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 information
And information
The population comprises: completely susceptible population
A group of individuals, both information of which are in a susceptible state; first active population
To information
In a forwarding state, for information
A population of individuals in a susceptible state; second active population
To information
In a forwarding state, for information
A population of individuals in a susceptible state; third active population
To information
And information
Individuals who are in a forwarding state and who forward information
Forwarding information earlier than it is
(ii) a Fourth active population
To information
And information
Individuals who are in a forwarding state, and forwarding information individually
Forwarding information earlier than it is
(ii) a Fifth active population
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
(ii) a Sixth active population
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
(ii) a Seventh active population
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
(ii) a Eighth active population
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
(ii) a First immune population
To information
In an immune state, to the message
A population of individuals in a susceptible state; second immune population
To information
In an immune state, to the message
A population of individuals in a susceptible state; complete immune population
To information
And information
The 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 rate
Information, information
Average contact rate of (a); second average contact velocity
Information, information
Average contact rate of (a); first average forwarding rate
Information, information
Average forwarding probability of (d); second average forwarding rate
Information, information
Average forwarding probability of (d); first strong attraction index
Information, information
For information
Strong attraction index of (d); second strong attractive force index
Information, information
For information
Strong attraction index of (d); first sustained attraction index
Information, information
For information
A sustained attraction index of; second sustained attraction index
Information, information
For information
A sustained attraction index of; first mean immune Rate
Information, information
Average immune rate of (a); second mean immune rate
Information, information
Average immune rate of (a); third mean immune Rate
Individuals from the seventh active population
Transfer to fully immune populations
Average immune rate of (a); fourth mean immune rate
Individuals from the eighth active population
Transfer to fully immune populations
Average 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 the content of the first and second substances,
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 represent
First active group of people at all times
Total 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 information
Content pair information of
To 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 period
To information
The 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. 3a is information
A schematic representation of the kinetic process of propagation;
FIG. 3b is information
A schematic representation of the kinetic process of propagation;
FIG. 4a is information
For information
Schematic representation of the strong attractive force propagation dynamics of (1);
FIG. 4b is information
For information
Schematic representation of the strong attractive force propagation dynamics of (1);
FIG. 5a is information
For information
Schematic representation of the continuous gravity propagation dynamics process of (a);
FIG. 5b is information
For information
Schematic representation of the continuous gravity propagation dynamics process of (a);
FIG. 6a is information
Schematic representation of the kinetics of the time-out immune propagation;
FIG. 6b is information
Schematic representation of the kinetics of the time-out immune propagation of (a);
FIG. 6c is information
And information
Schematic 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 parameters
Sitting of effects on cross-propagationMarking a graph;
FIGS. 10a, 10b, 10c and 10d are model parameters
A graph of the effect on cross-propagation;
FIG. 11 shows the variation of parameters of multiple models
A graph of the PRCCs results of (a);
FIG. 12 shows the variation of parameters of multiple models
And
a graph of the PRCCs results of (a);
FIG. 13 shows the variation of parameters of multiple models
，
，
And
a 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 information
Wherein, in the step (A),
，
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 population
Satisfy the following requirements
The 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 population
Satisfy the following requirements
To information
In a forwarding state (active), for information
A population of individuals in a vulnerable state, the population having forwarded information
And still in information
Within a forward exposure period of (2), enabling access to information
Individual awareness information in a vulnerable state
And possibly a forwarding action. And, at this time, the group is about the information
Remains in a vulnerable state;
second active population
Satisfy the following requirements
To information
In a forwarding state (active), for information
A population of individuals in a vulnerable state, the population having forwarded information
And still in information
Within a forward exposure period of (2), enabling access to information
Individual awareness information in a vulnerable state
And possibly a forwarding action. And, at this time, the group is about the information
Remains in a vulnerable state;
third active population
Satisfy the following requirements
To information
And information
Individuals who are all in a forwarding state (active) make up a crowd of people and the individuals forward information
Forwarding information earlier than it is
The group has forwarded the information in sequence
And information
And to information
And information
Are all in the forwarding exposure period and have the ability to make the pair information
Or information
Individual awareness information in a vulnerable state
Or information
And possibly forwarding behavior;
fourth active population
Satisfy the following requirements
To information
And information
Individuals who are in a forwarding state, and forwarding information individually
Forwarding information earlier than it is
The group has forwarded the information in sequence
And information
And to information
And information
Are all in the forwarding exposure period and have the ability to make the pair information
Or information
Individual awareness information in a vulnerable state
Or information
And possibly forwarding behavior;
fifth active population
Satisfy the following requirements
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
The group first generates pair information
Then forwards the information
. Here, the information
Is within a forwarding exposure period, i.e., the group has the ability to make a request for information
Individual awareness information in a vulnerable state
And possibly forwarding behavior;
sixth active population
Satisfy the following requirements
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
The group first generates pair information
Then forwards the information
. Here, the information
Is within a forwarding exposure period, i.e., the group has the ability to make a request for information
Individual awareness information in a vulnerable state
And possibly forwarding behavior;
seventh active population
Satisfy the following requirements
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
The group having forwarded the information first
Then pair information is generated
The immunization of (1); here, the information
Is within a forwarding exposure period, i.e., the group has the ability to make a request for information
Individual awareness information in a vulnerable state
And possibly forwarding behavior;
eighth active population
Satisfy the following requirements
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
The group having forwarded the information first
Then pair information is generated
The immunization of (1); here, the information
Is within a forwarding exposure period, i.e., the group has the ability to make a request for information
Individual awareness information in a vulnerable state
And possibly forwarding behavior;
first immune population
Satisfy the following requirements
To information
In an immune state, to the message
In a vulnerable stateA population of individuals, the population consisting of two parts: partly only information is forwarded
Over time, exceeds the information
No longer has the ability to influence others to know the information
And generating a total number of individuals behaving; another part is the exposure of the individual in a susceptible state (S) to information
Later, due to subjectively aligning information
Is directly converted into information without interest
Total number of individuals immunized;
second immune population
Satisfy the following requirements
To information
In an immune state, to the message
A population of individuals in a susceptible state, the population consisting of two parts: partly only information is forwarded
Over time, exceeds the information
No longer has the ability to influence others to know the information
And generating a total number of individuals behaving; another part is the exposure of the individual in a susceptible state (S) to information
Later, due to subjectively aligning information
Is directly converted into information without interest
Total number of individuals immunized;
complete immune population
Satisfy the following requirements
To information
And information
The 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 information
When one is in a vulnerable state
(iii) an individual (individual)x) Contact to information
In a forwarding state
(iii) an individual (individual)y) Knowing the information
After the content, a subjective decision is made whether to forward the message, thereby moving to the message
Form of forward
Or immune state
。
In conjunction with the entire cross-information simultaneous propagation dynamics process of FIG. 2, a pair of information
The individual in the forwarding state is exposed to the average in unit time
An individual, wherein,
personal individuals may choose to forward information
To do so
Individual selective non-forwarding information
. Since the probability that an individual is a susceptible person is
To do so
， 
，
，
Is that the individual is in the pair information
For example, the newly generated information for a unit time
The number of forwarding individuals and the number of immunized individuals are respectively
And
。
similarly, for information
The 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 message
During the forward exposure period, the individual forwards the information
To information
The strong attraction and thus the resulting cross-propagation dynamics can be expressed as when one is in the information
Forward state pair information
In a susceptible state
(iii) an individual (individual)x) Contact to information
In a forwarding state
(iii) an individual (individual)y) Knowing the information
After the content, a subjective decision is made whether to forward the message, thereby moving to the message
And information
Are all in a forwarding state
Or for information
Is in forwarding pair information
Is 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 forwarded
Will be paired with relevant information during the forward exposure period
Generate special interest, and can be used for information with higher probability
Forwarding is performed by using strong attraction index
To measure the degree of such enhanced forwarding. For pair information
In forwarding state to information
For a group in a vulnerable state, one pair of information per unit time
The individual in the forwarding state will be exposed to
Individuals in this population, similar to the dynamics of single message dissemination, relay messages among them
The number of individuals of
Not to information
The number of individuals for forwarding is
. It can be seen that the probability of forwarding or not is given by the strong attraction index
The 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 this
To forward information
Probability of (2)
Forwarding information independently more than if neither information is known
Probability of (2)
. Further, the pair information newly added in the process in unit time can be obtained
The number of forwarding individuals and the number of immunized individuals of (1), respectively
And
. Wherein the content of the first and second substances,
，
，
，
is that the individual is in the pair information
5 cases of the forwarding state of (1).
Similarly, information
For information
The 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 information
But beyond its exposure period, whether forwarded or merely contacted without forwarding, will provide information
Has certain memory retention, thereby generating the pair information
The dynamics may be expressed as when an on-message is present
Immune status of
In a susceptible state
(iii) an individual (individual)x) Contact to information
In a forwarding state
(iii) an individual (individual)y) Knowing the information
After the content, a subjective decision is made whether to forward the message, thereby moving to the message
In the immune pair information
Are all in a forwarding state
Or for information
And information
Are 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 2
Even if the individual exceeds the forwarding exposure period, the individual never contacts the relevant information
Will still have a higher probability of pairing information
Forwarding is performed using sustained attractiveness index
To measure the degree of such enhanced forwarding. For pair information
In an immune state to information
For a group in a vulnerable state, one pair of information per unit time
The individual in the forwarding state will be exposed to
The individuals in this group, as such, are similar to the dynamics of single message dissemination, wherein messages are forwarded
The number of individuals of
Not to information
The number of individuals for forwarding is
. It can be seen that the probability of forwarding or not is subject to a sustained attractiveness index
The continuous attractiveness index is generally a quantity greater than 1, so that the information is forwarded for a longer time
To forward information
Probability of (2)
Forwarding information independently more than if neither information is known
Probability of (2)
. Further, the pair information newly added in the process in unit time can be obtained
The number of forwarding individuals and the number of immunization individuals of (1) are respectively
And
。
similarly, information
For information
The 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 information
Time-out of immune propagation kinetics, using the mean immune rate
Representing individual information
Forwarding state transition information
Including in particular the average rate of the immune status of the information
Respectively in a susceptible state, a forwarding state and an immune state, as shown in fig. 6a, i.e. three state transitions, namely a slave state
Is changed to
From state
Is changed to
And slave state
Is changed to
。
Similarly, the second type is information
Time-out of immune propagation kinetics, using the mean immune rate
Representing individual information
Forwarding state transition information
The average rate of the immune status of (2), also including for the information
In 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 state
Is changed to
From state
Is changed to
And slave state
Is changed to
。
The third transition process is more special, such as the figure6c is shown by
Representing individual slave status
Transition to a fully immune state
Average immune rate of (c). This is information
But not useful in the state transition process of
As the mean immunity rate, this is because there is already a fraction of slave states in this population
Transfer to Pair information
State of immunity
During this time, information is also consumed
And thus, this fraction of the population will have a faster average immune rate. When the slave status is comprehensively considered
To a state of complete immunity
When 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 status
Transition to a fully immune state
Average 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 the content of the first and second substances,
and
are respectively information
And information
An 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 the content of the first and second substances,
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,
and
respectively indicate the time
Presence of a parameter
Information under conditions
And information
An estimate of the cumulative forwarding amount of (a),
representing information
Arrival time
The amount of forwarding is actually accumulated so far,
representing information
Arrival time
The 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 totals
Two important parts of, information
Accumulated forwarding amount of
And information
Accumulated forwarding amount of
Are all quantities that can be acquired during propagation, as shown in equation (5)
As shown in FIG. 7a, information may also be obtained
And information
Active forwarding amount of
And
) Co-composed cross-information co-propagated co-active forwarding volumes
As shown in formula (6)
Wherein:
FIG. 7b shows the cross-accumulated forwarding total for two information cross-propagations
To contact information first
Re-forwarding information
Examples of the case include accumulation of forwarding amounts by strong attraction during the exposure period
And sustained attractive force cumulative forwarding over exposure period
：
Wherein
Similarly, first contact information can be obtained
Re-forwarding information
Cross-propagated cross-active forwarding volumes of
Forwarding of quantities by strong attraction during the exposure period
And sustained attractive forwarding of energy beyond the exposure period
The common components are shown in formulas (12) to (14).
Contact information first due to symmetry of the model
Re-forwarding information
Similarly, the cross-accumulated forwarding total of the cross-propagation of two messages
Accumulation of forwarding by strong attraction during exposure
And sustained attractive force cumulative forwarding over exposure period
The components are combined together to form the composite material,
first contact information
Re-forwarding information
Cross-propagated cross-active forwarding volumes of
Forwarding of energy by strong attraction during exposure
And sustained attractive forwarding of energy beyond the exposure period
The 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 population
The 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 not
The number of the users in the forwarding state is reduced, and information cannot be exploded; if it is not
Indicating that the number of users in the forwarding state will increase exponentially; if it is not
Indicating 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 time
The public sentiment propagation peak represents a propagation peak of a public sentiment hot event, and as shown in fig. 8, represents a curve
Maximum 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 moment
Predicting 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 moment
Predicting 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 moment
Predicting the finish time of public sentiment outbreak,
is the period of public sentiment outbreak
As 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 rate
The 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 decline
For 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 with
When it is known
The public sentiment outbreak rate and decline rate can be defined as
And
mean 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 the content of the first and second substances,
is a population with an infectious effect, is also an active population, is also a population containing users in a forwarding state, and
wherein the content of the first and second substances,
is composed of
The time instant translates into the total number of individuals in the active population,
is composed of
The time of day is converted into a total number of individuals of the inactive population;
obtaining balance in the absence of information propagation
And
derivative matrix of
And
and
thus, it is possible to provide
Wherein the content of the first and second substances,
is shown in
The set of population populations at that time, at an initial time,
；
deriving matrices by roots of the characteristic equation
Characteristic value of (d):
obtaining public sentiment outbreak index through characteristic value
Public sentiment outbreak index
Is that
Radius 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 information
And a persistent attractiveness index for one information piece after a forwarding exposure period of more than one information piece
Not 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 attraction
And sustained attraction index
Will analyze the accumulated forwarding amount of strong attraction force in the exposure period under the condition that two parameters are changed in a certain range
And sustained attractive force cumulative forwarding over exposure period
And corresponding strong attractive forwarding of light during the exposure period
And sustained attraction forwarding beyond the exposure periodMeasurement of
Will be analyzed separately here
，
，
，
Four groups of cases.
FIGS. 9a-9d show model parameters
Influence on cross propagation, where FIG. 9a is information
For information
Analyzing the sensitivity of strong attraction force; FIG. 9b is information
For information
Analyzing the sensitivity of strong attraction force; FIG. 9c is information
For information
Continuous attractiveness sensitivity analysis of; FIG. 9d is information
For information
Continuous attractiveness sensitivity analysis. As shown in fig. 9a, parameters
Accumulated forwarding amount for strong attraction
And forwarding amount
Has very obvious effect of increasing the index of strong attraction
Will be greatly increased due to the pair information
Interested in information during the forward exposure period
Probability of forwarding, resulting in a forwarded amount
Higher peak sum
Larger final scale. Conversely, as shown in FIG. 9b, the strong attraction index is increased
Accumulated forwarding amount for strong attraction
And forwarding amount
It has no great effect. As shown in figures 9c and 9d,
for accumulating forwarding amount regardless of continuous attraction
And forwarding amount
Or continuously attracting accumulated forwarding capacity
And forwarding amount
The effect of (a) is not significant. Therefore, a strong attraction force parameter
Can effectively influence the information in a short time
To information
Cross propagation of (c).
FIGS. 10a-10d show the parameters
Influence on cross propagation, where FIG. 10a is information
For information
Analyzing the sensitivity of strong attraction force; FIG. 10b is information
For information
Analyzing the sensitivity of strong attraction force; FIG. 10c is information
For information
Continuous attractiveness sensitivity analysis of; FIG. 10d is information
For information
Continuous attractiveness sensitivity analysis. And parameters
Similarly, as shown in FIG. 10c, the parameters
Cumulative forwarding for sustained attractions
And forwarding amount
Has very obvious effect of increasing the index of strong attraction
Will be greatly increased due to the pair information
Interested in comparing information after exceeding the forwarding exposure period
Probability of forwarding, resulting in a forwarded amount
Higher peak sum
Larger final scale. And parameters
Different from the parameters
Plays a certain role in other cross propagation processes and can also influence the information due to the pair
To forward information
As shown in FIGS. 10b and 10d, and information
To forward information
The strong attraction process of (2), as shown in FIG. 10a, during these cross-propagation processes, the parameters
The influence on the cumulative forwarding amount is not information as shown in FIG. 10c
For information
Is obvious but not negligible. Parameters of strong attraction
To cross transmissionThe influence of the broadcast is stronger than the constant attraction parameter
Influence on cross propagation.
For parameter
It only works in a short time, reflecting that the information is forwarded
But affects the event to forward the information
The cross-propagation phenomenon of (a), which has no effect on the burst period of the entire event. For parameter
It 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 parameters
Can affect the already paired information
Individuals 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 parameters
Various 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 propagation
The 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 with
PRCC| 
Indicating that the model parameters have a general impact on the hotspot events; while | PRCC
The impact of this model parameter on hot-spot events will be quite limited.
As shown in fig. 11, parameters
The 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 parameters
Reproducible number to public opinion
All have strong effects. Wherein the average contact rate is determined by
And average forwarding probability
Increase of (2), reproducible number of public sentiments
Will increase with increasing; in contrast, with average immunization rate
Increase of (2), reproducible number of public sentiments
And 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 parameters
And
for the peak value of accumulated forwarding amount reflecting comprehensive propagation capacity
And maximum value of forwarding amount
Plays 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 parameters
And
will increase the final scale
Peak 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 time
Model parameters
Plays an important role, the relevant parameters are more than 0.4, and the model parameters
And
the general function is exerted, and the relevant parameters are between 0.2 and 0.4; peak time for the public sentiment event
Model parameters
And
is the main factor controlling it. Public sentiment index for rate class
And
only model parameters
Are the main factors for controlling them, the relevant parameters are more than 0.4; for rate of public opinion outbreak
Model parameters
Has 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 rate
The relevant parameters are determined by the network architecture, of case 1
And
the 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 2
And
the 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 2
0.097，
0.068，
= 0.654，
=0.654, here
And
the behavior rules of most forwarding groups are embodied,
and
behavior 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,
，
，
and
the 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 of
1.201，
= 0.686; case 2 has strong attraction indexes of
=0.550，
0.525 and sustained attraction index of
0.333，
= 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 1
This is a relatively large number, indicating that case 1 has a very rapid initial burst tendency and passes quickly
The peak value of public sentiment is reached in hours
. Compared to case 1, case 2 has a lower regenerability number, just
Its outbreak is also slow and has passed
The peak of the public sentiment is reached only in hours but the peak of the public sentiment is reached
Higher than case 1. For final scale of public opinion, case 2
Slightly larger than in case 1
That is, case 2 has a wider public opinion coverage than case 1.
TABLE 5
In this embodiment, according to the reference value
The initial value of the initially acquired information data exceeds
That is to say
Correspondingly, the duration of the public sentiment is the ending time of the public sentiment
Only given
The 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 sentiment
Average rate of decay with public opinion
Two 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 information
And information
The population comprises: completely susceptible population
A group of individuals, both information of which are in a susceptible state; first active population
To information
In a forwarding state, for information
A population of individuals in a susceptible state; second active population
To information
In a forwarding state, for information
A population of individuals in a susceptible state; third active population
To information
And information
Individuals who are in a forwarding state and who forward information
Forwarding information earlier than it is
(ii) a Fourth active population
To information
And information
Individuals who are in a forwarding state, and forwarding information individually
Forwarding information earlier than it is
(ii) a Fifth activityJumping population
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
(ii) a Sixth active population
To information
In an immune state, to the message
A population of individuals in a forwarding state, and the individuals are immunized against the information
Forwarding information earlier than it is
(ii) a Seventh active population
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
(ii) a Eighth active population
To information
In a forwarding state, for information
A population of individuals in an immune state, and the individuals forwarding information
Before immunizing to information
(ii) a First immune population
To information
In an immune state, to the message
A population of individuals in a susceptible state; second immune population
To information
In an immune state, to the message
A population of individuals in a susceptible state; complete immune population
To information
And information
Individuals 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:
first average contact rate
Information, information
Average contact rate of (a);
second average contact velocity
Information, information
Is connected toThe rate of contact;
first average forwarding rate
Information, information
Average forwarding probability of (d);
second average forwarding rate
Information, information
Average forwarding probability of (d);
first strong attraction index
Information, information
For information
Strong attraction index of (d);
second strong attractive force index
Information, information
For information
Strong attraction index of (d);
first sustained attraction index
Information, information
For information
A sustained attraction index of;
second sustained attraction index
Information, information
For information
A sustained attraction index of;
first mean immune Rate
Information, information
Average immune rate of (a);
second mean immune rate
Information, information
Average immune rate of (a);
third mean immune Rate
Individuals from the seventh active population
Transfer to fully immunized humanGroup of
Average immune rate of (a);
fourth mean immune rate
Individuals from the eighth active population
Transfer to fully immune populations
Average immune rate of (a);
initial value of total number of individuals of completely susceptible population
。
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,
wherein the content of the first and second substances,
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 represent
Person first alive at momentGroup of
Total number of individuals.
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
Wherein the content of the first and second substances,
public opinion outbreak index;
judging whether the public opinion outbreak index is more than 1, less than 1 or equal to 1;
if it is not
If the number of the users in the forwarding state is reduced, the information cannot be exploded; if it is not
Indicating that the number of users in the forwarding state will increase exponentially; if it is not
Indicating 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 the content of the first and second substances,
and
are respectively information
And information
An 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 the content of the first and second substances,
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,
and
respectively indicate the time
Presence of a parameter
Information under conditions
And information
An estimate of the cumulative forwarding amount of (a),
representing information
Arrival time
The amount of forwarding is actually accumulated so far,
representing information
Arrival time
The 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 the content of the first and second substances,
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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