CN111460679B - Dynamics-based synchronous cross information propagation analysis method and system - Google Patents
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Abstract
The invention provides a synchronous cross information propagation analysis method and a system based on dynamics, which comprises the following steps: dividing the state of a network user into three user states of a susceptible state, a forwarding state and an immune state; constructing a cross information synchronous propagation dynamic model of the user changing between different user states along with the propagation of the two pieces of information; collecting two pieces of information of which the release time interval is smaller than a set value, dividing the user states of network users of the two pieces of information, inputting a plurality of user states of the two pieces of divided information into a cross information synchronous propagation dynamic model, and predicting the total number of individuals of different crowds changing along with time. The above method and system consider the interaction between two pieces of information.
Description
Technical Field
The invention relates to the technical field of public opinion transmission power system construction, in particular to a dynamics-based synchronous cross information transmission analysis method and system.
A public hot spot event on the internet usually contains a plurality of information, and the mutual influence between the information plays an important role in the overall propagation of the event. Therefore, as a basis for researching the propagation of the complex public opinion, the dynamic modeling of two pieces of information is an important problem of the complex public opinion ecosystem.
Traditionally, information dissemination research has been focused on a single piece of information, and a series of studies have been conducted on rumor dissemination in particular. Considering the similarity between rumors and epidemiology in multiple aspects, many researchers have studied rumors using the susceptible-infection (SI) model and the susceptible-infection-recovery (SIR) model, respectively, and the susceptible-infection-exposure-recovery (SEIR) model, and improved the basic model to make the model more targeted and effective. On the one hand, some scholars consider different states of propagation, introducing different modules. In 2012, researchers developed a new rumor propagation model called susceptible-infected-latent-deleted (SIHR) model that introduced a new latent module to reduce the maximum impact of rumors. In 2014, some researchers provided an SIR model, which considers a refuting mechanism of a homogeneous social network, analyzes a dynamic process of rumor propagation, and can reduce the maximum influence of rumors. On the other hand, there are also scholars who introduce more important influencing factors into the model to study the complex real world. In 2015, researchers studied the cumulative effect of human memory on rumor propagation by using microblog data sets, and proposed an influence model of the change of memory on rumor propagation rate with time in artificial networks and real social networks. Meanwhile, some researchers establish a dynamic 8-state ignorant-carrier-propagator-advocate-deleter (ICSAR) rumor propagation model to study the rumor propagation mechanism, further study the effect of each influence factor, and improve the rumor rejection and the efficiency of making an emergency plan. In addition, some studies have also addressed other factors such as the degree of trust between people, tie strength, and social affinity.
Research on information dissemination is not limited to rumors, but models are constructed for other types of information dissemination without distinguishing rumors from normal information. Researchers build parameterization (Susc epidemic users (S), super-broadcasts (A), normal broadcasts (I) recycled users (R), SAIR) models based on basic epidemic models, and the influence of superpropagators in information propagation is researched. By analyzing the topological characteristics of microblogs, a scholars introduces an epidemiological susceptibility-exposure-infection-resistance (SEIR) model and explores the mode of information propagation in a microblog network to consider that the network has obvious small world and non-standard property, so that the network is successful in information transfer but fails in resisting negative effects.
In 2018, researchers studied the propagation of crossbars at different release times, introducing two models: a double-infected-recovered (DSIR) model and a comprehensive-DSIR (C-DSIR) model. The study constructed a model of the effect of the first rumor on the second rumor but neglected the interaction of the second rumor on the first rumor and neglected the interaction between the information, by investigating the propagation of two rumors released in sequence, giving the mechanism of dual rumors and introducing a selection parameter to express the attractiveness of the different rumors.
Disclosure of Invention
In view of the above, the present invention provides a method and system for analyzing information propagation based on dynamics and synchronization crossing, which considers the interaction between two pieces of information.
According to an aspect of the present invention, there is provided a synchronous cross information propagation analysis method based on dynamics, including:
dividing the state of a network user into three user states, namely a susceptible state, a forwarding state and an immune state, wherein the susceptible state represents the state that the user is not contacted with published information but has information forwarding capability; the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state that the user loses the active ability after forwarding the information;
constructing a cross information synchronous propagation dynamic model in which users are converted between different user states along with propagation of two pieces of information, wherein in the cross information synchronous propagation dynamic model, one user is taken as an individual and is divided into different crowds according to the user states of the different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, the derivative of the total number of the individuals of one crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the conversion direction, wherein the related crowds are other crowds except the crowds in which the two pieces of information are in an immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
setting an initial value of a model parameter of a cross information synchronous propagation dynamic model, obtaining a curve of the individual total number of each crowd along with the change of time, setting one piece of information which can be transmitted only once by each user, so that the individual total number of each crowd corresponds to the transmitted amount of two pieces of information, collecting the accumulated transmitted amount of the two pieces of information with the release time interval smaller than a set value as an actual value, obtaining the accumulated transmitted amount through the cross information synchronous propagation dynamic model as an estimated value, obtaining the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, carrying out model parameter assignment by adopting the optimal value, and predicting the individual total number of different crowds of the two pieces of information along with the change of time by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
The synchronous cross information transmission analysis methodWherein, the cross information synchronous propagation dynamics model divides the users into 12 crowds according to the user states in the two pieces of information, and the two pieces of information are informationAnd informationThe population comprises: completely susceptible populationA group of individuals, both information of which are in a susceptible state; first active populationTo informationIn a forwarding state, for informationA population of individuals in a susceptible state; second active populationTo informationIn a forwarding state, for informationA population of individuals in a susceptible state; third active populationTo informationAnd informationIndividuals who are in a forwarding state and who forward informationForwarding information earlier than it is(ii) a Fourth active populationTo informationAnd informationIndividuals who are in a forwarding state, and forwarding information individuallyForwarding information earlier than it is(ii) a Fifth active populationTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it is(ii) a Sixth active populationTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it is(ii) a Seventh active populationTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to information(ii) a Eighth active populationTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to information(ii) a First immune populationTo informationIn an immune state, to the messageA population of individuals in a susceptible state; second immune populationTo informationIn an immune state, to the messageA population of individuals in a susceptible state; complete immune populationTo informationAnd informationThe total number of individuals who are all in an immune state.
The synchronous cross information transmission analysis method is characterized in that the cross information synchronous transmission dynamic modelThe model parameters include: first average contact rateInformation, informationAverage contact rate of (a); second average contact velocityInformation, informationAverage contact rate of (a); first average forwarding rateInformation, informationAverage forwarding probability of (d); second average forwarding rateInformation, informationAverage forwarding probability of (d); first strong attraction indexInformation, informationFor informationStrong attraction index of (d); second strong attractive force indexInformation, informationFor informationStrong attraction index of (d); first sustained attraction indexInformation, informationFor informationA sustained attraction index of; second sustained attraction indexInformation, informationFor informationA sustained attraction index of; first mean immune RateInformation, informationAverage immune rate of (a); second mean immune rateInformation, informationAverage immune rate of (a); third mean immune RateIndividuals from the seventh active populationTransfer to fully immune populationsAverage immune rate of (a); fourth mean immune rateIndividuals from the eighth active populationTransfer to fully immune populationsAverage immune rate of (a); initial value of total number of individuals of completely susceptible population。
The synchronous cross information transmission analysis method is characterized in that the cross information synchronous transmission dynamic model is constructed by a formula (1),
wherein,a time index, representing a time of day, the combined identifier of the group of people and the time of day representing the total number of individuals of the group of people at the time of day,to representFirst active group of people at all timesTotal number of individuals.
According to a second aspect of the present invention, there is provided a dynamics-based synchronous cross information propagation analysis system, comprising:
the user state dividing module is used for dividing the state of the network user into three user states, namely a susceptible state, a forwarding state and an immune state, wherein the susceptible state represents the state that the user is not contacted with the issued information but has the information forwarding capability; the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state that the user loses the active ability after forwarding the information;
the model building module is used for building a cross information synchronous propagation dynamic model which is changed between different user states along with the propagation of two pieces of information according to the user states divided by the user state dividing module, wherein in the cross information synchronous propagation dynamic model, one user serves as an individual, different crowds are divided according to the user states of different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, and the derivative of the total number of the individuals of one crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the transformation direction, wherein the related crowds are other crowds except the crowds in which the two pieces of information are in the immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
the acquisition module is used for acquiring two pieces of information with the release time interval smaller than a set value as an actual value, setting an initial value of a model parameter of the cross information synchronous propagation dynamic model, acquiring a curve of the individual total number of each crowd along with the change of time, setting that each user of one piece of information can only forward once, so that the individual total number of each crowd corresponds to the forward quantity of the two pieces of information, acquiring the accumulated forward quantity through the cross information synchronous propagation dynamic model as an estimated value, acquiring the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, performing model parameter assignment by adopting the optimal value, and predicting the individual total number of different crowds of the two pieces of information along with the change of time by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
The synchronous cross information transmission analysis method and system based on dynamics considers the interaction between two pieces of information, and provides a cross transmission susceptibility-forwarding-immunity (CT-SFI) transmission dynamics model, and the core of the method comprises two important processes of cross transmission: one is dynamic cross propagation with strong attraction and the other dynamic cross propagation with continuous attraction. In the former process, after a user forwards a piece of information in a short time, the user can generate strong interest in the other piece of information, and for this purpose, the invention provides a strong attraction index which describes the informationContent pair information ofTo learn about the state transitions during the forwarding exposure period. In addition, due to the timeliness of the activity state of the user, people who produce cross-propagation behavior are temporally differentiated. In the latter process, when a user is exposed to a message and after a period of time, the relevant message is still of interest, the invention proposes a continuous attraction index describing the slave message when the user is exposed beyond the forward exposure periodTo informationThe attractive force of the state transition of (1). And a set of cross propagation indexes is established, and the interaction between CT-SFI model information is explored by using numerical simulation and sensitivity analysis on a real data set so as to realize the cross propagation of the information.
Drawings
FIG. 1 is a flow chart of a dynamics-based synchronous cross-information propagation analysis method of the present invention;
FIG. 2 is a schematic diagram of a cross-information synchronous propagation dynamics model according to the present invention;
FIG. 4a is informationFor informationSchematic representation of the strong attractive force propagation dynamics of (1);
FIG. 4b is informationFor informationSchematic representation of the strong attractive force propagation dynamics of (1);
FIG. 5a is informationFor informationSchematic representation of the continuous gravity propagation dynamics process of (a);
FIG. 5b is informationFor informationSchematic representation of the continuous gravity propagation dynamics process of (a);
FIG. 6b is informationSchematic representation of the kinetics of the time-out immune propagation of (a);
FIG. 6c is informationAnd informationSchematic representation of the complex time-out immune propagation kinetics process of (a);
FIG. 7a is a graph of co-cumulative total forwarded and co-active forwarded amounts over time for co-propagation of two pieces of information;
FIG. 7b is a graph of cross-cumulative total forwarded amount and cross-active forwarded amount over time for cross propagation of two pieces of information;
FIG. 8 is a schematic diagram of the public sentiment indicator of the present invention varying with time;
FIGS. 9a, 9b, 9c, and 9d are model parametersSitting of effects on cross-propagationMarking a graph;
FIG. 13 shows the variation of parameters of multiple models,,Anda graph of the PRCCs results of (a);
FIG. 14 is a schematic diagram of a block diagram of a dynamics-based synchronized cross-information propagation analysis system of the present invention;
FIGS. 15a and 15b are graphs comparing real data and simulated data obtained by the cross-information simultaneous propagation dynamics model of the present invention in one embodiment.
Detailed Description
In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It may be evident, however, that such embodiment(s) may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate describing one or more embodiments.
Various embodiments according to the present invention will be described in detail below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a synchronous cross information propagation analysis method based on dynamics according to the present invention, and as shown in fig. 1, the synchronous cross information propagation analysis method includes:
step S1, dividing the state of the network user into three user states, namely a susceptable state (abbreviated as S), a Forwarding state (abbreviated as F) and an Immune state (Immune, abbreviated as I), wherein the susceptable state represents a state in which the user does not contact the published information but has an information Forwarding capability (users who are in an attention relationship with the original publisher or information propagator in the social network, and users who may obtain information through active search, such as smart phone users, networked computer users, and the like); the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state in which the user loses activity after forwarding the information (for example, the user does not have any operation (browsing, commenting, editing, and the like) on the information within a set time period after the user forwards the information);
step S2, constructing a cross information synchronous propagation dynamic model, namely a cross-transmission reliable-forwarding-equalized model (CT-SFI) model, which is changed between different user states along with propagation of the two pieces of information, wherein in the cross information synchronous propagation dynamic model, one user is taken as an individual, the cross information synchronous propagation dynamic model is divided into different crowds according to the user states of the different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, and the derivative of the total number of the individuals of the crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the transformation direction, wherein the related crowds are other crowds except the crowd in which the two pieces of information are in an immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
step S3, setting an initial value of a model parameter of the cross information synchronous propagation dynamic model, obtaining a curve of the individual total number of each crowd along with the change of time, setting that each user of one piece of information can only forward once, so that the individual total number of each crowd corresponds to the forward quantity of two pieces of information, collecting the accumulated forward quantity of the two pieces of information with the release time interval smaller than the set value as an actual value, using the accumulated forward quantity obtained by the cross information synchronous propagation dynamic model as an estimated value, obtaining the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, carrying out model parameter assignment by adopting the optimal value, and predicting the individual total number of different crowds of the two pieces of information along with the change of time by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
The synchronous cross information transmission analysis method based on dynamics is used for researching an information cross transmission mechanism, analyzing a general mode of the cross information transmission mechanism, researching the mutual influence among information and the effect of cross transmission on the whole event transmission by establishing a model, mastering the popularity of the internet in advance, detecting microblog information transmission, judging and predicting the current development desktop and future changes of the information transmission in time, and has great significance for maintaining social stability and constructing a harmonious society.
In a preferred embodiment of the present invention, step S2 includes:
assuming that the information is spread in a closed and stable environment, only two pieces of information and the crowd which can be reached in the cross-spread process are considered, and the total number (N) of the crowd is kept unchanged. Here, only information diffusion due to individual transfer behavior is focused, and at any time, any individual (individual) in the population (individual)) For two pieces of information (information)And informationWherein,and is) Respectively possess two states, denoted as:。
analyzing the individual state transition in the cross information synchronous transmission process, and counting the total number of the accessible people in the information transmission process () The classification is divided into 12 groups, specifically:
completely susceptible populationSatisfy the following requirementsThe group is not contacted with any one of the two pieces of information, but is contacted with one or two pieces of information in the future, is easy to be influenced by the information, and possibly generates a forwarding behavior;
first active populationSatisfy the following requirementsTo informationIn a forwarding state (active), for informationA population of individuals in a vulnerable state, the population having forwarded informationAnd still in informationWithin a forward exposure period of (2), enabling access to informationIndividual awareness information in a vulnerable stateAnd possibly a forwarding action. And, at this time, the group is about the informationRemains in a vulnerable state;
second active populationSatisfy the following requirementsTo informationIn a forwarding state (active), for informationA population of individuals in a vulnerable state, the population having forwarded informationAnd still in informationWithin a forward exposure period of (2), enabling access to informationIndividual awareness information in a vulnerable stateAnd possibly a forwarding action. And, at this time, the group is about the informationRemains in a vulnerable state;
third active populationSatisfy the following requirementsTo informationAnd informationIndividuals who are all in a forwarding state (active) make up a crowd of people and the individuals forward informationForwarding information earlier than it isThe group has forwarded the information in sequenceAnd informationAnd to informationAnd informationAre all in the forwarding exposure period and have the ability to make the pair informationOr informationIndividual awareness information in a vulnerable stateOr informationAnd possibly forwarding behavior;
fourth active populationSatisfy the following requirementsTo informationAnd informationIndividuals who are in a forwarding state, and forwarding information individuallyForwarding information earlier than it isThe group has forwarded the information in sequenceAnd informationAnd to informationAnd informationAre all in the forwarding exposure period and have the ability to make the pair informationOr informationIndividual awareness information in a vulnerable stateOr informationAnd possibly forwarding behavior;
fifth active populationSatisfy the following requirementsTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it isThe group first generates pair informationThen forwards the information. Here, the informationIs within a forwarding exposure period, i.e., the group has the ability to make a request for informationIndividual awareness information in a vulnerable stateAnd possibly forwarding behavior;
sixth active populationSatisfy the following requirementsTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it isThe group first generates pair informationThen forwards the information. Here, the informationIs within a forwarding exposure period, i.e., the group has the ability to make a request for informationIndividual awareness information in a vulnerable stateAnd possibly forwarding behavior;
seventh active populationSatisfy the following requirementsTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to informationThe group having forwarded the information firstThen pair information is generatedThe immunization of (1); here, the informationIs within a forwarding exposure period, i.e., the group has the ability to make a request for informationIndividual awareness information in a vulnerable stateAnd possibly forwarding behavior;
eighth active populationSatisfy the following requirementsTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to informationThe group having forwarded the information firstThen pair information is generatedThe immunization of (1); here, the informationIs within a forwarding exposure period, i.e., the group has the ability to make a request for informationIndividual awareness information in a vulnerable stateAnd possibly forwarding behavior;
first immune populationSatisfy the following requirementsTo informationIn an immune state, to the messageIn a vulnerable stateA population of individuals, the population consisting of two parts: partly only information is forwardedOver time, exceeds the informationNo longer has the ability to influence others to know the informationAnd generating a total number of individuals behaving; another part is the exposure of the individual in a susceptible state (S) to informationLater, due to subjectively aligning informationIs directly converted into information without interestTotal number of individuals immunized;
second immune populationSatisfy the following requirementsTo informationIn an immune state, to the messageA population of individuals in a susceptible state, the population consisting of two parts: partly only information is forwardedOver time, exceeds the informationNo longer has the ability to influence others to know the informationAnd generating a total number of individuals behaving; another part is the exposure of the individual in a susceptible state (S) to informationLater, due to subjectively aligning informationIs directly converted into information without interestTotal number of individuals immunized;
complete immune populationSatisfy the following requirementsTo informationAnd informationThe total number of individuals who are all in an immune state.
The following model parameters were constructed:
TABLE 1
The cross information synchronous propagation kinetic model is constructed by formula (1), as shown in fig. 2, the cross information synchronous propagation CT-SFI kinetic model has a special attraction to one piece of information when the other piece of information is touched compared with the event that the other piece of information is not touched for two pieces of related information, so that a cross-propagation (cross-propagation) condition of the two pieces of information is generated. And, for the action that the second piece of information is forwarded when the first piece of information contacted is still in the exposure period, it is called strong attraction; in addition, when the first piece of information touched exceeds the forwarding exposure period, a part of the individual still forwards the second piece of information with a certain probability due to retention of memory, which is called continuous attraction.
The user state conversion in the cross information synchronous propagation dynamic model comprises the following processes:
first, the dynamics of single information dissemination, specifically:
as shown in fig. 3a, for informationWhen one is in a vulnerable state(iii) an individual (individual)x) Contact to informationIn a forwarding state(iii) an individual (individual)y) Knowing the informationAfter the content, a subjective decision is made whether to forward the message, thereby moving to the messageForm of forwardOr immune state。
In conjunction with the entire cross-information simultaneous propagation dynamics process of FIG. 2, a pair of informationThe individual in the forwarding state is exposed to the average in unit timeAn individual, wherein,personal individuals may choose to forward informationTo do soIndividual selective non-forwarding information. Since the probability that an individual is a susceptible person isTo do so, ,,Is that the individual is in the pair informationFor example, the newly generated information for a unit timeThe number of forwarding individuals and the number of immunized individuals are respectivelyAnd。
similarly, for informationThe propagation kinetics of (c), as shown in fig. 3b, have similar state transitions.
Secondly, the double information strong attraction cross propagation dynamic process in the forwarding exposure period specifically comprises the following steps:
as shown in fig. 4a, in the messageDuring the forward exposure period, the individual forwards the informationTo informationThe strong attraction and thus the resulting cross-propagation dynamics can be expressed as when one is in the informationForward state pair informationIn a susceptible state(iii) an individual (individual)x) Contact to informationIn a forwarding state(iii) an individual (individual)y) Knowing the informationAfter the content, a subjective decision is made whether to forward the message, thereby moving to the messageAnd informationAre all in a forwarding stateOr for informationIs in forwarding pair informationIs in an immune state. This is a very different propagation dynamics process of the CT-SFI model from the traditional SFI model, which fully considers the cross propagation in the short term due to the existence of strong attraction of the two pieces of related information.
In conjunction with the entire cross-information synchronous propagation dynamics process of FIG. 2, information is forwardedWill be paired with relevant information during the forward exposure periodGenerate special interest, and can be used for information with higher probabilityForwarding is performed by using strong attraction indexTo measure the degree of such enhanced forwarding. For pair informationIn forwarding state to informationFor a group in a vulnerable state, one pair of information per unit timeThe individual in the forwarding state will be exposed toIndividuals in this population, similar to the dynamics of single message dissemination, relay messages among themThe number of individuals ofNot to informationThe number of individuals for forwarding is. It can be seen that the probability of forwarding or not is given by the strong attraction indexThe control of (2) is, in general, a strong attraction index which is again a quantity greater than 1, so that, in a relatively short time, information is forwarded on account of thisTo forward informationProbability of (2)Forwarding information independently more than if neither information is knownProbability of (2). Further, the pair information newly added in the process in unit time can be obtainedThe number of forwarding individuals and the number of immunized individuals of (1), respectivelyAnd. Wherein,,,,is that the individual is in the pair information 5 cases of the forwarding state of (1).
Similarly, informationFor informationThe strong attractive force propagation kinetics of (2) as shown in fig. 4b, have similar state transitions.
Third, the dual information beyond the forward exposure period continuously attracts the cross-propagation dynamics processes, specifically:
as shown in FIG. 5a, when an individual has been exposed to informationBut beyond its exposure period, whether forwarded or merely contacted without forwarding, will provide informationHas certain memory retention, thereby generating the pair informationThe dynamics may be expressed as when an on-message is presentImmune status ofIn a susceptible state(iii) an individual (individual)x) Contact to informationIn a forwarding state(iii) an individual (individual)y) Knowing the informationAfter the content, a subjective decision is made whether to forward the message, thereby moving to the messageIn the immune pair informationAre all in a forwarding stateOr for informationAnd informationAre all in an immune state. This process takes into account the cross-propagation from the long-term effect due to the presence of the continuing attraction of the two pieces of relevant information.
The whole cross information synchronous propagation dynamic process combined with the figure 2Even if the individual exceeds the forwarding exposure period, the individual never contacts the relevant informationWill still have a higher probability of pairing informationForwarding is performed using sustained attractiveness indexTo measure the degree of such enhanced forwarding. For pair informationIn an immune state to informationFor a group in a vulnerable state, one pair of information per unit timeThe individual in the forwarding state will be exposed toThe individuals in this group, as such, are similar to the dynamics of single message dissemination, wherein messages are forwardedThe number of individuals ofNot to informationThe number of individuals for forwarding is. It can be seen that the probability of forwarding or not is subject to a sustained attractiveness indexThe continuous attractiveness index is generally a quantity greater than 1, so that the information is forwarded for a longer timeTo forward informationProbability of (2)Forwarding information independently more than if neither information is knownProbability of (2). Further, the pair information newly added in the process in unit time can be obtainedThe number of forwarding individuals and the number of immunization individuals of (1) are respectivelyAnd。
similarly, informationFor informationThe sustained attractive force propagation kinetics of (a), as shown in fig. 5b, have similar state transitions.
Fourth, a timeout immunization process, specifically: in the CT-SFI model, as shown in FIG. 2, there are 8 overtime immune processes, since when a message exceeds its burst period () Later, the state transition process generated by the fact that people are not exposed to old information, and 8 overtime immune processes can be divided into three types:
the first type is informationTime-out of immune propagation kinetics, using the mean immune rateRepresenting individual informationForwarding state transition informationIncluding in particular the average rate of the immune status of the informationRespectively in a susceptible state, a forwarding state and an immune state, as shown in fig. 6a, i.e. three state transitions, namely a slave stateIs changed toFrom stateIs changed toAnd slave stateIs changed to。
Similarly, the second type is informationTime-out of immune propagation kinetics, using the mean immune rateRepresenting individual informationForwarding state transition informationThe average rate of the immune status of (2), also including for the informationIn three cases, namely a vulnerable state, a forwarding state and an immune state, respectively, as shown in FIG. 6b, the three states transition, i.e. the slave stateIs changed toFrom stateIs changed toAnd slave stateIs changed to。
The third transition process is more special, such as the figure6c is shown byRepresenting individual slave statusTransition to a fully immune stateAverage immune rate of (c). This is informationBut not useful in the state transition process ofAs the mean immunity rate, this is because there is already a fraction of slave states in this populationTransfer to Pair informationState of immunityDuring this time, information is also consumedAnd thus, this fraction of the population will have a faster average immune rate. When the slave status is comprehensively consideredTo a state of complete immunityWhen the average immune rate is higher than the predetermined value, a single average immune rate parameter is set. In a similar manner, the first and second substrates are,representing individual slave statusTransition to a fully immune stateAverage immune rate of (c).
In one embodiment, the assumption that each user forwards the same information only once is defined, and in step S3, the step of corresponding the total number of individuals of each group to the forwarding amount of the two pieces of information includes:
an estimation model of the accumulated forwarding amount of two pieces of information is constructed by the following formula
Wherein,andare respectively informationAnd informationAn estimate of the cumulative forwarding amount of (a),
the step of obtaining the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting the parameter estimation method comprises the following steps:
method for estimating parameters of cross information synchronous propagation dynamic model by adopting least square method
Wherein,is the square error of the parameter(s),the dynamic model parameter vectors are propagated synchronously for the cross information,,which is indicative of the time of the sampling,andrespectively indicate the timePresence of a parameterInformation under conditionsAnd informationAn estimate of the cumulative forwarding amount of (a),representing informationArrival timeThe amount of forwarding is actually accumulated so far,representing informationArrival timeThe actual accumulated forwarding amount is present.
In one embodiment, the above method for analyzing the propagation of synchronization cross information further includes:
analyzing a common accumulated forwarding total amount, a cross accumulated forwarding total amount, a common active forwarding amount or/and a cross active forwarding amount of the two pieces of information according to the cross information synchronous propagation dynamic model after the model parameter assignment, and monitoring public sentiment, wherein the common accumulated forwarding total amount is the sum of the accumulated forwarding amounts of the two pieces of information for a period of time until the monitoring moment; the common active forwarding amount is the sum of the forwarding amounts of the two pieces of information at the monitoring moment; the cross accumulated forwarding total amount is the sum of accumulated forwarding amounts of a period of time from the moment of monitoring to the moment of first contacting one piece of information and then forwarding the other piece of information; the cross active forwarding amount is the sum of the forwarding amounts of contacting one information before forwarding another information at the monitoring moment.
As shown in fig. 7a, the co-accumulated total amount of forwarding and the co-active amount of forwarding that are co-propagated by two pieces of information. Collectively accumulating forwarding totalsTwo important parts of, informationAccumulated forwarding amount ofAnd informationAccumulated forwarding amount ofAre all quantities that can be acquired during propagation, as shown in equation (5)
As shown in FIG. 7a, information may also be obtainedAnd informationActive forwarding amount ofAnd) Co-composed cross-information co-propagated co-active forwarding volumesAs shown in formula (6)
Wherein:
FIG. 7b shows the cross-accumulated forwarding total for two information cross-propagationsTo contact information firstRe-forwarding informationExamples of the case include accumulation of forwarding amounts by strong attraction during the exposure periodAnd sustained attractive force cumulative forwarding over exposure period:
Wherein
Similarly, first contact information can be obtainedRe-forwarding informationCross-propagated cross-active forwarding volumes ofForwarding of quantities by strong attraction during the exposure periodAnd sustained attractive forwarding of energy beyond the exposure periodThe common components are shown in formulas (12) to (14).
Contact information first due to symmetry of the modelRe-forwarding informationSimilarly, the cross-accumulated forwarding total of the cross-propagation of two messagesAccumulation of forwarding by strong attraction during exposureAnd sustained attractive force cumulative forwarding over exposure periodThe components are combined together to form the composite material,first contact informationRe-forwarding informationCross-propagated cross-active forwarding volumes ofForwarding of energy by strong attraction during exposureAnd sustained attractive forwarding of energy beyond the exposure periodThe components are combined together to form the composite material,。
in one embodiment, the method further comprises the step of predicting public sentiment by public sentiment indexes including a public sentiment outbreak index, a public sentiment outbreak peak, a maximum public sentiment propagation index, a public sentiment outbreak rate, a public sentiment decline rate and an average rate, the step comprising:
public opinion outbreak index obtained from initial total number of individuals in susceptible populationThe public sentiment outbreak index represents the severity of a public sentiment event outbreak;
judging whether the public opinion outbreak index is more than 1, less than 1 or equal to 1;
if it is notThe number of the users in the forwarding state is reduced, and information cannot be exploded; if it is notIndicating that the number of users in the forwarding state will increase exponentially; if it is notIndicating that the number of users in the forwarding state is unchanged;
predicting public opinion transmission peak value by adopting numerical simulation method through curve of total number of individuals of crowd in forwarding state changing along with timeThe public sentiment propagation peak represents a propagation peak of a public sentiment hot event, and as shown in fig. 8, represents a curveMaximum value of (d);
the moment when the number of the users in the forwarding state is increased to the first set proportion of the first public sentiment propagation peak value is taken as the public sentiment outbreak starting momentPredicting the public sentiment outbreak starting moment, as shown in fig. 8;
the moment when the number of the users in the forwarding state is increased to the public sentiment propagation peak value is taken as the public sentiment outbreak peak value momentPredicting the public sentiment outbreak peak moment, as shown in fig. 8;
the moment when the number in the forwarding state is reduced to a second set proportion of the public sentiment propagation peak value is taken as the public sentiment outbreak ending momentPredicting the finish time of public sentiment outbreak,is the period of public sentiment outbreakAs shown in fig. 8;
the number of users in a forwarding state in unit time from the starting moment of public sentiment outbreak to the peak moment of the public sentiment outbreak is taken as the public sentiment outbreak rateThe public opinion outbreak rate is predicted;
the number of users in a forwarding state in unit time from the peak moment of public sentiment outbreak to the end moment of the public sentiment outbreak is taken as the rate of public sentiment declineFor example, the first set proportion and the second set proportion are equal, and the threshold value is set in advance,When is coming into contact withWhen it is knownThe public sentiment outbreak rate and decline rate can be defined asAndmean rate from start to peak and mean rate from peak to end of a public opinion hotspot event outbreak;
the number of users in a forwarding state in unit time from the starting moment of public sentiment outbreak to the ending moment of the public sentiment outbreak is taken as an average rate, and the public sentiment average rate is predicted;
and predicting a maximum public opinion propagation index by a numerical simulation method through a curve of the cumulative quantity of the total number of individuals of the crowd in a forwarding state changing along with time, wherein the maximum public opinion propagation index represents the maximum boundary number which can be reached by public opinion event outbreak, namely the forwarding cumulative quantity of the whole event outbreak period.
The public opinion outbreak index obtaining method comprises the following steps:
extracting differential equation establishing equation of crowd with infection capacity
Wherein,is a population with an infectious effect, is also an active population, is also a population containing users in a forwarding state, and
wherein,is composed ofThe time instant translates into the total number of individuals in the active population,is composed ofThe time of day is converted into a total number of individuals of the inactive population;
and
thus, it is possible to provide
obtaining public sentiment outbreak index through characteristic valuePublic sentiment outbreak indexIs thatRadius of spectrum of
In a third embodiment, the method further comprises the step of analyzing the sensitivity of the model parameters to the cross-information synchronous propagation dynamics model, the step comprising:
constructing a strong attraction accumulated forwarding quantity model, a continuous attraction accumulated forwarding quantity model, a strong attraction forwarding quantity model and a continuous attraction forwarding quantity model through formulas (10) - (14);
predicting the total number of individuals of different crowds of which the two pieces of information change along with time through a cross information synchronous propagation dynamic model after model parameters of the two pieces of information are assigned, inputting a strong attraction accumulated forwarding amount model, a continuous attraction accumulated forwarding amount model, a strong attraction forwarding amount model and a continuous attraction forwarding amount model, and analyzing the influence of the change on the output of the strong attraction accumulated forwarding amount model, the continuous attraction accumulated forwarding amount model, the strong attraction forwarding amount model and the continuous attraction forwarding amount model through the change of a strong attraction index and a continuous attraction index;
and analyzing the influence of the model parameters on the public opinion indexes by adopting a partial rank correlation coefficient method.
In the steps, the first aspect analyzes the influence of the mutual attraction of two pieces of information on the cross propagation of the public sentiment, and the second aspect analyzes the comprehensive influence of each parameter on the public sentiment propagation index. In the cross information synchronous propagation CT-SFI dynamic model, the strong attraction index of one piece of information in the forwarding exposure period of the other piece of informationAnd a persistent attractiveness index for one information piece after a forwarding exposure period of more than one information pieceNot only plays a decisive role in cross propagation, but also plays a decisive role in the propagation of the whole event.
To analyze the index of strong attractionAnd sustained attraction indexWill analyze the accumulated forwarding amount of strong attraction force in the exposure period under the condition that two parameters are changed in a certain rangeAnd sustained attractive force cumulative forwarding over exposure periodAnd corresponding strong attractive forwarding of light during the exposure periodAnd sustained attraction forwarding beyond the exposure periodMeasurement ofWill be analyzed separately here,,,Four groups of cases.
FIGS. 9a-9d show model parametersInfluence on cross propagation, where FIG. 9a is informationFor informationAnalyzing the sensitivity of strong attraction force; FIG. 9b is informationFor informationAnalyzing the sensitivity of strong attraction force; FIG. 9c is informationFor informationContinuous attractiveness sensitivity analysis of; FIG. 9d is informationFor informationContinuous attractiveness sensitivity analysis. As shown in fig. 9a, parametersAccumulated forwarding amount for strong attractionAnd forwarding amountHas very obvious effect of increasing the index of strong attractionWill be greatly increased due to the pair informationInterested in information during the forward exposure periodProbability of forwarding, resulting in a forwarded amountHigher peak sumLarger final scale. Conversely, as shown in FIG. 9b, the strong attraction index is increasedAccumulated forwarding amount for strong attractionAnd forwarding amountIt has no great effect. As shown in figures 9c and 9d,for accumulating forwarding amount regardless of continuous attractionAnd forwarding amountOr continuously attracting accumulated forwarding capacityAnd forwarding amountThe effect of (a) is not significant. Therefore, a strong attraction force parameterCan effectively influence the information in a short timeTo informationCross propagation of (c).
FIGS. 10a-10d show the parametersInfluence on cross propagation, where FIG. 10a is informationFor informationAnalyzing the sensitivity of strong attraction force; FIG. 10b is informationFor informationAnalyzing the sensitivity of strong attraction force; FIG. 10c is informationFor informationContinuous attractiveness sensitivity analysis of; FIG. 10d is informationFor informationContinuous attractiveness sensitivity analysis. And parametersSimilarly, as shown in FIG. 10c, the parametersCumulative forwarding for sustained attractionsAnd forwarding amountHas very obvious effect of increasing the index of strong attractionWill be greatly increased due to the pair informationInterested in comparing information after exceeding the forwarding exposure periodProbability of forwarding, resulting in a forwarded amountHigher peak sumLarger final scale. And parametersDifferent from the parametersPlays a certain role in other cross propagation processes and can also influence the information due to the pairTo forward informationAs shown in FIGS. 10b and 10d, and informationTo forward informationThe strong attraction process of (2), as shown in FIG. 10a, during these cross-propagation processes, the parametersThe influence on the cumulative forwarding amount is not information as shown in FIG. 10cFor informationIs obvious but not negligible. Parameters of strong attractionTo cross transmissionThe influence of the broadcast is stronger than the constant attraction parameterInfluence on cross propagation.
For parameterIt only works in a short time, reflecting that the information is forwardedBut affects the event to forward the informationThe cross-propagation phenomenon of (a), which has no effect on the burst period of the entire event. For parameterIt has an effect on the rate of the overall event burst and decay, as well as no effect on the burst period. By influencing the parametersCan affect the already paired informationIndividuals who are immunized or not in the forwarding active phase are again involved in the dissemination of public sentiment events. That is, when attempting to expand the spread of public sentiment, although two pieces of related information have different influences on the spread of the entire event, the co-spread of the entire event can be promoted by influencing a group in which the two pieces of information are co-spread due to mutual influence between the events.
The sensitivity analysis of the second aspect is a method for researching the comprehensive influence of each model parameter on the public opinion propagation index and utilizing the partial rank correlation coefficient PRCCs. FIG. 11 shows different model parametersVarious public opinion indexes under variable conditions, The PRCCs results of (a), scatter plots and their significance levels p-value. Setting a significance level of 0.01 as a judgment standard for judging whether the parameters are important or not; setting a correlation coefficient | PRCC! noncircular ray according to the actual situation of public opinion propagationThe model parameter has strong effect on the influence of the hot event, and the public sentiment is controlled most effectively by influencing the model parameter; is provided withPRCC| Indicating that the model parameters have a general impact on the hotspot events; while | PRCCThe impact of this model parameter on hot-spot events will be quite limited.
As shown in fig. 11, parametersThe significance level p-value of is more than 0.01, and the absolute values of the correlation coefficients of the significance level p-value and the significance level p-value are all more than 0.4, which indicates that the parametersReproducible number to public opinionAll have strong effects. Wherein the average contact rate is determined byAnd average forwarding probabilityIncrease of (2), reproducible number of public sentimentsWill increase with increasing; in contrast, with average immunization rateIncrease of (2), reproducible number of public sentimentsAnd is reduced accordingly.
Fig. 12 shows the influence of each model parameter on joint propagation, and shows how cross propagation affects the overall public opinion diffusion effect. Comprehensively comparing the model parametersAndfor the peak value of accumulated forwarding amount reflecting comprehensive propagation capacityAnd maximum value of forwarding amountPlays the most important role, the significance level p-value of the compounds is more than 0.01, and the absolute values of the correlation coefficients of the compounds are more than 0.4. Augmenting model parametersAndwill increase the final scalePeak of harmony. This suggests that the attraction index may drive public sentiment diffusion by promoting cross propagation. In a real network, the cross propagation of different events can have different effects on the development of the whole public sentiment event.
As shown in fig. 13, the duration of the public sentiment event, i.e. the public sentiment ending timeModel parametersPlays an important role, the relevant parameters are more than 0.4, and the model parametersAndthe general function is exerted, and the relevant parameters are between 0.2 and 0.4; peak time for the public sentiment eventModel parametersAndis the main factor controlling it. Public sentiment index for rate classAndonly model parametersAre the main factors for controlling them, the relevant parameters are more than 0.4; for rate of public opinion outbreakModel parametersHas general influence on the public sentiment decay rate, parameter,With a general influence. From the results, the strong attraction index and the continuous attraction index have large influence on the final scale of public sentiment and the peak value of public sentiment, and have weak influence on time and speed.
Fig. 14 is a schematic diagram of a block diagram of a dynamics-based synchronous cross information propagation analysis system according to the present invention, and as shown in fig. 14, the synchronous cross information propagation analysis system includes:
the user state dividing module 1 is used for dividing the state of the network user into three user states, namely a susceptible state, a forwarding state and an immune state, wherein the susceptible state represents the state that the user is not contacted with the issued information but has the information forwarding capability; the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state that the user loses the active ability after forwarding the information;
the model building module 2 is used for building a cross information synchronous propagation dynamic model which is changed between different user states along with the propagation of two pieces of information according to the user states divided by the user state dividing module, wherein in the cross information synchronous propagation dynamic model, one user serves as an individual, different crowds are divided according to the user states of the different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, and the derivative of the total number of the individuals of one crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the transformation direction, wherein the related crowds are other crowds except crowds with two pieces of information in an immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
the acquisition module 3 acquires two pieces of information with the release time interval smaller than a set value as actual values, sets an initial value of a model parameter of the cross information synchronous propagation dynamic model, obtains a curve of the individual total number of each crowd along with the time change, sets that each user of one piece of information can only forward once, so that the individual total number of each crowd corresponds to the forward amount of the two pieces of information, obtains an accumulated forward amount through the cross information synchronous propagation dynamic model as an estimated value, obtains an optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, performs model parameter assignment by adopting the optimal value, and predicts the individual total number of different crowds of the two pieces of information along with the time change by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
In one embodiment, the acquisition module 3 comprises:
the message accumulated forwarding amount estimation model building unit is used for building an estimation model of accumulated forwarding amounts of two pieces of information through formulas (2) and (3);
and the model parameter obtaining unit estimates the parameters of the cross information synchronous propagation dynamic model by adopting a least square method.
In one embodiment, the system further comprises a monitoring module 4, which analyzes the common accumulated forwarding total amount, the cross accumulated forwarding total amount, the co-active forwarding amount or/and the cross-active forwarding amount of the two pieces of information according to the cross information synchronous propagation dynamic model after the model parameter assignment, and monitors the public sentiment, wherein the common accumulated forwarding total amount is the sum of the accumulated forwarding amounts of the two pieces of information for a period of time up to the monitoring time; the common active forwarding amount is the sum of the forwarding amounts of the two pieces of information at the monitoring moment; the cross accumulated forwarding total amount is the sum of accumulated forwarding amounts of a period of time from the moment of monitoring to the moment of first contacting one piece of information and then forwarding the other piece of information; the cross active forwarding amount is the sum of the forwarding amounts of contacting one information before forwarding another information at the monitoring moment.
In one embodiment, the system further comprises a public opinion index construction module for constructing a public opinion index for public opinion prediction, wherein the public opinion index comprises a public opinion outbreak index, a public opinion outbreak peak value, a maximum public opinion spreading index, a public opinion outbreak rate, a public opinion decline rate and an average rate.
In one embodiment, further comprising: and the sensitivity analysis module 5 is used for analyzing the sensitivity of the model parameters to the cross information synchronous propagation dynamic model, and comprises the following steps:
the model building unit is used for building a strong attraction accumulated forwarding amount model, a continuous attraction accumulated forwarding amount model, a strong attraction forwarding amount model and a continuous attraction forwarding amount model;
the first sensitivity analysis unit predicts the total number of individuals of different crowds of two pieces of information changing along with time through a cross information synchronous propagation dynamic model after model parameter assignment of the two pieces of information, inputs a strong attraction force cumulative forwarding amount model, a continuous attraction force cumulative forwarding amount model, a strong attraction force forwarding amount model and a continuous attraction force forwarding amount model, and analyzes the influence of the change on the output of the strong attraction force cumulative forwarding amount model, the continuous attraction force cumulative forwarding amount model, the strong attraction force forwarding amount model and the continuous attraction force forwarding amount model through the change of a strong attraction force index and a continuous attraction force index;
and the second sensitivity analysis unit analyzes the influence of the model parameters on the public opinion indexes by adopting a bias rank correlation coefficient method.
The propagation of a public hotspot event is typically affected by several related pieces of information. The co-propagation of two different pieces of information is critical to the integrated analysis and control of the entire event. The synchronous cross information transmission analysis system based on dynamics applies the mathematical theory to public opinion analysis through cross discipline, information dynamics is combined with public opinion event information transmission, information dynamics analysis is combined with news public opinion event analysis to establish a model, and the influence of cross transmission of information is particularly concerned. Taking two pieces of information as an example, modeling is carried out aiming at attractions of different degrees between the information, a model parameter is constructed through the forwarding quantity construction of two pieces of related information, an index of public opinion outbreak is constructed and analyzed, a model with a key parameter of strong attraction index and continuous attraction index is constructed, and under the same condition, users with cross propagation are better cooperative propagators, so that a group of the cross propagators is an object which controls information propagation and takes a strategy to be considered preferentially.
In one embodiment of the invention, the invention uses the microblog truth data to verify the validity of our CT-SFI model. Through an Application Program Interface (API), the exact time that the user forwarded can be obtained.
Table 2 and table 3 respectively show two groups of microblog posting cumulative forwarding amounts which are propagated in a cross manner, two groups of data are obtained through microblog APIs, and sampling frequency is 1 hour. Case 1 described in table 2 is an event. Two microblogs which are issued simultaneously are selected. Case 2 described in table 3 is another event. Two microblogs in the same time period are selected. The sampling frequency was 1 hour, the cumulative forwarding amounts of the two pieces of information obtained for the two cases are shown in tables 2 and 3,
TABLE 2
TABLE 3
Fig. 15a and 15b show the numerical simulation results for two cases, in which the circle is the actual cumulative forwarding value of the information and the asterisk is the cumulative forwarding estimation value based on the cross-information simultaneous propagation CT-SFI dynamical model drawn from the results of the parameter estimation. Observing the real accumulated forwarding amount of the two groups of cases, wherein the initial propagation rate of the information 2 in the case 1 is slower than that of the information 1, but the explosion period is longer than that of the information 1; the initial propagation rates of the two pieces of information of case 2 are similar, but the propagation force of information 2 is higher than that of information 1 as a whole. As can be seen from the parameter estimation fitting curve in the graph, for various types of cross-synchronous propagation events, the CT-SFI dynamic model provided by the invention can well estimate parameters, and the fitting curves are very close to real values, so that the feasibility of the model is fully verified.
Table 4 shows the results of parameter estimation for two cases that can represent the overall propagation effect and the cross propagation effect. With average contact rateThe relevant parameters are determined by the network architecture, of case 1Andthe number of the fans is different, which shows that the fan groups owned by the publishers of the two information are very different from the multi-level attention relationship owned by the fan groups; accordingly, case 2Andthe difference in values is not great, which shows that the network densities of the multi-level fan structures of the two information publishers are similar. As a measure of event dissemination engagement, from case 1,=0.029, of case 2,=0.020 can see that, for two different pieces of information of an event, the average active forwarding probability of a population is in a large range, and the content of the information is different, so that the attraction degree is different, which results in a difference in the forwarding probability in a certain range. Parameter(s)() Is the average immunization rate of the information, i.e. the() Is the average exposure period of the information; in addition, the parameters( ) Is the rate of immunization of an individual from a partially immune state to a fully immune state, and, correspondingly,() An exposure period during which the individual shifts from a partially immune state to a fully immune state. Results of parameter estimation show that of case 1,,= 0.410,=0.410, case 20.097,0.068,= 0.654,=0.654, hereAndthe behavior rules of most forwarding groups are embodied,andbehavior rules of a forwarding group immunized against one piece of information after the other piece of information has been immunized can be embodied. In the case of a sampling period of 1 hour,,,andthe typical value range is [2.5,33 ]]Corresponding to 2.5 hours to 33 hours.
TABLE 4
The strong attraction indexes of case 1 are respectively=0.798,0.724, sustained attraction index of1.201,= 0.686; case 2 has strong attraction indexes of=0.550,0.525 and sustained attraction index of0.333,= 0.345. Comparative analysis shows that the cross-propagation of case 1 is significantly larger than that of case 2. In case 1, the effect of the sustained attraction is greater than that of the strong attraction, and in case 2, the strong attraction is greater than that of the sustained attraction.
Table 5 shows the result of the main cross synchronization information and the sentiment propagation index, and the overall effect of cross information synchronization propagation can be evaluated. First, for public opinion renewable number, case 1This is a relatively large number, indicating that case 1 has a very rapid initial burst tendency and passes quicklyThe peak value of public sentiment is reached in hours. Compared to case 1, case 2 has a lower regenerability number, justIts outbreak is also slow and has passedThe peak of the public sentiment is reached only in hours but the peak of the public sentiment is reachedHigher than case 1. For final scale of public opinion, case 2Slightly larger than in case 1That is, case 2 has a wider public opinion coverage than case 1.
TABLE 5
In this embodiment, according to the reference valueThe initial value of the initially acquired information data exceedsThat is to sayCorrespondingly, the duration of the public sentiment is the ending time of the public sentimentOnly givenThe result of (1). From the results, it can be seen that the public sentiment outbreak period of both cases took 17 hours, but the outbreak and decay rates were different, with respect to the average outbreak rate of the public sentimentAverage rate of decay with public opinionTwo rates for case 1 (/h),All are lower than the casesTwo rates of 2(/h),(/ h), which illustrates that case 2 is more concerned and the rate of propagation is faster than both cases.
While the foregoing disclosure shows illustrative embodiments of the invention, it should be noted that various changes and modifications could be made herein without departing from the scope of the invention as defined by the appended claims. The functions, steps and/or actions of the method claims in accordance with the inventive embodiments described herein need not be performed in any particular order. Furthermore, although elements of the invention may be described or claimed in the singular, the plural is contemplated unless limitation to a single element is explicitly stated.
Claims (10)
1. A synchronous cross information propagation analysis method based on dynamics is characterized by comprising the following steps:
dividing the state of a network user into three user states, namely a susceptible state, a forwarding state and an immune state, wherein the susceptible state represents the state that the user is not contacted with published information but has information forwarding capability; the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state that the user loses the active ability after forwarding the information;
constructing a cross information synchronous propagation dynamic model in which users are converted between different user states along with propagation of two pieces of information, wherein in the cross information synchronous propagation dynamic model, one user is taken as an individual and is divided into different crowds according to the user states of the different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, the derivative of the total number of the individuals of one crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the conversion direction, wherein the related crowds are other crowds except the crowds in which the two pieces of information are in an immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
setting an initial value of a model parameter of a cross information synchronous propagation dynamic model, obtaining a curve of the individual total number of each crowd along with the change of time, setting one piece of information which can be transmitted only once by each user, so that the individual total number of each crowd corresponds to the transmitted amount of two pieces of information, collecting the accumulated transmitted amount of the two pieces of information with the release time interval smaller than a set value as an actual value, obtaining the accumulated transmitted amount through the cross information synchronous propagation dynamic model as an estimated value, obtaining the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, carrying out model parameter assignment by adopting the optimal value, and predicting the individual total number of different crowds of the two pieces of information along with the change of time by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
2. The synchronous cross information propagation analysis method of claim 1, further comprising:
analyzing a common accumulated forwarding total amount, a cross accumulated forwarding total amount, a common active forwarding amount or/and a cross active forwarding amount of the two pieces of information according to the cross information synchronous propagation dynamic model after the model parameter assignment, and monitoring public sentiment, wherein the common accumulated forwarding total amount is the sum of the accumulated forwarding amounts of the two pieces of information for a period of time until the monitoring moment; the common active forwarding amount is the sum of the forwarding amounts of the two pieces of information at the monitoring moment; the cross accumulated forwarding total amount is the sum of accumulated forwarding amounts of a period of time from the moment of monitoring to the moment of first contacting one piece of information and then forwarding the other piece of information; the cross active forwarding amount is the sum of the forwarding amounts of contacting one information before forwarding another information at the monitoring moment.
3. The synchronous cross information propagation analysis method of claim 1, wherein the cross information synchronous propagation dynamics model divides users into 12 groups according to user states in two pieces of information, the two pieces of information being informationAnd informationThe population comprises: completely susceptible populationA group of individuals, both information of which are in a susceptible state; first active populationTo informationIn a forwarding state, for informationA population of individuals in a susceptible state; second active populationTo informationIn a forwarding state, for informationA population of individuals in a susceptible state; third active populationTo informationAnd informationIndividuals who are in a forwarding state and who forward informationForwarding information earlier than it is(ii) a Fourth active populationTo informationAnd informationIndividuals who are in a forwarding state, and forwarding information individuallyForwarding information earlier than it is(ii) a Fifth activityJumping populationTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it is(ii) a Sixth active populationTo informationIn an immune state, to the messageA population of individuals in a forwarding state, and the individuals are immunized against the informationForwarding information earlier than it is(ii) a Seventh active populationTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to information(ii) a Eighth active populationTo informationIn a forwarding state, for informationA population of individuals in an immune state, and the individuals forwarding informationBefore immunizing to information(ii) a First immune populationTo informationIn an immune state, to the messageA population of individuals in a susceptible state; second immune populationTo informationIn an immune state, to the messageA population of individuals in a susceptible state; complete immune populationTo informationAnd informationIndividuals who are all in an immune state.
4. The synchronous cross information propagation analysis method of claim 3, wherein the model parameters of the cross information synchronous propagation dynamics model comprise:
second strong attractive force indexInformation, informationFor informationStrong attraction index of (d);
first sustained attraction indexInformation, informationFor informationA sustained attraction index of;
second sustained attraction indexInformation, informationFor informationA sustained attraction index of;
third mean immune RateIndividuals from the seventh active populationTransfer to fully immunized humanGroup ofAverage immune rate of (a);
fourth mean immune rateIndividuals from the eighth active populationTransfer to fully immune populationsAverage immune rate of (a);
5. The synchronous cross information propagation analysis method of claim 4, wherein the cross information synchronous propagation dynamics model is constructed by the following formula,
6. The synchronous cross information dissemination analysis method according to claim 4, further comprising the step of predicting public sentiments by public sentiment indexes including a public sentiment outbreak index, a public sentiment outbreak peak, a maximum public sentiment dissemination index, a public sentiment outbreak rate, a public sentiment decline rate and an average rate, said step comprising:
obtaining a public opinion outbreak index by the total number of individuals of the initial susceptible population according to the following formula, the public opinion outbreak index representing the severity of the public opinion event outbreak
judging whether the public opinion outbreak index is more than 1, less than 1 or equal to 1;
if it is notIf the number of the users in the forwarding state is reduced, the information cannot be exploded; if it is notIndicating that the number of users in the forwarding state will increase exponentially; if it is notIndicating that the number of users in the forwarding state is unchanged;
predicting a public opinion propagation peak value through a curve of the total number of individuals of the crowd in a forwarding state changing along with time by adopting a numerical simulation method, wherein the public opinion propagation peak value represents a propagation peak value of a public opinion hotspot event;
the moment when the number of users in a forwarding state is increased to a first set proportion of a public sentiment propagation peak value is used as a public sentiment outbreak starting moment, and the public sentiment outbreak starting moment is predicted;
the moment when the number of users in a forwarding state is increased to the public sentiment propagation peak value is used as the public sentiment outbreak peak value moment, and the public sentiment outbreak peak value moment is predicted;
the moment when the quantity in the forwarding state is reduced to a second set proportion of the public sentiment propagation peak value is taken as the public sentiment outbreak ending moment, and the public sentiment outbreak ending moment is predicted;
the number of users in a forwarding state in unit time from the starting moment of public sentiment outbreak to the peak moment of the public sentiment outbreak is used as the public sentiment outbreak rate, so that the public sentiment outbreak rate is predicted;
the number of users in a forwarding state in unit time from the peak moment of public sentiment outbreak to the end moment of the public sentiment outbreak is taken as the rate of public sentiment decline, so that the rate of the public sentiment decline is predicted;
the number of users in a forwarding state in unit time from the starting moment of public sentiment outbreak to the ending moment of the public sentiment outbreak is taken as an average rate, and the public sentiment average rate is predicted;
and predicting a maximum public opinion propagation index by a numerical simulation method through a curve of the cumulative quantity of the total number of individuals of the crowd in a forwarding state changing along with time, wherein the maximum public opinion propagation index represents the maximum boundary number which can be reached by public opinion event outbreak, namely the forwarding cumulative quantity of the whole event outbreak period.
7. The synchronous cross information propagation analysis method according to claim 4, wherein the step of correlating the total number of individuals of each population with the forwarding amounts of the two pieces of information comprises:
an estimation model of the accumulated forwarding amount of two pieces of information is constructed by the following formula
Wherein,andare respectively informationAnd informationAn estimate of the cumulative forwarding amount of (a),
the step of obtaining the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting the parameter estimation method comprises the following steps:
method for estimating parameters of cross information synchronous propagation dynamic model by adopting least square method
Wherein,is the square error of the parameter(s),the dynamic model parameter vectors are propagated synchronously for the cross information,,which is indicative of the time of the sampling,andrespectively indicate the timePresence of a parameterInformation under conditionsAnd informationAn estimate of the cumulative forwarding amount of (a),representing informationArrival timeThe amount of forwarding is actually accumulated so far,representing informationArrival timeThe actual accumulated forwarding amount is present.
8. The synchronous cross information propagation analysis method of claim 6, further comprising the step of analyzing the sensitivity of model parameters to a cross information synchronous propagation dynamics model, the step comprising:
constructing a strong attraction accumulated forwarding amount model, a continuous attraction accumulated forwarding amount model, a strong attraction forwarding amount model and a continuous attraction forwarding amount model through the following formulas
Wherein,in order to accumulate the forwarding amount by strong attraction,in order to accumulate the forwarding capacity for sustained attraction,in order to transfer the amount by strong attraction force,forwarding the traffic for sustained attractiveness;
predicting the total number of individuals of different crowds of which the two pieces of information change along with time through a cross information synchronous propagation dynamic model after model parameters of the two pieces of information are assigned, inputting a strong attraction accumulated forwarding amount model, a continuous attraction accumulated forwarding amount model, a strong attraction forwarding amount model and a continuous attraction forwarding amount model, and analyzing the influence of the change on the output of the strong attraction accumulated forwarding amount model, the continuous attraction accumulated forwarding amount model, the strong attraction forwarding amount model and the continuous attraction forwarding amount model through the change of a strong attraction index and a continuous attraction index;
and analyzing the influence of the model parameters on the public opinion indexes by adopting a partial rank correlation coefficient method.
9. A dynamics-based synchronized cross-information propagation analysis system, comprising:
the user state dividing module is used for dividing the state of the network user into three user states, namely a susceptible state, a forwarding state and an immune state, wherein the susceptible state represents the state that the user is not contacted with the issued information but has the information forwarding capability; the forwarding state represents a state that forwarding is performed and that is in an active state and can affect other users; the immune state represents a state that the user loses the active ability after forwarding the information;
the model building module is used for building a cross information synchronous propagation dynamic model which is changed between different user states along with the propagation of two pieces of information according to the user states divided by the user state dividing module, wherein in the cross information synchronous propagation dynamic model, one user serves as an individual, different crowds are divided according to the user states of different individuals relative to the two pieces of information, the user states of the individuals in one crowd are the same, and the derivative of the total number of the individuals of one crowd relative to time and the total number of the individuals of related crowds are in a linear relation through model parameters according to the transformation direction, wherein the related crowds are other crowds except the crowds in which the two pieces of information are in the immune state; the model parameters comprise average contact rate, forwarding average probability, strong attraction index, continuous attraction index and average immunity rate; the average exposure rate represents an average rate at which an individual of a message in a susceptible state can be exposed to the message; the forwarding average probability represents the average probability that an individual in a susceptible state of one information is exposed to the one information for forwarding; the strong attraction index refers to an individual of one piece of information in a forwarding state and is in a susceptible state of another piece of information at the same time, and the attraction degree of the another piece of information to the individual; the continuous attraction refers to an individual in an immune state of one message and a susceptible state of another message, and the attraction transfer degree of the another message to the individual;
the acquisition module is used for acquiring two pieces of information with the release time interval smaller than a set value as an actual value, setting an initial value of a model parameter of the cross information synchronous propagation dynamic model, acquiring a curve of the individual total number of each crowd along with the change of time, setting that each user of one piece of information can only forward once, so that the individual total number of each crowd corresponds to the forward quantity of the two pieces of information, acquiring the accumulated forward quantity through the cross information synchronous propagation dynamic model as an estimated value, acquiring the optimal value of the model parameter of the cross information synchronous propagation dynamic model by adopting a parameter estimation method, performing model parameter assignment by adopting the optimal value, and predicting the individual total number of different crowds of the two pieces of information along with the change of time by adopting the cross information synchronous propagation dynamic model after the model parameter assignment.
10. The system of claim 9, further comprising a public opinion index constructing module for constructing a public opinion index for public opinion prediction, wherein the public opinion index comprises a public opinion outbreak index, a public opinion outbreak peak value, a maximum public opinion propagation index, a public opinion outbreak rate, a public opinion decay rate, and an average rate.
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