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DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks

DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks. By: Yousef Naderi mnaderi@gmail.com Authors: Motahhare Eslami HamidReza Rabiee Mostafa Salehi 2011, October, 9th. Outline. Introduction Problem Definition Problem Importance Related Work Link Prediction

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DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks

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  1. DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks By: Yousef Naderi mnaderi@gmail.com Authors: Motahhare Eslami HamidReza Rabiee Mostafa Salehi 2011, October, 9th

  2. Outline • Introduction • Problem Definition • Problem Importance • Related Work • Link Prediction • Network Completion • Network Inference • Proposed Method: “DNE” • Experimental Evaluation • Contribution • Future Work • References P2P Live Video Streaming Diffusion Network Extraction DML DML DML 2

  3. Introduction • Diffusion and Cascading behavior: • A process by which information, viruses, ideas and new behavior spread over the network. Figure 1: An E-mail Recommendation Network[1] P2P Live Video Streaming Diffusion Network Extraction DML DML DML 3

  4. Introduction P2P Live Video Streaming Diffusion Network Extraction DML DML DML 4

  5. An Example of Diffusion Process Figure 2: Diffusion process over information networks P2P Live Video Streaming Diffusion Network Extraction DML DML DML 5

  6. Diffusion Network Extraction: Problem Definition • The network that diffusion takes place on itis usually unknown and unobserved. • we only observe the times of infection not the one who causes it. So Who-infects-whom? • Figure 3: The diffusion network extraction problem[3] Diffusion Network Extraction DML DML 6

  7. Problem Importance P2P Live Video Streaming Diffusion Network Extraction DML DML DML 7

  8. Related Work A few work had been done…

  9. Related Work • [7] for the first time tries to reconstruct epidemic trees of a disease propagation and estimates the sickness outbreak history. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 9

  10. Proposed Method • Graph G with |V|=n and |E|=e • C: The set of propagating cascades over G • Ncmembers • A time vector: • Goal: Finding the diffusion network which is generated by propagating cascades over G. • The only information which is available is infection times. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 10

  11. Cascade transmission Model • Information Propagation models • Threshold model • Cascade model • Independent cascade model • Pc(u, v)  P(tv - tu) tv > tu Δ = tv - tu P2P Live Video Streaming Diffusion Network Extraction DML DML DML 11

  12. Initial Graph Construction • As cascade c propagates over G, it remains a path of information • Sorting its time vector as • Constructing initial graph Gc by considering all probable links attending in diffusion process: • Each (i,j) which ti<tj • Assumptions • At each moment, only one node can get infected. • As each node can infect more than one node but each node only have one parent, we consider the state transitions from infected node to infecting node. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 12

  13. An Example of Initial Graph Figure5(a)General Initial Graph (b)Initial Graph of cascade 1 from Figure 2 Figure 4: Initial graph construction P2P Live Video Streaming Diffusion Network Extraction DML DML DML 13

  14. Random walk Markov Model P2P Live Video Streaming Diffusion Network Extraction DML DML DML 14

  15. Hitting Time • Hij: The expected number of steps before node j is visited, if we start from node i [23]. • Intuitively as Hij increases, the probability of direct infection transmission from i to j will decrease. • A recursive relation for calculating Hij in a strongly connected graph[36,37] • Being strongly connected is necessary for having irreducibility condition. • Calculating this equation needs stationary distribution[23]. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 15

  16. Hitting Time(cont’d) P2P Live Video Streaming Diffusion Network Extraction DML DML DML 16

  17. Reaching Time • A new measure based on hitting time • RTij: The expected number of steps from node i to j by “feasible paths”. • As the Reaching time between two nodes’ infection times increases, the probability of infection transmission will decrease. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 17

  18. Diffusion Network Extraction Problem • Constructing Gtotal Gtotal = • Defining RT for each edge(i,j) in Gtotal RTij = • Problem converts to: G’=argmin P2P Live Video Streaming Diffusion Network Extraction DML DML DML 18

  19. Proposed Algorithm: “DNE” Recursive equation to find RT: P2P Live Video Streaming Diffusion Network Extraction DML DML DML 19

  20. Proposed Algorithm: “DNE” • Considering infected nodes instead of infecting ones! • Defining set Sj as all the nodes with lower infection time respect to node j: • As the size of S increases, there will be more candidates to infect j: • Furthermore, the members of S have different priorities to infect j. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 20

  21. Proposed Algorithm: “DNE” • Considering the order of infection instead of infection times difference. • More independency to cascade transmission model • Introducing a new parameter named Rank: • Converting the problem to finding m links with least Ranks to construct G’. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 21

  22. Proposed Algorithm: “DNE” For each c∊C for each (i,j) ∊ c if (ti < tj) then Gc ⟵ Gc∪(i,j) Scj ⟵ Scj ∪{i} sort nodes of Gc by infection time. for each (i,j) ∊ Gc which i < j rcij⟵ | Scj | . (j-i) Gtotal ⟵ Gtotal ∪ (i,j) rij ⟵ rij +rcij Sort edges of Gtotal respect to rij For i ⟵ 1 to m G’⟵ G’ ∪ {ei ∊ Gtotal } Return (G’) P2P Live Video Streaming Diffusion Network Extraction DML DML DML 22

  23. Experimental Evaluation • NetInf[5] for comparison. P2P Live Video Streaming Diffusion Network Extraction DML DML DML 23

  24. Dataset • Synthetic Networks • Forest Fire[38] • Kronecker[22] • Barabasi-Albert(BA)[39] P2P Live Video Streaming Diffusion Network Extraction DML DML DML 24

  25. Dataset • Real Networks • Co-authorship network[42] • Football network[43] • President election network[3] P2P Live Video Streaming Diffusion Network Extraction DML DML DML 25

  26. Evaluation Metrics P2P Live Video Streaming Diffusion Network Extraction DML DML DML 26

  27. Cascade Dependency P2P Live Video Streaming Diffusion Network Extraction DML DML DML 27

  28. Cascade Dependency P2P Live Video Streaming Diffusion Network Extraction DML DML DML 28

  29. Extracting Important Diffusion Links P2P Live Video Streaming Diffusion Network Extraction DML DML DML 29

  30. Extracting Important Diffusion Links P2P Live Video Streaming Diffusion Network Extraction DML DML DML 30

  31. Running Time P2P Live Video Streaming Diffusion Network Extraction DML DML DML 31

  32. Contributions P2P Live Video Streaming Diffusion Network Extraction DML DML DML 32

  33. Future Work… P2P Live Video Streaming Diffusion Network Extraction DML DML DML 33

  34. References [1] G. Kossinets, J. M. Kleinberg and D.J. Watts, The structure of information pathways in a social communication network, KDD ’08, pages 435-443. 2008. [2] D. Easley and J. Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World, Cambridge University Press, 2010. [3] L.A. Adamic and N. Glance, The political blogosphere and the 2004 US Election, Proc. of the WWW-2005 Workshop on the Weblogging Ecosystem, 2005. [4] E. Adar and L. A. Adamic, Tracking Information Epidemics in Blogspace, Web Intelligence, pages 207–214, 2005. [5] M. Gomez-Rodriguez, J. Leskovec and A. Krause, Inferring networks of diffusion and influence, In proc. of KDD ’10, pages 1019-1028, 2010. [6] E. Adar, L. Zhang, L. Adamic and R.M. Lukose, Implicit Structure and the Dynamics of Blogspace, Workshop on the Weblogging Ecosystem, 2004. [7] D.T. Haydon, M. Chase-Topping, D.J. Shaw, L. Matthews, JK. Friar, J. Wilesmith, The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak, In proc. of Biol Sci, 270(1511):121-127, 2003. [8] D. Gruhl, R. Guha, D. Liben-Nowell and A. Tomkins, Information diffusion through blogspace, In proc. of of the 13th international conference on World Wide Web, pages 491–501, 2004. [9] J. Leskovec, M. McGlohon, C. Faloutsos, N. S. Glance and M. Hurst, Patterns of Cascading Behavior in Large Blog Graphs, In proc. of SDM’07, 2007. [10] D. Liben-Nowell and J. Kleinberg, Tracing information flow on a global scale using Internet chain-letter data, Proc. of the National Academy of Sciences, 105(12):4633-4638, 25 Mar, 2008. [11] S.A. Myers and J. Leskovec, On the Convexity of Latent Social Network Inference, Advances in Neural Infromation Processing Systems, 2010. [12] M. Eslami, H.R. Rabiee and M. Salehi, DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks, IEEE SocialComputing, 2011. [23] L. Lov´asz, Random walks on graphs: a survey, Combinatorics, 2:353–398, 1993. [13] N. Eagle, A.S. Pentland and D. Lazer, Inferring friendship network structure by using Mobile Phone Data, PNAS, pages 15274-15278, 2009. [14] J. Leskovec, L. Backstrom and J. Kleinberg, Meme-tracking and the dynamics of the news cycle, KDD ’09: Proc. of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 497-506, 2009. [15] J. Yang and J. Leskovec, Modeling Information Diffusion in Implicit Networks, ICDM, IEEE Computer Society, pages 599-608, 2010. [16] E. Sadikov, M. Medina, J. Leskovec and H. Garcia-Molina, Correcting for missing data in information cascades, WSDM, pages 55-64, 2011. P2P Live Video Streaming Extracting Network of Information DML DML DML 34

  35. References(cont’d) [17] D.L. Nowell and J. Kleinberg, The link prediction problem for social networks, CIKM ’03: Proc. of the twelfth international conference on Information and knowledge management, pages 556-559, 2003. [18] B. Taskar, M. Wong, P. Abbeel and Daphne Koller, Link Prediction in Relational Data, Advances in Neural Information Processing Systems (NIPS) 16, 2004. [19] T. Murata and S. Moriyasu, Link Prediction of Social Networks Based on Weighted Proximity Measures, Web Intelligence, IEEE Computer Society, pages 85-88, 2007. [20] A. Clauset, C. Moore and M. E. J. Newman, Hierarchical structure and the prediction of missing links in networks, Nature, 453: pages 98-101, 2008. [21] M. Kim and J. Leskovec, The Network Completion Problem: Inferring Missing Nodes and Edges in Networks, SIAM Conference on Data Mining, 2011. [22] J. Leskovec and C. Faloutsos, Scalable modeling of real graphs using Kronecker multiplication, ICML,ACM International Conference Proceeding Series, 227: pages 497-504, 2007. [23] L. Lov´asz, Random walks on graphs: a survey, Combinatorics, 2:353–398, 1993. [24] M. Chen, Mixing time of random walks on graphs, M.S. Thesis, Mathematics Department, University of York, 2004. [25] D. Aldous and J. Fill, Reversible Markov Chains and RandomWalks on Graphs, Book in preparation, 2001. [26] http://wikipedia.org/Markov-chain.htm [27] P.Pastor-Satorras and A.Vespignani, Epidemic Spreading in Scale-free Networks, ICTP,2000. [28] S.Boccaletti, V.Latora, Y.Moreno, M.Chavez and D.U Hwang, Complex Networks: Structure and Dynamics, Elsevier, Science Direct- Physics Reports, 2006. [29] F. Bass,A new product growth for model consumer durables, Management Science, 15(5):215–227, 1969. [30] J. Leskovec, L. Adamic and B. Huberman, The dynamics of viral marketing,ACM Transactions on the Web, 1(1),2007. [31] J. Leskovec, A. Singh and J. Kleinberg, Patterns of Influence in a Recommendation Network, Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), 2006. P2P Live Video Streaming Extracting Network of Information DML DML DML 35

  36. References(cont’d) [32]لیلا پیشداد، ماکسیمم سازی انتشار تاثیرات اجتمامی در شبکه های اجتماعی، پایان نامه کارشناسی ارشد، دانشکده علوم ریاضی، دانشگاه صنعتی شریف، خرداد . 1388 [33] M. Granovetter, Threshold models of collective behavior, American Journal of Sociology,83(6):1420–1443, 1978. [34] D. Kempe, J. Kleinberg and E. Tardos, Maximizing the spread of influence through a social network, KDD ’03: Proc. of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, ACM Press, pages 137-146, 2003. [35] J. Goldenberg, B. Libai, and E. Muller, Talk of the network: A complex systems look at the underlying process of word-of-mouth, Marketing Letters, 3(12):211–223, 2001. [36] M. Chen, J. Liu and X. Tang, Clustering via Random Walk Hitting Time on Directed Graphs, AAAI Press, 2008 [37] A. Langville and C. Meyer, Deeper inside pagerank, Internet Mathematics, 2005. [38] J. Leskovec, J. Kleinberg and C. Faloutsos, Graphs over Time: Densication Laws, Shrinking Diameters and Possible Explanations, KDD ’05, 2005. [39] A.L. Barabasi and R. Albert, Emregence of scaling in random networks, Science, 1999. [40] P.Erdős and A. Rényi, On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 5: page 17, 1960. [41] J. Leskovec, K.J. Lang, A. Dasgupta and M.W. Mahoney, Statistical properties of community structure in large social and information networks, WWW, pages 695-704, 2008. [42] M. E. J. Newman, Finding community structure in networks using the eigenvectors of matrices, Preprint physics/0605087, 2006. [43] M. Girvan and M. E. J. Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, pages 7821-7826, 2002. P2P Live Video Streaming Extracting Network of Information DML DML DML 36

  37. Q&A

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