dne: a method for extracting cascaded diffusion networks from social networks
DESCRIPTION
DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks. By: Yousef Naderi [email protected] Authors: Motahhare Eslami HamidReza Rabiee Mostafa Salehi 2011, October, 9th. Outline. Introduction Problem Definition Problem Importance Related Work Link Prediction - PowerPoint PPT PresentationTRANSCRIPT
DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks
DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks
By: Yousef [email protected]
Authors: Motahhare EslamiHamidReza Rabiee
Mostafa Salehi
2011, October, 9th
2 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction2
Outline Introduction Problem Definition Problem Importance Related Work
Link Prediction Network Completion Network Inference
Proposed Method: “DNE” Experimental Evaluation Contribution Future Work References
3 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction3
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]
4 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction4
Introduction
5 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction5
An Example of Diffusion Process
Figure 2: Diffusion process over information networks
6 DMLDML6
The network that diffusion takes place on it is 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: Problem Definition
Diffusion Network Extraction
7 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction7
Problem Importance
Related WorkRelated Work
A few work had been done…
9 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction9
Related Work
[7] for the first time tries to reconstruct epidemic trees of a disease propagation and estimates the sickness outbreak history.
10 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction10
Proposed Method
Graph G with |V|=n and |E|=eC: The set of propagating cascades over G
Nc members 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.
1 2{ , ,..., }c nT t t t
11 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction11
Cascade transmission Model
Information Propagation models Threshold model Cascade model
• Independent cascade model Pc(u, v) P(tv - tu)
tv > tu Δ = tv - tu
( )P e
1( )P
12 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction12
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.
1 2{ , ,..., }i i in ct t t
13 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction13
An Example of Initial Graph
Figure5(a)General Initial Graph
(b)Initial Graph of cascade 1 from Figure 2
Figure 4: Initial graph construction
14 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction14
Random walk Markov Model
15 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction15
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].
ijH 0
1
0
1n
ik kjk
p H
i j
i j
16 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction16
Hitting Time(cont’d)
17 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction17
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.
18 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction18
Diffusion Network Extraction Problem
Constructing Gtotal
Gtotal =
Defining RT for each edge(i,j) in Gtotal
RTij =
Problem converts to:G’=argmin
cc C
G
cij
c C
RT
( , ) total
iji j G
RT | ' |G m
19 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction19
Proposed Algorithm: “DNE”
Recursive equation to find RT:1
( 1)j
ij iw wjw i
RT p RT
0iiRT
20 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction20
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.
1 2{ , ,..., }jj kS n n n
1
| |ijj
PS
21 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction21
Proposed Algorithm: “DNE”
Considering the order of infection instead of infection times difference.
More independency to cascade transmission modelIntroducing a new parameter named Rank:
Converting the problem to finding m links with least Ranks to construct G’.
ijr 0 i j| | ( )jS j i i j
22 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction22
Proposed Algorithm: “DNE”For each c C∊
for each (i,j) c∊if (ti < tj)
then Gc G⟵ c (i,j)∪ Sc
j S⟵ cj {i}∪
sort nodes of Gc by infection time.for each (i,j) G∊ c which i < j
rcij | S⟵ c
j | . (j-i)Gtotal G⟵ total (i,j)∪ rij r⟵ ij + rc
ij
Sort edges of Gtotal respect to rij
For i 1 to m⟵G’ G’ {e⟵ ∪ i Gtotal }∊
Return (G’)
23 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction23
Experimental Evaluation
NetInf[5] for comparison.
24 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction24
Dataset
Synthetic Networks Forest Fire[38] Kronecker[22] Barabasi-Albert(BA)[39]
Synthetic Network Parameter matrix
a B n e Nc
Forest-Fire [5;0.12;0.1;1;0] 1 0.5 1024 1221 2786
Hierarchical [0.5;0.5;0.5;0.5] 2 0.5 1024 2048 4000
Random(ER) [0.9;0.1;0.1;0.9] 2 0.4 1024 2048 1813
Core-Periphery [0.9;0.5;0.5;0.3] 2 0.1 1024 2048 2350
Barabasi-Albert [2] 2 0.5 1000 2000 4824
25 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction25
Dataset
Real Networks Co-authorship network[42] Football network[43] President election network[3]
Real Network n e Nc
Co-authorship 1589 2742 6427
Football 115 615 993
President election 1490 19090 5717
26 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction26
Evaluation Metrics
P2
RF
P R
27 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction27
Cascade Dependency
28 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction28
Cascade Dependency
29 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction29
Extracting Important Diffusion Links
30 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction30
Extracting Important Diffusion Links
31 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction31
Running Time
32 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction32
Contributions
33 DMLP2P Live Video Streaming DMLDMLDiffusion Network Extraction33
Future Work…
34 DMLP2P Live Video Streaming DMLDMLExtracting Network of Information34
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.
35 DMLP2P Live Video Streaming DMLDMLExtracting Network of Information35
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.
36 DMLP2P Live Video Streaming DMLDMLExtracting Network of Information36
References(cont’d)لیال پیشداد، ماکسیمم سازی انتشار تاثیرات اجتمامی در شبکه های اجتماعی، پایان نامه کارشناسی ارشد، دانشکده علوم ریاضی، دانشگاه ]32[
1388صنعتی شریف، خرداد .
[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.
Q&AQ&A