CN112464082B - Rumor-dagger game propagation control method based on sparse representation and tensor completion - Google Patents

Rumor-dagger game propagation control method based on sparse representation and tensor completion Download PDF

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CN112464082B
CN112464082B CN202011226185.XA CN202011226185A CN112464082B CN 112464082 B CN112464082 B CN 112464082B CN 202011226185 A CN202011226185 A CN 202011226185A CN 112464082 B CN112464082 B CN 112464082B
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徐玮
肖云鹏
李茜
李暾
卢星宇
桑春艳
刘宴兵
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Chongqing University of Post and Telecommunications
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Abstract

The invention belongs to the field of network public opinion analysis, and particularly relates to a rumor-ballad splitting game propagation control method based on sparse representation and tensor complementation, which comprises the following steps of: acquiring user data information, and preprocessing the user data information; extracting relevant attributes of the preprocessed user data information; inputting relevant attributes of user data information into a rumor-ballad game propagation model based on sparse representation and tensor complementation, and predicting the trend of user propagation rumors; controlling rumor spreading users according to the predicted rumor spreading trend of the users to prevent the rumor spreading; the invention predicts whether the users join in the rumor-dagger topic by utilizing the evolutionary game theory and the neural network, can dynamically predict when the users participate in the topic discussion, and can sense the situation of the development trend of the rumor topic.

Description

Rumor-dagger game propagation control method based on sparse representation and tensor completion
Technical Field
The invention belongs to the field of network public opinion analysis, and particularly relates to a rumor-ballad gambling propagation control method based on sparse representation and tensor complementation.
Background
Network rumors refer to network information that is propagated through a network medium (e.g., twitter) without the facts of being offensive and targeted. With the promotion of the rapid development of the internet to social media, the social media has the characteristics of freedom, interactivity, diversity, rapidness, popularity and the like, so that the generation and the propagation of network rumors are easier, and when the network rumors are propagated in a large quantity, the scare is generally caused to the masses of people, and meanwhile, the bad influence is caused to social economy and social order. The research on rumors and propagation prediction models of the dagger rumors is developed, the population forwarding characteristic distribution is mastered, and the method has important significance on guidance and control of network public sentiments.
In recent years, a lot of studies have been conducted on rumor propagation models by many scholars, mainly from three aspects of rumor propagation influence factors, rumor propagation models and rumor control mechanisms. The influence factors for rumor propagation are mainly analyzed from the user's own attributes (including user emotion and user behavior) and rumor propagation space. For the rumor propagation model, the internal mechanism of rumor propagation is mainly studied from three points of view, namely, user, social relationship and rumor information content. The rumor control mechanism controls rumors by controlling user nodes and rumor propagation scenarios based on rumor propagation factors.
Understanding the propagation law of rumors is a key problem for rumor control, but most studies on rumor propagation models ignore the sparsity problem of valid data in the rumor propagation space, leading to one-sidedness in the conclusions drawn, the paper Chen J, Wu Y, Fan L, et al.n2 vscdnr: a Local recommendation System Based on Node2vec and Rich Information Network [ J ]. IEEE Transactions on comparative Social Systems,2019. capturing complex potential relationships between users from the corresponding networks using Node2vec alleviates the sparsity problem of data. However, in the papers, only the influence factors of the user and the rumor information are considered, and the influence of other information in the same time propagation space on the rumor propagation is neglected, so that the subsequent control effect on the rumor is poor.
Disclosure of Invention
In order to solve the problems of the prior art, the invention provides a rumor-ballad gambling propagation control method based on sparse representation and tensor complementation, which comprises the following steps: acquiring user data information, and preprocessing the user data information; extracting relevant attributes of the preprocessed user data information; inputting the relevant attributes of the user data information into a rumor-splitting game propagation model based on sparse representation and tensor completion, and predicting the trend of the rumor propagation of the user; controlling rumor spreading users according to the predicted rumor spreading trend of the users to prevent the rumor spreading;
The process of constructing the rumor-dagger rumor game propagation model based on sparse representation and tensor completion comprises the following steps:
s1: processing the relevant attributes of the user data information by adopting a sparse representation algorithm, so that the data in the rumor topic space is densified;
s2: compensating the relevant attributes of the user data information by adopting a tensor model to obtain a complete tensor of the user interaction degree;
s3: calculating the information influence of the user according to the complete tensor of the user interaction degree and the relevant attributes of the user after data densification;
s4: establishing a rumor-dagger rumor interaction influence model according to the information influence of the user, and inputting the user data into the model to obtain the rumor interaction influence;
s5: and constructing a rumor-dagger topic propagation group behavior prediction model according to the rumor interaction influence and the graph convolution neural network.
Preferably, the process of extracting the correlation attribute includes:
step 1: extracting internal factors of a user, wherein the internal factors comprise personal attributes Att (u) of the useri) And history transfer Rate (u)i)；
Step 2: extracting external factors of a user, the external factors including a user interaction degree Mutual (u)i) Participant influence Pinfluence (u)i) And information basic attribute Iattribute (I) i)。
Preferably, the processing the acquired user data by using the sparse representation algorithm includes:
s11: converting the rumor topic space data into a rumor topic space matrix Y;
s12: decomposing the rumor topic space matrix Y into a rumor topic space dictionary matrix D and a rumor topic space sparse coding matrix X;
s13: optimizing a rumor topic space matrix Y according to the rumor topic space dictionary matrix D and the sparse coding matrix X; the optimized expression is as follows:
Figure BDA0002763735480000031
s14: converting the optimized data by adopting a Lagrange multiplier method to obtain an unconstrained rumor topic space matrix Y;
Figure BDA0002763735480000032
s15: and solving an unconstrained rumor topic space matrix Y by adopting a k-SVD algorithm to obtain sparse effective data of a rumor topic propagation space.
Preferably, the process of compensating the relevant attribute of the user data information by using the tensor model includes:
step 1: acquiring tensors of 'rumor splitting users-potential users-interaction degrees' of relevant attributes in user data information;
step 2: calculating the minimum nuclear norm of the tensor in the step 1 according to the optimal mode rank;
and step 3: completing the minimum nuclear norm of the tensor by adopting a high-precision low-rank tensor completion algorithm to obtain an equivalent form of the tensor nuclear norm;
And 4, step 4: processing the equivalent form of the tensor nuclear norm by adopting an augmented Lagrangian function to obtain a Lagrangian function:
Figure BDA0002763735480000033
and 5: solving extreme values of Lagrange function by adopting an alternative direction multiplier method, and according to the extreme values, obtaining the delta PiX and YiUpdating is carried out; and obtaining a complete tensor X of the user interaction degree.
Further, for Δ PiX and YiThe formula for updating is:
ΔPithe update formula of (2):
Figure BDA0002763735480000041
updating formula of X:
Figure BDA0002763735480000042
Yithe update formula of (2):
Figure BDA0002763735480000043
preferably, the information influence of the user includes internal factors and external factors; the internal factors comprise the user self attribute and the historical forwarding rate; constructing rumor and dagger information influence functions by adopting a multiple linear regression algorithm according to internal factors and external factors; the influence function is:
Iinfluencerumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsrumor(ui)
Iinfluenceanti-rumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsanti-rumor(ui)
preferably, the process of acquiring rumor interaction comprises:
step 1: defining two game strategies according to game theory, namely 'forwarding rumor information' and 'forwarding ballad information';
step 2: respectively calculating the revenue functions of the two strategies according to the information influence of the user;
and step 3: the rumor interaction was calculated according to the revenue function of both strategies.
Further, the formula for rumor interaction is:
Figure BDA0002763735480000044
Figure BDA0002763735480000045
Preferably, the process of constructing the rumor-dagger topic propagation population behavior prediction model comprises the following steps:
step 1: obtaining a feature matrix X-NxF and an adjacency matrix under a game
Figure BDA0002763735480000046
The characteristic matrix is a user characteristic matrix after the user data is sparsely represented; constructing an adjacency matrix under the game according to data after tensor completion and rumor interaction influence;
step 2: randomly initializing weight and bias, multiplying the feature matrix X by the initial weight, and adding deviation in the multiplying process; multiplying the result with a normalized symmetric matrix
Figure BDA0002763735480000051
Multiplying to obtain a feature matrix of the next layer of input after convolution;
and step 3: inputting the characteristic matrix of the step 2 into a double-layer graph convolution neural network added with a middle Dropout layer for model training; carrying out Dropout operation in the process of carrying out model training; the activation function of the middle Dropout layer is a RELU function;
and 4, step 4: expressing the convolution output into probability values of different classes of nodes by adopting a SoftMax activation function; rumor-the expression of the group behavior prediction model of the propagation of the diner topic is as follows:
Figure BDA0002763735480000052
preferably, the propagation trend of the propagation rumor of the user is predicted as follows:
Z＝P(r,a,d|ui)
Figure BDA0002763735480000053
if Y is 1, the potential user uiRumors will be forwarded for the next time period; if Y is-1, then the potential user u iThe balladry is forwarded in the next time period; otherwise, potential user uiWill not participate in the rumor topic during the next period.
The invention utilizes the evolutionary game theory and the neural network to predict whether the users join in the rumor-dagger topic, can dynamically predict when the users participate in the topic discussion, and can sense the situation of the development trend of the rumor topic. The method can be applied to propagation and diffusion of rumors in social networks, and government departments can master fermentation and propagation of network rumors more accurately and guide and control the network rumors.
Drawings
Fig. 1 shows a rumor-dagger topic game propagation prediction model based on sparse representation and tensor completion;
fig. 2 rumor topic space sparse representation iterative model;
figure 3 is a diagram of tensor total rumor/m user interaction effect.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A rumor-bary game propagation control method based on sparse representation and tensor complementation, as shown in fig. 1, the method comprises: acquiring user data information, and preprocessing the user data information; extracting relevant attributes of the preprocessed user data information; inputting relevant attributes of user data information into a rumor-ballad game propagation model based on sparse representation and tensor complementation, and predicting the trend of propagating rumors by users; users of rumor transmission were controlled according to predicted trend of rumor transmission, preventing rumor transmission.
The method for acquiring the user data information comprises the steps of directly downloading the existing public data source and acquiring by utilizing a mature social network public API. The obtained information is the participation situation of the participants in the rumor-dagger topic in the life cycle and the historical behavior data of the participants in the topic. What the topic participation situation needs to obtain is the time when the topic is forwarded and commented, the basic information of the participating users and the friend relationship information (including the concerned and concerned information) of the participating users; the historical behavior of the topic participant includes information that the user has historically forwarded and rated.
The process of preprocessing the user data information includes cleaning data, such as deleting repeated data, cleaning invalid nodes and the like, and structuring unstructured data.
In social networks, the propagation of users to rumors and public ballad information is influenced by a number of factors, such as: personal interests of users, interaction behavior among users, and mutual influence of rumors and daggers in the process of propagation, etc. Based on the method, factors influencing the user propagation behavior are defined according to internal and external factors of the user, and relevant attributes of the preprocessed user data information are extracted.
The process of extracting relevant attributes of the user data comprises the following steps:
step 1: extracting internal factors of a User, wherein the internal factors comprise a personal attribute User (u) of the Useri) And history transfer Rate (u)i)。
Step 11: user personal attribute User (u)i) The method comprises the steps of including the age of a user, the number of fans of the user and the number of concerns of the user, wherein the correlation is certain with whether the user participates in a rumor topic; personal attribute User (u) of a Useri) Comprises the following steps:
User(ui)＝[gender(ui),fans(ui),follows(ui)]
wherein, gene (u)i) Indicates the age, fans (u) of the useri) Indicates the number of fans of the user, follows (u)i) Representing the number of friends of the user;
step 12: historical forwarding Rate (u) of a useri) Comprises the following steps:
Figure BDA0002763735480000071
wherein, transNums (u)i) Indicating the number of historical forwarded microblogs of the user, allNums (u)i) Representing the number of all microblogs that the user gets from the friends.
The historical forwarding rate of the user can show the activity of the user and the participation degree of topics to a certain extent, and has certain guiding significance for predicting future behaviors of the user.
And 2, step: extracting external factors of a user, the external factors including a user interaction degree Mutual (u)i) Participant influence Pinfluence (u)i) And information basic attribute Iattribute (I)i)。
Step 21: user interactivity Mutual (u)i) Comprises the following steps:
Figure BDA0002763735480000072
Figure BDA0002763735480000073
Figure BDA0002763735480000074
wherein, IijTo indicate a function, uiDenoted as message neighbor propagators, vjDenoted as potential message propagator, K denotes the kth microblog, K denotes the neighbor propagation user uiTotal number of microblogs released, b represents behavior (including forwarding, comments, praise), interct (blog)kb) Representing the degree of interaction, blog, of two users in the kth microblogkbRepresenting the behaviour of the kth microblog user, IkbRepresenting the behavior of potential propagating users, t being the time of the current message, tkPropagating user u for neighborsiAnd releasing the time of the kth microblog.
The user interaction represents the behaviors of mutual forwarding, approval and comment of the user and friends of the user. The more frequently users interact, the more likely it is to forward the microblog of the other party. Meanwhile, the user interaction degree has stronger timeliness, so a time attenuation function e is introduced tTo quantify the impact of user interactivity.
Step 22: participant influence pinfluent (u)i) Comprises the following steps:
Figure BDA0002763735480000081
wherein u iskIndicating the users who are participating in the topic,
Figure BDA0002763735480000082
represents participant ukAverage forwarding number of original microblogs.
The participators refer to users who issue the microblog and the use for forwarding the microblog. The participant influence also influences the forwarding behavior of the user to a certain extent, and the greater the participant influence, the higher the possibility of forwarding of the potential user.
Step 23: information basic attribute Iattrib (I)i) Comprises the following steps:
Iattribute(Ii)＝[themeNums(Ii),timeNums(Ii),tagNums(Ii)]
wherein, the themeNums (I)i) Number of hops, timeNums (I), representing the topic of the current informationi) TagNums (I), which represents the number of transfers of information 1 hour after the time of issuancei) Number of retransmissions, allNums (I), indicating the current presence or absence of a hashTagi) Indicating the number of hops 3 days after the information was released.
The subject content of the information, the time of information release, whether hashTag exists in the information, and the like are all related to the influence of the information, and the influence of the information also determines the forwarding condition of the user.
The method mainly comprises three stages in constructing a rumor-dagger game propagation model based on sparse representation and tensor completion, as shown in fig. 1, in the first stage, the content, structure and behavior characteristics of a rumor-dagger propagation space are considered, and the rumor topic propagation space is vectorized and expressed by utilizing sparse representation. And in the second stage, compensating the sparse effective data by using low-rank tensor completion, and optimizing the sparse effective data by introducing a time attenuation function. And in the third stage, on the basis of comprehensively considering the mutual influence of the rumor-seeking messages, a rumor topic group behavior prediction model is constructed by combining a graph convolution neural network, and the propagation rule of the rumor-seeking rumor messages is predicted and analyzed.
The process of constructing the rumor-ballad game propagation model based on sparse representation and tensor complementation comprises the following steps of:
s1: and processing the relevant attributes of the user data information by adopting a sparse representation algorithm, so that the data in the rumor topic space is densified. And processing the user related attributes by adopting a sparse representation algorithm to obtain the most essential and important characteristics, and finally enabling data in a rumor topic space to be concise and low-dimensional.
S2: compensating the relevant attributes of the user data information by adopting a tensor model to obtain a complete tensor of the user interaction degree;
s3: calculating the information influence of the user according to the complete tensor of the user interaction degree and the relevant attributes of the user after the data densification;
s4: establishing a rumor-dagger rumor interaction influence model according to the information influence of the user, and inputting the user data into the model to obtain the rumor interaction influence;
s5: and constructing a rumor-dagger topic propagation group behavior prediction model according to the rumor interaction influence and the graph convolution neural network.
As shown in fig. 2, the process of processing the acquired user data by using the sparse representation algorithm includes:
s11: and converting the rumor topic space data into a rumor topic space matrix Y. Where each column of Y represents a user forwarding a rumor and each row represents each attribute of a user.
S12: decomposing the rumor topic space matrix Y into a rumor topic space dictionary matrix D and a rumor topic space sparse coding matrix X;
Y≈D*X
the requirements in the decomposition process are as follows: x is as sparse as possible, while each column of D is a constraint on the normalized vector.
S13: and optimizing the rumor topic space matrix Y according to the rumor topic space dictionary matrix D and the sparse coding matrix X. The optimization process comprises the following steps: and continuously updating the dictionary D and the corresponding sparse coding matrix X to ensure that the value of DX continuously approaches Y, thereby obtaining the minimum value of the target function of Y-DX under the constraint condition. The dictionary D and the sparse matrix X are solved to obtain an approximate expression of a rumor topic space matrix Y; the optimized expression is as follows:
Figure BDA0002763735480000091
s14: converting the optimized data by adopting a Lagrange multiplier method to obtain sparse effective data of a rumor topic propagation space; and the constrained problem in the S13 is converted into an unconstrained problem by a Lagrange multiplier method, so that the solution of the next step is facilitated.
Figure BDA0002763735480000092
Wherein, XiRepresents YiSparse representation of (1), T0Representing sparsenessThe degree constraint parameter, which is a constant,
Figure BDA0002763735480000093
representing the square of the F-norm of the matrix, F representing the F-norm of the matrix, and λ representing a parameter greater than 0.
S15: and solving an unconstrained rumor topic space matrix Y by adopting a k-SVD algorithm to obtain sparse effective data of a rumor topic propagation space. The process of solving the unconstrained rumor topic space matrix Y comprises the steps of fixing one variable in the rumor topic space dictionary matrix D and the rumor topic space sparse coding matrix X, optimizing the other variable, and solving alternately.
The invention utilizes the advantage of high precision of tensor completion in data compensation to construct a tensor M for a rumor splitting user-potential user-interaction degreeI ×J×KWherein, I represents the dimension of the rumor or forwarding users, J represents the dimension of the potential users, and K represents the dimension of the interactivity.
The process of compensating the relevant attributes of the user data information by adopting the tensor model comprises the following steps:
s21: acquiring a tensor of 'rumor users-potential users-interaction degree' of related attributes in user data information, wherein the expression is as follows:
Figure BDA0002763735480000101
s.t.XΩ＝MΩ
where rank (X) denotes the rank of tensor X.
S22: since the matrix kernel norm is the convex envelope of the rank function, the pair
Figure BDA0002763735480000102
Carrying out convex relaxation treatment; calculating the minimum nuclear norm of the tensor according to the optimal mode rank; the minimum nuclear norm of the tensor is:
Figure BDA0002763735480000103
Wherein wiNot less than 0 and
Figure BDA0002763735480000104
representing the weights of the tensors after each stage of matrixing.
S23: the minimum nuclear norm of the tensor is complemented by adopting a high-precision low-rank tensor complementing algorithm, and N auxiliary variables (delta P) are introduced in the complementing processi∈RI×J×K} order of
Figure BDA0002763735480000105
Obtaining an equivalent form of a tensor nuclear norm:
Figure BDA0002763735480000106
wherein X represents a tensor obtained by tensor completion, Δ PiRepresenting each of the intermediate variable matrices introduced, N representing the number of variable matrices, wiRepresents the weight of the tensor after each level of matrixing, and wiIs not less than 0 and
Figure BDA0002763735480000111
||ΔPi(i)||*representing the two-norm, X, of each auxiliary variableΩRepresenting the tensor to be recovered under the set of samples omega, MΩRepresenting the tensor constructed under the sampling set omega.
The process of completing the minimum nuclear norm of the tensor by the high-precision low-rank tensor completion algorithm comprises the following steps: for the existing incomplete data with low rank, the principle of matrix decomposition (different rows/columns of the bottom decomposition matrix usually have similar characteristics) is utilized, the actual matrix is approximated by the matrix with lower rank based on the convex approximation constraint item of the matrix kernel norm, and the completion effect is achieved.
S24: processing the equivalent form of the tensor kernel norm by adopting an augmented Lagrange function to obtain the Lagrange function:
Figure BDA0002763735480000112
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002763735480000113
is a lagrange multiplier tensor set, and lambda is a penalty factor; | | Δ Pi(i)||*Representing the two-norm of each auxiliary variable,<X-ΔPi,Yi>the representation tensor X- Δ PiAnd tensor YiThe inner product of (a) is,
Figure BDA0002763735480000114
the squared value of the F norm representing the difference of each intermediate variable introduced from the user's full tensor.
S25: solving extreme values of the Lagrange function by adopting an alternative direction multiplier method, and according to the extreme values, obtaining the delta PiX and YiUpdating is carried out; and obtaining a complete tensor X of the user interaction degree.
For Δ PiX and YiThe formula for updating is:
ΔPithe update formula of (2):
Figure BDA0002763735480000115
updating formula of X:
Figure BDA0002763735480000116
Yithe update formula of (2):
Figure BDA0002763735480000121
wherein, Δ PiEach matrix of intermediate variables introduced is represented, an
Figure BDA0002763735480000122
Figure BDA0002763735480000123
The variable value when the objective function L takes the minimum value is expressed,
Figure BDA0002763735480000124
denotes Y at the k +1 th iterationiValue of (1), foldn(.) represents the recomposition of the matrix into a tensor,
Figure BDA0002763735480000125
representing a singular value contraction operation with the contraction operator being wi/λ，X(i)I-mode matrix, Y, representing tensor Xi(i)An i-mode matrix representing a Lagrange multiplier tensor, λ represents a penalty factor, Ω represents a sampling index set, and M is an RI ×J×KRepresenting the existing incomplete tensor.
The result of the updated formula of X contains the complete tensor of user interaction under the implicit attention relationship.
Information influence Iifluence (u)i) By user internal factors Infactors (u)i) And external factors Outfactors (u)i) And (4) forming. The internal factors of the user comprise the attributes of the user and the historical forwarding rate, and the expression is as follows:
Infactors(ui)＝User(ui)*Rate(ui)
the external factors are composed of user interaction degree, participant influence and basic information attributes, and the formula is as follows:
Outfactors(ui)＝Mutual(ui)*Pinfluence(ui)*Iattribute(Ii)
constructing rumor and dagger rumor information influence force functions by adopting a multiple linear regression algorithm according to internal factors and external factors; the influence function is:
Iinfluencerumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsrumor(ui)
Iinfluenceanti-rumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsanti-rumor(ui)
where ρ is0、ρ1、ρ2Is a partial regression coefficient, rho, obtained by training a multiple linear regression algorithm1、ρ2The factors account for the information influence after reaction.
Due to the particularity and complexity of the social network, when a rumor information is spread, the rumor information playing with the rumor information is spread, and the game relationship is also an important factor influencing the forwarding behavior of the user. Thus, the present invention uses evolutionary game theory to quantify this rumor interaction.
The process of acquiring rumor interaction includes:
step 1: two game strategies are defined according to the game theory, namely 'rumor information forwarding' and 'rumor splitting information forwarding', respectively.
Step 2: and respectively calculating the revenue functions of the two strategies according to the information influence of the user.
The revenue function for the strategy of forwarding rumor information is:
Prorumor(ui)＝P1×Iinfluencerumor(ui)
the benefit function of the strategy for forwarding the ballad information is:
Proanti-rumor(ui)＝P1×Iinfluenceanti-rumor(ui)
wherein, P1And P2Are users u respectivelyiThe ratio of rumor and dagger information is spread among friends.
And step 3: the rumor interaction was calculated according to the revenue function of both strategies. The formula for rumor interaction is:
Figure BDA0002763735480000131
Figure BDA0002763735480000132
wherein Mutrumor(ui) Representing rumor to user u after gamingiInfluence of the propagation behavior, uiRepresenting the user, Prorumor(ui) Prod as a revenue function for the strategy of forwarding rumor informationanti-rumor(ui) The revenue function of the strategy for forwarding the dagger rumors information is expressed,
Figure BDA0002763735480000133
mut, an index function after policy game for expressing forwarding rumor information and forwarding dagger informationrumor(ui) Representing rumor information to user u after gamingiThe influence of the behavior is propagated.
A rumor-dagger topic propagation group behavior prediction model based on a graph convolution neural network is provided based on rumor interaction force. The goal of the model prediction task is to predict the participation condition of the potential user nodes to the rumor topic, if the potential user nodes participate in the rumor topic, the forwarding rumor or the splitting message is judged, and then the forwarding rumor or message can be converted into a three-classification task.
As shown in fig. 3, the model inputs are:
the feature matrix X is N multiplied by F, wherein N represents the number of user nodes in the rumor topic propagation network, F is the input feature dimension of each node, and the features are the user attribute features and external factor features which are subjected to sparse representation processing.
Adjacency matrix under game
Figure BDA0002763735480000134
Shows the connection information between all users under rumor and dagger two messages in t time period. The game adjacency matrix is constructed by the data after tensor completion and rumor interaction. This matrix is useful in the next step, which is one of the inputs to the GCN model.
In the present application, use is made ofA two-layer graph convolution neural network added with an intermediate Dropout layer is used as a network rumor forwarding prediction model. First, weight and bias are initialized randomly, then X is multiplied by W and offset is added, and the sum of X and W is compared
Figure BDA0002763735480000141
Multiplication. Then, the RELU function is used as an activation function of the layer, and Dropout operation is carried out during model training, and finally, the SoftMax activation function is used for representing convolution output as probability values of different classes of the nodes. The specific formula is expressed as:
Figure BDA0002763735480000142
wherein N represents the number of user nodes in the rumor topic propagation network, F represents the input characteristic dimension of each node, and UtRepresenting the set of propagation spaces at time t,
Figure BDA0002763735480000143
representing a set of edges between the propagation spaces,
Figure BDA0002763735480000148
representing the edge weight value after the game, A representing an adjacency matrix, ReLU (mean) representing an activation function, softmax (mean) representing normalization processing, and W iTo convolve the weight matrix corresponding to the i-th network in the network,
Figure BDA0002763735480000144
representing a normalized symmetric matrix.
The expression of the normalized symmetric matrix is:
Figure BDA0002763735480000145
wherein I represents an identity matrix, D represents a diagonal matrix of the matrix A, and
Figure BDA0002763735480000146
since a three-classification prediction problem is discussed herein, let the model output Z ═ P (r, a, d | u)i) The specific definition is as follows:
Figure BDA0002763735480000147
wherein Z represents the probability of three types of user tags, P (r, a, d | ui) Probability of each user label is shown, r is the user forwarding rumor topic, a is the user forwarding rumor, d is the user not participating in topic, P (r | u |)i) Representing user uiProbability of rumors forwarded, P (a | u |)i) Representing user uiProbability of repeating an rumor, P (d | u)i) Representing user uiProbability of not participating in a topic.
If the corresponding Y is 1, judging the potential user uiRumors will be forwarded for the next time period; if Y is equal to-1, judging the potential user uiForwarding the rumor in the next time period; otherwise, potential user uiWill not participate in the rumor topic during the next period.
The above-mentioned embodiments, which are further detailed for the purpose of illustrating the invention, technical solutions and advantages, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A rumor-rumor game propagation control method based on sparse representation and tensor complementation is characterized by comprising the following steps of: acquiring user data information, and preprocessing the user data information; extracting relevant attributes of the preprocessed user data information; inputting the relevant attributes of the user data information into a rumor-dagger game propagation model based on sparse representation and tensor completion, and predicting the trend of propagation rumors of users; according to predicted useThe trend of spreading the rumors controls the users of the rumors, and prevents the rumors from spreading; extracting relevant attributes of the user data information includes: extracting internal factors of a user, wherein the internal factors comprise personal attributes Att (u) of the useri) And a historical forwarding Rate (u)i) (ii) a Extracting external factors of a user, the external factors including a user interaction degree Mutual (u)i) Participant influence pinfluent (u)i) And information basic attribute Iattribute (I)i)；
The process of constructing the rumor-dagger rumor game propagation model based on sparse representation and tensor completion comprises the following steps:
s1: processing the relevant attributes of the user data information by adopting a sparse representation algorithm to thicken the data in the rumor topic space;
s11: converting the rumor topic space data into a rumor topic space matrix Y;
S12: decomposing the rumor topic space matrix Y into a rumor topic space dictionary matrix D and a rumor topic space sparse coding matrix X;
s13: optimizing a rumor topic space matrix Y according to the rumor topic space dictionary matrix D and the sparse coding matrix X; the optimized expression is as follows:
Figure FDA0003644367860000011
s14: converting the optimized data by adopting a Lagrange multiplier method to obtain an unconstrained rumor topic space matrix Y;
Figure FDA0003644367860000012
s15: solving an unconstrained rumor topic space matrix Y by adopting a k-SVD algorithm to obtain sparse effective data of a rumor topic propagation space;
wherein, XiRepresents YiSparse representation of (1), T0The constraint parameter, representing the sparsity, is a constant,
Figure FDA0003644367860000013
representing the square of the F norm of the matrix, F representing the F norm of the matrix, and λ representing a parameter greater than 0;
s2: compensating the relevant attributes of the user data information by adopting a tensor model to obtain a complete tensor of the user interaction degree;
s21: acquiring tensors of 'rumor splitting users-potential users-interaction degrees' of relevant attributes in user data information;
s22: calculating the minimum nuclear norm of the tensor in the step 1 according to the optimal mode rank;
s23: completing the minimum nuclear norm of the tensor by adopting a high-precision low-rank tensor completion algorithm to obtain an equivalent form of the tensor nuclear norm;
S24: processing the equivalent form of the tensor nuclear norm by adopting an augmented Lagrangian function to obtain the Lagrangian function:
Figure FDA0003644367860000021
s25: solving extreme values of Lagrange function by adopting an alternative direction multiplier method, and according to the extreme values, obtaining the delta PiX and YiUpdating is carried out; obtaining a complete tensor X of the user interaction degree;
wherein X represents a tensor obtained by tensor completion, delta P represents each introduced intermediate variable matrix, Y represents a Lagrange multiplier tensor set, lambda represents a penalty factor, N represents the number of variable matrices, and w representsiRepresents the weight of tensor after each level of matrixing, | Δ Pi(i)||*Denotes the two-norm, < X- Δ P, of each auxiliary variablei,YiThe > representation tensor X- Δ PiAnd tensor YiThe inner product of (a) is,
Figure FDA0003644367860000022
the squared value of the F norm representing the difference value of each introduced intermediate variable and the complete tensor of the user;
s3: calculating the information influence of the user according to the complete tensor of the user interaction degree and the relevant attributes of the user after data densification;
s4: establishing a rumor-dagger rumor interaction influence model according to the information influence of the user, and inputting the user data into the model to obtain the rumor interaction influence;
s5: and constructing a rumor-dagger topic propagation group behavior prediction model according to the rumor interaction influence and the graph convolution neural network.
2. The method of claim 1, wherein the method for game propagation of rumors-daggers based on sparse representation and tensor completion is characterized in that the method is applied to Δ PiX and YiThe formula for updating is:
ΔPithe update formula of (2):
Figure FDA0003644367860000031
updating formula of X:
Figure FDA0003644367860000032
Yithe update formula of (2):
Figure FDA0003644367860000033
wherein, Δ PiEach of the matrices of intermediate variables introduced is represented,
Figure FDA0003644367860000034
representing the value of the variable at which the Lagrangian function L assumes a minimum, Yi k+1Denotes Y at the k +1 th iterationiValue of (1), foldn(.) denotes the reconstruction of the matrix into a tensor, Dwi/λRepresenting singular value contraction operations, wiLambda represents the contraction calculationA sub-group is X(i)I-mode matrix, Y, representing tensor Xi(i)An i-mode matrix representing a Lagrange multiplier tensor, λ represents a penalty factor, Ω represents a sampling index set, and M is an RI×J×KRepresenting the existing incomplete tensor, k represents the number of iterations.
3. The rumor-splitting game propagation control method based on sparse representation and tensor completion as claimed in claim 1, wherein the information influence of the users includes internal factors and external factors; the internal factors comprise the self attribute of the user and the historical forwarding rate; constructing a rumor and a rumor splitting information influence function by adopting a multiple linear regression algorithm according to internal factors and external factors; the influence function is:
Iinfluencerumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsrumor(ui)
Iinfluenceanti-rumor(ui)＝ρ0+ρ1*Infactors(ui)+ρ2*Outfactorsanti-rumor(ui)
Wherein ρ0、ρ1、ρ2Respectively representing partial regression coefficients, rho, trained using a multiple linear regression algorithm1、ρ2Reflect the proportion of factors in the information influence, Infactors (u)i) Representing internal factors of the user, out factorsrumor(ui) Representing factors external to the user.
4. The rumor-refrain game propagation control method according to claim 1, wherein the process of obtaining the rumor interaction influence comprises:
step 1: defining two game strategies according to game theory, namely 'forwarding rumor information' and 'forwarding ballad information';
step 2: respectively calculating the revenue functions of the two strategies according to the information influence of the user;
and step 3: the rumor interaction was calculated according to the revenue function of both strategies.
5. The method of claim 4, wherein the rumor-nursery game propagation control method based on sparse representation and tensor completion is characterized in that the formula of rumor interaction influence is as follows:
Figure FDA0003644367860000041
Figure FDA0003644367860000042
wherein Mutrumor(ui) Representing rumor to user u after gamingiInfluence of the propagation behavior, uiIndicating the user, Prorumor(ui) Prod as a revenue function for the strategy of forwarding rumor informationanti-rumor(ui) represents the revenue function of the strategy for forwarding the ballad,
Figure FDA0003644367860000043
Mut, an exponential function after strategy gaming for expressing forwarding rumor information and forwarding rumor splitting informationrumor(ui) Representing rumor information to user u after gamingiInfluence of the propagation behavior.
6. The rumor-nursery game propagation control method based on sparse representation and tensor completion as claimed in claim 1, wherein the process of constructing the rumor-nursery topic propagation group behavior prediction model comprises:
step 1: obtaining a feature matrix X-NxF and an adjacency matrix under a game
Figure FDA0003644367860000044
The characteristic matrix is a user characteristic matrix after the user data is sparsely represented; number compensated by tensorConstructing an adjacency matrix under the game according to the mutual influence of the rumors and the rumors;
step 2: randomly initializing weight and bias, multiplying the feature matrix X by the initial weight, and adding deviation in the multiplying process; multiplying the result with a normalized symmetric matrix
Figure FDA0003644367860000045
Multiplying to obtain a feature matrix of the next layer of input after convolution;
and step 3: inputting the characteristic matrix of the step 2 into a double-layer graph convolution neural network added with a middle Dropout layer for model training; carrying out Dropout operation in the process of carrying out model training; the activation function of the middle Dropout layer is a RELU function;
And 4, step 4: expressing the convolution output into probability values of different classes of nodes by adopting a SoftMax activation function; rumor-the expression of the group behavior prediction model of the propagation of the diner topic is as follows:
Figure FDA0003644367860000051
wherein N represents the number of user nodes in the rumor topic propagation network, F represents the input characteristic dimension of each node, and UtRepresenting the set of propagation spaces at time t,
Figure FDA0003644367860000052
representing a set of edges between the propagation spaces,
Figure FDA0003644367860000053
representing the edge weight value after the game, A representing an adjacency matrix, ReLU (mean) representing an activation function, softmax (mean) representing normalization processing, and WiAnd the weight matrix corresponding to the i-layer network in the graph convolution network is obtained.
7. The rumor-splitting game propagation control method based on sparse representation and tensor completion as claimed in claim 1, wherein the propagation trend of the rumors propagated by the users is predicted as follows:
Z＝P(r,a,d|ui)
Figure FDA0003644367860000054
if Y is 1, the potential user uiRumors will be forwarded for the next time period; if Y is-1, then the potential user uiForwarding the rumor in the next time period; otherwise, potential user uiNot participating in the rumor topic in the next period;
wherein Z represents the probability of three types of user tags, P (r, a, d | ui) Probability of each user label is shown, r is the user forwarding rumor topic, a is the user forwarding rumor, d is the user not participating in topic, P (r | u |) i) Representing user uiProbability of rumor forwarding, P (a | u |)i) Representing user uiProbability of forwarding balladry, P (d | u)i) Representing user uiProbability of not participating in a topic.
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