DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks By: Yousef Naderi [email protected] Authors: Motahhare Eslami HamidReza

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

OutlineIntroductionProblem DefinitionProblem ImportanceRelated WorkProposed Method: “DNE”Experimental EvaluationContributionFuture WorkReferences


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]


An Example of Diffusion Process

Figure 2: Diffusion process over information networks

5 DMLDML5

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


Related Work

[7] for the first time tries to reconstruct epidemic trees of a disease propagation and estimates the sickness outbreak history.


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


An Example of Initial Graph

Figure5(a)General Initial Graph

(b)Initial Graph of cascade 1 from Figure 2

Figure 4: Initial graph construction


Random walk Markov Model


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


Reaching Time

Not being strongly connected leads to 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.


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


Proposed Algorithm: “DNE”

Recursive equation to find RT:1

( 1)j

ij iw wjw i

RT p RT

0iiRT



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



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


Experimental Evaluation

DatasetsSynthetic Networks

Forest Fire[38]Kronecker[22]Barabasi-Albert(BA)[39]

Real NetworksCo-authorship network[42]Football network[43]U.S. president election network[3]

NetInf[5] for comparison. Evaluation metrics:

PrecisionRecallF-measure


Cascade Dependency


Extracting Important Diffusion Links


Running Time


Future Work…

29 DMLP2P Live Video Streaming DMLDMLExtracting Network of Information29

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.

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[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.

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DNE: A Method for Extracting Cascaded Diffusion Networks from Social Networks By: Yousef Naderi [email protected] Authors: Motahhare Eslami HamidReza