1. THE CO-EVOLUTION MODEL FOR SOCIAL NETWORK EVOLVING AND OPINION MIGRATION
Yupeng Gu1, Yizhou Sun1, Jianxi Gao2
1University of California, Los Angeles
2Northeastern University
September 18, 2018

2. Observations Social network is evolving People’s ideology is migrating1 1
People’s ideology is migrating
User 1
User 2
User 3
User 4
User 5
User 6
0.8
1.2
0.7
-1.5
-2.1
-0.3
0.9
1.4
0.8
-1.6
-2.0
-0.5
Time t = t1
t = t2

3. Goals Modeling Prediction Intervention
Build a co-evolution model that can explain the phenomenon, e.g., clustering forming; opinion divergence
Prediction
Given the history, predict what will happen in the future
Intervention
Propose the policies that potentially guide the evolution

4. Modeling Assumptions: Limitations of existing approaches:
Ideology -> Network (network generation)
Links are formed according to homophily
Limitations of existing approaches:
Treating the two problems as orthogonal issues 1
Network -> Ideology (ideology migration)
People are influenced by their neighbors
network
0.8
1.2
0.7
-1.5
-2.1
-0.3
0.8
1.2
0.7
-1.5
-2.1
-0.3
0.9
1.4
0.8
-1.6
-2.0
-0.5
ideology

5. Network Generation
Homophily: people with similar ideology tend to link together
How to define similarity?
Dot product based similarity 𝑠𝑖 𝑚 𝑖𝑗 =𝑓( 𝒙 𝑖 ⋅ 𝒙 𝑗 )
Euclidean distance based similarity 𝑠𝑖 𝑚 𝑖𝑗 =𝑓(|| 𝒙 𝑖 − 𝒙 𝑗 | ​ 2 )
Dot product-based similarity
Euclidean distance-based similarity

6. Gravity-based Score Function
Observations
Opinion leader have more connections
Model opinion leaders explicitly: 𝑏 𝑖 𝑓𝑜𝑟 𝑎𝑐𝑡𝑜𝑟 𝑖
Opinion leaders tend to have a non-extreme ideology
Choose Euclidean distance-based score
The score function: extending Gaussian Kernel
𝐹=𝐺⋅ 𝑚 1 𝑚 2 𝑟 2
Link Generation:
𝐺 𝑖𝑗 =1, 𝑖𝑓 𝑝 𝑖𝑗 >𝑑, where 𝑑 is the system parameter controlling how easy to form a link

7. Opinion Migration
Social influence: actors are influenced by their neighbors
What are influenced?
Position of ideology?
Moving direction?

8. Opinion Propagation Model
𝝈 𝟐 :𝒔𝒚𝒔𝒕𝒆𝒎 𝒍𝒆𝒗𝒆𝒍 𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓
𝒄𝒐𝒏𝒕𝒓𝒐𝒍𝒊𝒏𝒈 𝒕𝒉𝒆 𝒏𝒐𝒊𝒔𝒆
Moving directions are influenced by social neighbors
Moving directions determine the position
Continuous form:
Discrete from:

9. Putting it together The co-evolution model moving direction ideology
network

10. Simulation System level parameters: Actor popularity: b
Network sparsity: d
Noise in propagation: 𝜎 2

11. Simulation System level parameters: Actor popularity: b
Network sparsity: d
Noise in propagation: 𝜎 2
𝜎=0.5, 𝑑= 𝑒 −0.4
𝜎=0.5, 𝑑= 𝑒 −2

12. Small noise, fewer friends
Communities appear, opinion divergence

13. Small noise, more friends
Opinion convergence

14. Big noise
Random

15. Discovery
System level parameters can control the behavior of evolution

16. Intervention How to alleviate opinion divergence?
Increase number of friends (diversity)
Strong opinion leaders

17. Application
Dataset: Co-sponsorship between legislators, extracted from congress voting record
Coponsor animation/example

18. Application 1: Identify Opinion Leaders
Learning popularity score: b
68th U.S. Secretary of State
45th U.S. Vice President
the majority leader of
the Senate since 2015

19. Application 2: Predicting Co-Sponsorship
Learning system-level parameters, and then run simulation

20. Q & A
Thank you!
Yupeng Gu Homepage: