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

Observations Social network is evolving People’s ideology is migrating 1 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

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

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

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

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

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

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:

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

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

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

Small noise, fewer friends Communities appear, opinion divergence

Small noise, more friends Opinion convergence

Big noise Random

Discovery System level parameters can control the behavior of evolution

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

Application Dataset: Co-sponsorship between legislators, extracted from congress voting record https://www.govtrack.us Coponsor animation/example

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

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

Q & A Thank you! Yupeng Gu Email: ypgu@cs.ucla.edu Homepage: http://web.cs.ucla.edu/~ypgu/