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UBLF：An Upper Bound Based Approach to Discover Influential Nodes in Social Networks

IEEE ICDM 2013. UBLF：An Upper Bound Based Approach to Discover Influential Nodes in Social Networks. Authors: C. Zhou, P. Zhang, J. Guo, X. Zhu, L. Guo Presenter: Peng Zhang , Chinese Academy of Sciences December 7-10, 2013 , Dallas, Texas. Content. Background Problem Formulation

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UBLF：An Upper Bound Based Approach to Discover Influential Nodes in Social Networks

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  1. IEEE ICDM 2013 UBLF：An Upper Bound Based Approach to Discover Influential Nodes in Social Networks Authors: C. Zhou, P. Zhang, J.Guo, X. Zhu, L. Guo Presenter: Peng Zhang, Chinese Academy of Sciences December 7-10, 2013, Dallas, Texas

  2. Content • Background • Problem Formulation • Related work • Our solution • Experiments • Conclusion

  3. Background • Social networks are popularly used • Viral marketing • Information dissemination • Technology/Idea transfers • Influence propagation • Influence maximization • Community detection • Influence inference • Early warning of public opinion • Link Prediction/Friends Recommendation • Partner Recommendation/Social Cooperation/Team Formation

  4. Problem Formulation • Given a directed social graph G=(V,E), a budgetk, and a stochastic propagation model M, finding k nodes, such that the expected spread of the influence can be maximized [Kemp KDD’03] • Challenges: • How to measure the objective function M(S)? • How to find the optimal solution, i.e., the subset k of the most influential nodes?

  5. Problem Formulation b • How to measure the influence M(S)? • Stochastic propagation models • IC model • LT model • Other propagation models: e.g. continuous time IC or LT models • Monte Carlo (MC) simulation • Exact calculation under IC and LT is #P-hard (Chen, KDD’ 10). .3 c .1 .3 .1 .2 .1 e a .3 .4 f .2 .4 .1 .4 .3 h .1 d .2 .1 .2 .4 g I .4 .1 IC propagation model #P-hard

  6. Greedy Algorithm • How to find a subset k containing the most influential nodes • Influence maximization under both IC and LT models isNP-hard . (Kemp, KDD’03) • Property 1: M(S)is monotone: • Property 2: M(S)is submodular: The set cover problem

  7. Greedy Algorithm • Advantage: Performance guarantee of 1− 1/e =63% • Disadvantage: Heavy computation cost • Inner loop： M(S)needs many Monte-Carlo simulations • Outer loop：time complexity of O(Nk), where N is network size

  8. Improvement direction (I): Heuristic algorithms • Heuristic algorithms • ShortestPath: Kimura and Saito (PKDD’06) “Tractable models for information diffusion in social networks” • DegreeDiscount: Chen et al. (KDD'09) “Efficient influence maximization in social networks” • MIA: Chen et al. (KDD'10) “Scalable influence maximization for prevalent viral marketing in large-scale social networks” • DAG: Chen et al. (ICDM’10) “Scalable influence maximization in social networks under the linear threshold model” • SIMPATH： Goyal et al. (ICDM’11)“SIMPATH: An Efficient Algorithm for Influence Maximization under the Linear Threshold Model” e d f g Shortest Path from a to c Node 2’s degree will shrink 2 • Advantage: faster than the Greedy algorithm • Disadvantage: no performance guarantee 5 DegreeDiscount

  9. Improvement direction (II): Advanced greedy • Advanced greedy algorithms • CELF： Leskovec et al. (KDD'07) “Cost-effective outbreak detection in networks” • Goyal et al. (WWW’11) “CELF++: optimizing the greedy algorithm for influence maximization in social networks” Greedy algorithm reward d a b b a c e c d e

  10. Improvement direction (II): Advanced greedy • Advanced greedy algorithms • CELF： Leskovec et al. (KDD'07) “Cost-effective outbreak detection in networks” • Goyal et al. (WWW’11) “CELF++: optimizing the greedy algorithm for influence maximization in social networks” Greedy algorithm reward d a b b a c e c d e

  11. Improvement direction (II): Advanced greedy • Advanced greedy algorithms • CELF： Leskovec et al. (KDD'07) “Cost-effective outbreak detection in networks” • Goyal et al. (WWW’11) “CELF++: optimizing the greedy algorithm for influence maximization in social networks” CELF algorithm Greedy algorithm reward reward d a d a b b b a b a c e c e c c d d e e

  12. e c b d Improvement direction (II): Advanced greedy • Advanced greedy algorithms • CELF： Leskovec et al. (KDD'07) “Cost-effective outbreak detection in networks” • Goyal et al. (WWW’11) “CELF++: optimizing the greedy algorithm for influence maximization in social networks” Greedy algorithm CELF algorithm reward reward d a d a b b a b a e c e c c d e

  13. e b Improvement direction (II): Advanced greedy • Advanced greedy algorithms • CELF： Leskovec et al. (KDD'07) “Cost-effective outbreak detection in networks” • Goyal et al. (WWW’11) “CELF++: optimizing the greedy algorithm for influence maximization in social networks” Greedy algorithm CELF algorithm reward reward d a d a b b d a b a e • Advantage: by setting up an upper bound, CELF reduces the Monte-Carlo calls and improves the greedy algorithm by up to 700 times • Disadvantage: needs N Monte Carlo simulations to initialize the upper bound, where N is the network size. c e c c d c e

  14. Our work • Motivation • Can we initialize the upper bounds without actually computing the MC simulations ? UBLF algorithm CELF algorithm UBLF algorithm

  15. The upper bound of M(S) Local view Global view How many heads? Proposition 2 establishes a relationship among the activation probabilties in time t and t+1.

  16. The upper bound of M(S) M(S) is bounded by a sum of series. In what condition the series convergent? and what is the limit? Too hard! Its aera? But we know its upper bound!

  17. The upper bound of M(S) Convergent condition：the total influence to or from any node is less than 1. Under condition (14), we get a tractable upper bound. +……=

  18. Our UBLF algorithm • CELF: the first round is time-consuming, needs full MC simulations. • UBLF: the first round is analytical calculated.

  19. Monte-Carlo Simulation Node 1 is selected! (only 1 time MC simulation) Our work: An example for UBLF

  20. Experiments • Data collection • Ca-GrQc • Digger • Ca-HepPh • Email-Enron • Benchmark • CELF • Degree • DegreeDiscount • PageRank • Random Statistics of datas

  21. Experiments • Comparison results (Numbers of MC simulations) Observation: The total MC calls of UBLF is significantly reduced compared to CELF.

  22. Experiments • Comparison results (Influence spread) Observations: The spreads of UBLF and CELF are completely identical, which explains again that UBLF and CELF share the same logic in selecting nodes.

  23. Experiments • Comparison results (Time cost) Observation: UBLF is 2-5 times faster than CELF.

  24. Conclusions Background Problem Formulation Greedy Algorithm Heuristic algorithms: DegreeDiscount, PageRank, et al. Advanced greedy algorithms: CELF, CELF++ UBLF Comparisons

  25. Email: zhangpeng@iie.ac.cn Questions ?

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