信息传播模型与过滤技术研究-基于社会网络与媒体影响的SIR模型及其应用资源-CSDN文库

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For ofﬁce use only

Team Control Number

44173

Problem Chosen

For ofﬁce use only

2016 Mathematical Contest in Modeling (MCM) Summary Sheet

(Attach a copy of this page to each copy of your solution paper.)

How to Understand the Information

The ﬂow of information has never been as easy or wide-ranging as it is today.

This paper proposes some models to explore the relationship between speed/ﬂow

of information with inherent value of information.

First,to explore information ﬂow, we build up a SIIR model which takes the me-

dia inﬂuence into consideration. This model is developed from the classical SIR

model.We introduce the concept of hot transmission nodes to highlight the impact

of media. We demonstrate our design with American media data. The results show

that our model has a signiﬁcant performance in validating predicted values of the

characteristics of information network in 2050.

Second,the information ﬁltering can be regarded as a classiﬁcation problem. We

design a radial basis function network to implement the information ﬁltering. In

order to solve sample noises and improve the computing performance,we decide

to use K-means algorithm and RLS algorithm to implement our RBF network. We

demonstrate our network in online news dataset ,with an training accuracy of

75.1%,and testing accuracy of 74.3%.we are satisﬁed that the accuracy rate with

information ﬁltering as news.

Third, We have only considered the social network in the Internet and build a social

network SIR(SN-SIR) model to explore the problem-how public interest and opin-

ion can be changed through network.It simulates in the standard dataset: Facebook

social network dataset .By analyzing the factors which can implement our result-

s,we can make a plan to determinate information propagation. Then,we take infor-

mation values ,people ˛a´rs initial opinion and bias, form of the message or its source,

and topology or other reasons into account and propose a detailed scheme.

Finally, effects of external factors are considered in our models.And we analyze

the stability and sensitively of our models. Although there are some weakness in

our models,the results still demonstrate that our model can undergo disturbance in

certain extent.

Team # 44173 Page 2 of 22

Contents

1 Introduction 3

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Assumptions 4

3 A SIIR Model of Information Flow 4

3.1 Social Network Information Dissemination . . . . . . . . . . . . . . . . . . . . . . 4

3.1.1 Social Network Information Dissemination Characteristics . . . . . . . . . 4

3.1.2 Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Calculating and Simplifying the Model . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.1 The Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.2 Rationality validation And Sensitivity analysis . . . . . . . . . . . . . . . . 7

3.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 A Model of Information Filtering 11

4.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.2 Hybrid Learning Procedure For Networks . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 Sensitively Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 A SN-SIR Model 14

5.1 The Way of Information Dissemination in Network . . . . . . . . . . . . . . . . . 14

5.2 A Model of Public Opinion Dissemination in Social Network . . . . . . . . . . . . 14

5.2.1 Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Sensitivity Analysis and Model Validation . . . . . . . . . . . . . . . . . . . . . . . 16

5.3.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.3.2 Sensitivity, parameter validation analysis . . . . . . . . . . . . . . . . . . . 17

5.4 Result Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6 Analysis 21

6.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Team # 44173 Page 3 of 22

1 Introduction

1.1 Background

Broadly speaking, information is one of the important ways for us to perceive the outside

world. Today it spreads quickly in tech-connected communication network. Sometimes it is

due to the information ﬁnding its way to inﬂuential or central network nodes that accelerate its

spread through social media. Our prevailing premise is that this cultural characteristic to share

information (both serious and trivial) has always been three. At present, information propa-

gation is exposed explosive growth.Beacause our social networks and medium are more and

more complex.Without effective ways to solve these problems ,it will ﬁnally cause information

propagation is more and more difﬁcult to umderstand.Hence,our work has its unprecedented

signiﬁcance in world nowadays.

1.2 Our Work

This paper propose some models to explore the relationship between speed/ﬂow of informa-

tion with inherent value of information.

The Dilemma:

• An adaptive ﬂow model is established with the consideration of the complex network

changes.

• Make use of the existing parameters to ﬁlter the information reasonably.

• Reasonable analysis of inﬂuencing factors in the process of information transmission.

The Approach:

• FirstˇcˇnTo explore information ﬂow, we build up a SIIR model which takes the special fea-

tures if media inﬂuence into consideration. This model is developed from classical SIR

model.

• The Results show that our model has a signiﬁcant performance in validate the value of

prediction with real value. And then ,we predict the rate of daily contact in 2050.

• Information ﬁltering is regarded as classiﬁcation problem. we design a radial basis func-

tion network to implement information ﬁltering. In order to solve sample noise and com-

puting performance, we decide to use K-means algorithm and RLS algorithm to imple-

ment our RBF network.

• We have only considered the social network in the Internet and build a social network

SIR(SN-SIR) to explore the problem ˛a´s how public interest an opinion can be changed

through network ˛a´s.

• We can make a plan to determinate information propagation. Then ,we take information

value ,people ˛a´rs initial opinion and bias, form of the message or its source, and topology

or other reasons into account and build a detailed scheme.

Team # 44173 Page 4 of 22

2 Assumptions

The accuracy of our models rely on certain key, simplifying assumptions. These assumptions

are listed below:

• Do not consider factors such as natural birth,death,and population mobility.The total

population keeps as a constant K.

• Infected individuals once contact with susceptible individuals,Infected individuals change

to susceptible individuals at a certain probability.

• At a certain time,The number of individuals per unit time removing from the infected

individuals is proportional to the number of patients.

• The number of media is relatively ﬁxed in the same period.

Under the above and basic assumptions, we can set out to construct our model.

3 A SIIR Model of Information Flow

Information is created by the social network users and transmits in the entire network.The

result of transmission is that the receiver of the information translates into the transmitter and

disseminate the information to others,or translates to the recovered one and does not transmit

to others.Obviously, this transmission way is similar with the way Infectious diseases spread in

the crowd. Based on the analysis of social network structure,we introduce the hot transmission

node into network,and proposes an information transmission model based on the improved

SIR model [1],which is simulated with the data-based Facebook social network.

3.1 Social Network Information Dissemination

3.1.1 Social Network Information Dissemination Characteristics

In this section,we propose a to explore a general model of information ﬂow problems, which is

not subjected to the limitations of the times and mediums of communication.

The total number of user nodes in social networks is denoted as N.The network is assumed to

be an undirected graph and each node in the network may be in one of three states: susceptible(s),

infected(i), or recovered(r).Nodes in state i have received the message and have the ability to

transmit it.Nodes in state s have not received the message and have the possibility to receive

it.Nodes in state r have received the message and will not transmit it any more.

There are a variety of mediums of communication,such as newspapers,televisions,the Inter-

net and so on.Different mediums have different ability of transmission,but all of these medi-

ums owe stronger ability than human beings.We consider media as the hot transmission n-

odes.Their contact rate is denoted as λ

. Ordinary users in networks are considered as ordinary

nodes.Their contact rate is denoted as λ

The laws of Information dissemination of social networks with hot transmission nodes are as

below:[2]

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