization control problem is to reduce or eliminate the spread of intentional topics, therefore, the final result is:

[0125] λ S (t n )=λ I (t n )=λ V (t n )=λ C (t n )=λ R (t n )=0 (21)

[0126] In the formula, λ S (t n ) represents t n The accompanying variable value of susceptible state S at time λ I (t n ) represents t n The accompanying variable value of infection state I at time λ V (t n ) represents t n Prove the value of the accompanying variable λ of state V at each step. C (t n ) represents t n The value of the adjoint variable λ of the inhibited state C at time t. R (t n ) represents t n The values ​​of the accompanying variables of the immune status R at any given time.

[0127] According to Pontryagin's principle of extrema, the expression for the solution to the optimal control problem is obtained by solving... We obtain, and by solving, we get:

[0128]

[0129] By simplifying and considering the control conditions, we can obtain:

[0130]

[0131] In the formula, V1 * (t) represents the optimal cost incurred when, after implementing the annealing strategy, an infected user becomes an immune user or an inhibited user to some extent. V2 * (t) represents the optimal cost incurred when, after implementing the annealing strategy, a vulnerable user becomes an immune user to some extent. 1max V represents the maximum cost incurred by an infected user to become an immune user or an inhibited user to a certain extent. 2max This represents the maximum cost incurred by a susceptible user who, to a certain extent, becomes an immune user.

[0132] Because the spread of intentional misinformation is unidirectional, the state transitions of each user are also unidirectional. That is, a user's state can only change from a vulnerable state to a seeking state, an infected state, or a suppressed state, ultimately transitioning to an immune state. Assume user U... i A node has n neighbor nodes, among which the probability P(X=m) of the neighbor nodes forwarding the topic at time t follows a binomial distribution:

[0133]

[0134] Then any user U i The probability ψ of forwarding an intentional topic at time t I (t) is:

[0135]

[0136] Similarly, it can be known that any user U i The probabilities of verifying an intentional topic and suppressing its spread at time t are:

[0137]

[0138] In the formula, ψ V (t) represents any user U i The probability of proving an intentional topic at time t, ψ C (t) represents any user U i The probability of suppressing the spread of intentional topics at time t.

[0139] Combining mean-field theory, substituting equations (26)-(27) and (29)-(31) into equation (15) yields the optimized set of dynamic equations, which are as follows:

[0140]

[0141] Among them, V1 * (t) represents the optimal cost incurred when, after implementing the annealing strategy, an infected user becomes an immune user or an inhibited user to some extent. V2 * (t) represents the optimal cost incurred when, after implementing the annealing strategy, a user in a vulnerable state becomes an immune user to some extent. This represents the probability that a user will become infected at time t. Let represent the probability that the user transitions to the verification state at time t. Let represent the probability of a user transitioning to an inhibited state at time t, m represent the cost of an infected user becoming an immune user, and n represent the cost of an infected user becoming an inhibited user, where m+n=V1. Solving the above dynamic equation (32) yields the user state sets {St}, {Vt}, {It}, {Ct}, and {Rt} at different times, representing the propagation status of users towards intentional topics. Based on the output of the intentional topic propagation dynamic model of this invention, the propagation status of intentional topics and the propagation effect after adding control optimization during the topic propagation process can be obtained.

[0142] This invention, based on the SIR model and annealing strategy, constructs an intentional topic propagation control model, SVICR, and then builds and solves optimized dynamic equations. This allows for the depiction and prediction of the propagation trend of intentional topics. It can help governments, organizations, and individuals achieve goals such as public opinion guidance, brand promotion, and social dynamics management, possessing significant social and economic value. Simultaneously, it helps governments and regulatory agencies better manage and guide the propagation of intentional topics, maintaining social order and public interests.

[0143] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include ROM, RAM, disk, or optical disk, etc.

[0144] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the dissemination trends of intentional topics, characterized in that, include: We obtain topic data online in real time from social networks, and after preprocessing, we obtain basic user information, user history behavior, and basic topic information. Factors influencing the spread of intentional topics are extracted from user basic information, user historical behavior, and topic basic information, and the message influence of intentional topics is constructed based on these factors. By combining the aforementioned message influence with a Bayesian linear regression model, the emotional state of users towards the topic is dynamically quantified to obtain the proportion of users exhibiting different emotional states towards the topic; the formula for dynamically quantifying the emotional state of users towards the topic is as follows: in, This represents the emotional response effect of the i-th user to the intended topic. This represents the i-th user. This represents the first weight coefficient obtained by training and fitting the Bayesian linear regression model. Indicates topic factors, Indicates user factors, ε represents the first weight coefficient obtained by training and fitting the Bayesian linear regression model, and ε is the error term; By combining the aforementioned message influence with the Ising model, the probability of users shifting between different emotional states regarding a topic is obtained. The prediction process includes: The emotional state of users toward a topic is defined as a state space, which includes the susceptible state (S), the verification state (Q), the infection state (I), the inhibition state (C), and the immune state (R). The verification state (Q) refers to the state in which users seek verification of a topic after being exposed to it due to the doubt mechanism. The inhibition state (C) refers to the state in which users do not trust the topic and inhibit its spread after seeking verification of it. Define the energy function as: in, Represents emotional state energy. An energy value representing a user's susceptibility to topic-related information. This represents the energy value indicating a user's desire for verification regarding the topic information. This represents the energy value indicating a user's state of being "infected" by the topic information. This represents the energy value indicating a user's suppressed attitude towards topic information. An energy value representing a user's immunity to topic-related information. The weights represent the susceptibility state energy. This represents the weight corresponding to the state energy being verified. The weights represent the energy corresponding to the infection state. The weights represent the energy corresponding to the suppressed state. The weights corresponding to the energy of the immune status; Based on the energy function, the transition probability of a user moving from the current state to other states is defined as follows: Where P represents the probability of a user's attitude towards the topic information shifting from the current state to a new state. This indicates the user's current state regarding the topic information. This indicates the user's new state regarding the topic information. E(state_current) represents the energy corresponding to the user's new state in relation to the topic information, and T represents the temperature parameter used to control the randomness of the transition. Based on the defined transition probabilities, a random sampling method is used to perform state transitions and obtain the probability of users switching between different emotional states for a topic. Based on the proportion of users exhibiting different emotional states towards a topic, the probability of users switching between different emotional states towards a topic, and the SVICR model, a dynamic equation is constructed. Solving the dynamic equations yields a set of user sentiment states at different times during the dissemination of intentional topics, and the dissemination trend of intentional topics is obtained based on this set of sentiment states.

2. The method for predicting the dissemination trend of intentional topics according to claim 1, characterized in that, The factors influencing the spread of intentional topics include user factors and topic factors, with user factors including user sentiment matching degree. User engagement User influence and user credibility The topic factors include topic popularity. and the source of the topic .

3. The method for predicting the dissemination trend of intentional topics according to claim 2, characterized in that, The message influence of the intended topic is: in, This indicates the topic factor in the impact of a message. This refers to the user factor in the impact of a message.

4. The method for predicting the dissemination trend of intentional topics according to claim 1, characterized in that, The specific dynamic equation is as follows: in, This represents the proportion of users in the infected state I at any given time t during the spread of the topic. This represents the proportion of users who exhibit a susceptible state S at any given time t during the spread of the topic. This represents the proportion of users who are in the "seeking verification" state at any given time t during the spread of the topic. This represents the proportion of users who exhibit an inhibited state C at any given time t during the spread of the topic. This represents the proportion of users R who exhibit an immune state during the spread of the topic at any given time t. This represents the probability that a user changes from a susceptible state S to an infected state I during the spread of a topic. This represents the probability that a user transitions from a susceptible state S to a verification-seeking state V during the spread of a topic. This represents the probability that a user transitions from a susceptible state S to an inhibited state C during the spread of a topic. This represents the probability that a user transitions from the verification state V to the infection state I during the spread of the topic. This represents the probability that a user transitions from an infected state (I) to an immune state (R) during the spread of the topic. This represents the probability that a user transitions from the verification state V to the inhibition state C during the propagation of a topic. This represents the probability that a user transitions from a state of seeking verification (V) to a state of immunity (R) during the spread of a topic. This represents the probability that a user transitions from an immune state (R) to an inhibited state (C) during the spread of a topic.

5. The method for predicting the dissemination trend of intentional topics according to claim 4, characterized in that, Based on the annealing strategy, introducing control variables into the kinetic equations yields an optimized set of kinetic equations, specifically: in, This indicates the optimal cost incurred when implementing an annealing strategy, where infected users are to some extent transformed into immune users or suppressed users. This indicates that after implementing the annealing strategy, the cost incurred by users in a vulnerable state to become immune users to some extent is optimal. This represents the probability that a user will become infected at time t. Let represent the probability that the user transitions to the verification state at time t. Let t represent the probability that a user transitions to an inhibited state at time t, m represent the cost for an infected user to become an immune user, and n represent the cost for an infected user to become an inhibited user.

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