社交网络分析与挖掘 第四课：信息传播模型

Information Diffusion Models

Information Diffusion Categories

Influence Models （影响力模型）

• Influence models model how users influence each other in a network.
• Nodes are in two status:
  ==Inactive==:the nodes do not receive the information
  ==Active==:the nodes have received the information and can spread it to their neighbors

Independent Cascade (IC) 独立级联模型

• Nodes activated at time t,have a single chance,at time step t+1,to activate their neighbors
• Assume v is activated at time t,for any neighbor w of u,there is a probability p(vw) that node w gets activated at time t+1
  
• IC Model:Algorithm
  
• IC Model:Example
  

Linear Threshold (LT) 线性阈值模型

• At each time step，the active nodes can influence the inactive nodes
• Each node has an ==activation threshold==
• An inactive node becomes active if the sum of influence degrees ==exceeds== its threshold
• LT Model:Algorithm
  
• LT Model:Example
  

---

Infection Models （感染性模型/病毒模型）

• Infection Models, also called epidemic models, are
  used to describe the transmission of communicable
  ==disease== through individuals
• Nodes are in three status:
  • ==Susceptible==:a susceptible node can potentially get
    infected by the disease
  • ==Infected==: an infected node has the chance of infecting
    susceptible neighbors.
  • ==Recovered==: These are nodes who have recovered from
    the disease and hence have complete or partial ==immunity== against the infection.

Susceptible-Infected (SI)

• Two status of nodes：
  • Susceptible（S）
  • Infected（I）
• How to infect
  - Once a node is infected，it stays infected forever.
  - At each discrete time step，each infected node tries to infect its susceptible（uninfected）neighbors independently with probability p.
  
  
• SI Model:notations
  • N:size of the crowd，N=S(t)+I(t)
  • S(t)：number of susceptible ones at time t
  • I(t)：number of infected ones at time t
• SI Model:Example
  

Susceptible-Infecte-Recovered (SIR)

• Intuition:Some infected nodes may recover，and the recovered ones can no longer get infected and are no longer susceptible.
• Three status of nodes:Susceptible（S），Infected（T），Recovered（R）
• The infection status of a node changes
  
  β defines the probability of a success infection
  γ defines the recovering probability of an infected individual
• SIR Model:Example
  

Susceptible-Infected-Susceptible (SIS)

• Intuition:the infected nodes may recover，and the recovered nodes would become susceptible again
• Two status of nodes:Susceptible（S），Infected（I）
• The infection status of a node changes
  
  β defines the probability of a success infection
  γ defines the recovering probability of an infected individual
• SIS Model:Example
  

Susceptible-Infected-Recovered-Susceptible (SIRS)

• Intuition:the individuals who have recovered will lose immunity after a certain period of time and will become susceptible again.
• The infection status of a node changes
  
  β defines the probability of a success infection
  γ defines the recovering probability of an infected individual
  λ defines the probability of losing immunity for a recovered node
  
• SIRS Model:Example
  

以上内容出自小象学院