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A Framework for Finding Communities in Dynamic Social Networks

A Framework for Finding Communities in Dynamic Social Networks. Chayant Tantipathananandh, Tanya Berger-Wolf University of Illinois at Chicago. David Kempe University of Southern California. Social Networks. 1. Aggregated network. 2. 1. 3. 2. 3. 2. 5. 1. 1. 4.

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A Framework for Finding Communities in Dynamic Social Networks

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  1. A Framework for Finding Communities in Dynamic Social Networks Chayant Tantipathananandh, Tanya Berger-Wolf University of Illinois at Chicago David Kempe University of Southern California

  2. Social Networks

  3. 1 Aggregated network 2 1 3 2 3 2 5 1 1 4 History of interactions t=1 1 5 4 2 3 t=2 5 2 3 4 1 t=3 5 2 4 1 t=4 5 2 3 4 t=5 5 2 4 3 1 History of Interactions t=1 1 3 2 4 5 Assume discrete time and interactions in form of complete subgraphs.

  4. Community Identification What is community? “Cohesive subgroups are subsets of actors among whom there are relatively strong, direct, intense, frequent, or positive ties.” [Wasserman & Faust ‘97] • Centrality and betweenness [Girvan & Newman ‘01] • Correlation clustering [Basal et al. ‘02] • Overlapping cliques [Palla et al. ’05] Notions of communities: Static Dynamic • Metagroups [Berger-Wolf & Saia ’06]

  5. The Question: What is dynamic community? 5 4 t=1 2 3 1 5 2 3 1 t=2 4 • A dynamic community is a subset of individuals that stick together over time. • NOTE: Communities ≠ Groups 5 4 1 2 t=3 5 2 3 4 t=4 5 4 1 t=5 2 3

  6. t=1 1 5 4 2 3 5 1 2 3 4 t=2 5 2 3 4 1 5 1 2 3 4 t=3 5 2 4 1 5 1 2 3 4 t=4 5 2 3 4 5 1 2 3 4 t=5 5 1 2 3 4 5 2 4 3 1 Approach: Graph Model

  7. Approach: Assumptions Required • Individuals and groups represent exactly one community at a time. • Concurrent groups represent distinct communities. Desired • Conservatism: community affiliation changes are rare. • Group Loyalty: individuals observed in a group belong to the same community. • Parsimony: few affiliations overall for each individual.

  8. Approach: Color = Community Valid coloring: distinct color of groups in each time step

  9. Approach: Assumptions Required • Individuals and groups represent exactly one community at a time. • Concurrent groups represent distinct communities. Desired • Conservatism: community affiliation changes are rare. • Group Loyalty: individuals observed in a group belong to the same community. • Parsimony: few affiliations overall for each individual.

  10. Costs • Conservatism: switching cost (α) • Group loyalty: • Being absent (β1) • Being different (β2) • Parsimony: number of colors (γ)

  11. Approach: Assumptions Required • Individuals and groups represent exactly one community at a time. • Concurrent groups represent distinct communities. Desired • Conservatism: community affiliation changes are rare. • Group Loyalty: individuals observed in a group belong to the same community. • Parsimony: few affiliations overall for each individual.

  12. Costs • Conservatism: switching cost (α) • Group loyalty: • Being absent (β1) • Being different (β2) • Parsimony: number of colors (γ)

  13. Approach: Assumptions Required • Individuals and groups represent exactly one community at a time. • Concurrent groups represent distinct communities. Desired • Conservatism: community affiliation changes are rare. • Group Loyalty: individuals observed in a group belong o the same community. • Parsimony: few affiliations overall for each individual.

  14. Costs • Conservatism: switching cost (α) • Group loyalty: • Being absent (β1) • Being different (β2) • Parsimony: number of colors (γ)

  15. Problem Definition • Minimum Community InterpretationFor a given cost setting, (α,β1,β2,γ), find vertex coloring that minimizes total cost. • Color of group vertices = Community structure • Color of individual vertices = Affiliation sequences • Problem is NP-Complete and APX-Hard

  16. Model Validation and Algorithms • Model validation: exhaustive search for an exact minimum-cost coloring. • Heuristic algorithms evaluation: compare heuristic results to OPT. • Validation on data sets with known communities from simulation and social research • Southern Women data set (benchmark)

  17. Southern Women Data Setby Davis, Gardner, and Gardner, 1941 Aggregated network Photograph by Ben Shaln, Natchez, MS, October; 1935 Event participation

  18. Ethnography by Davis, Gardner, and Gardner, 1941 Core (1-4) Periphery (5-7) Periphery (11-12) Core (13-15)

  19. An Optimal Coloring: (α,β1,β2,γ)=(1,1,3,1) Core Periphery Core Periphery

  20. An Optimal Coloring: (α,β1,β2,γ)=(1,1,1,1) Core Core Periphery

  21. Conclusions • An optimization-based framework for finding communities in dynamic social networks. • Finding an optimal solution is NP-Complete and APX-Hard. • Model evaluation by exhaustive search. • Heuristic algorithms for larger data sets. Heuristic results comparable to optimal.

  22. Thank You Poster #6 this evening

  23. Computational PopulationBiology LabUIC compbio.cs.uic.edu David KempeUSC Dan RubensteinPrinceton TanyaBerger-Wolf Poster#6 this evening Jared SaiaUNM Ilya Fischoff Siva Sundaresan Simon LevinPrinceton MuthuGoogle Mayank Lahiri ChayantTantipathananandh Habiba

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