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Lecture 2-1 Influence Maximization

Lecture 2-1 Influence Maximization. Ding-Zhu Du University of Texas at Dallas. What is Social Network?. Wikipedia Definition: Social Structure Nodes: Social actors ( individuals or organizations) Links : Social r elations. What is Social Influence?.

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Lecture 2-1 Influence Maximization

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  1. Lecture 2-1 Influence Maximization • Ding-Zhu Du • University of Texas at Dallas

  2. What is Social Network? Wikipedia Definition: Social Structure • Nodes:Social actors (individuals or organizations) • Links:Social relations

  3. What is Social Influence? [1] http://en.wikipedia.org/wiki/Social_influence • Social influence occurs when one's opinions, emotions, or behaviors are affected by others, intentionally or unintentionally.[1] • Informational social influence: to accept information from another; • Normative social influence: to conform to the positive expectations of others.

  4. Kate Middleton effect “Kate Middleton effect The trend effect that Kate, Duchess of Cambridge has on others, from cosmetic surgery for brides, to sales of coral-colored jeans.”

  5. Hike in Sales of Special Products • According to Newsweek, "The Kate Effect may be worth £1 billion to the UK fashion industry." • Tony DiMasso, L. K. Bennett’s US president, stated in 2012, "...when she does wear something, it always seems to go on a waiting list."

  6. How to Find Kate? • Influential persons often have many friends. • Kate is one of the persons that have many friends in this social network. For more Kates, it’s not as easy as you might think!

  7. Influence Maximization • Given a digraph and • k>0, • Find k seeds (Kates) • to maximize the number of influenced persons (possibly in many steps).

  8. Theorem Proof

  9. Modularity of Influence

  10. What is a submodular function? Consider a function f on all subsets of a set E. f is submodular if

  11. What is monotone increasing f is monotone increasing if

  12. Property ofDecreasing Marginal Value 1 2

  13. Modularity of Influence

  14. Theorem

  15. Submadular Function Max

  16. Greedy Algorithm

  17. Performance Ratio Theorem (Nemhauser et al. 1978) Proof

  18. Proof Monotone increasing Submodular! Why?

  19. Diffusion Model • Deterministic diffusion model • Independent Cascade (IC) • Linear Threshold (LT)

  20. Deterministic Model 6 2 1 5 3 4 both 1 and 6 are source nodes. Step 1: 1--2,3; 6--2,4. .

  21. Example 6 2 1 5 3 4 Step 2: 4--5.

  22. Influence Maximization Problem • Influence spread of node set S: σ(S) • expected number of active nodes at the end of diffusion process, if set S is the initial active set. • Problem Definition (by Kempe et al., 2003): (Influence Maximization). Given a directed and edge-weighted social graph G = (V,E, p), a diffusion model m, and an integer k ≤ |V |,find a set S ⊆ V , |S| = k, such that the expected influence spread σm(S) is maximum.

  23. References

  24. THANK YOU!

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