A visual analytics approach to compare propagation models in social - - PowerPoint PPT Presentation

A visual analytics approach to compare propagation models in social networks

• J. Vallet, H. Kirchner, B. Pinaud, G. Melançon

LaBRI, UMR 5800 Inria Bordeaux

• Univ. Bordeaux

London, April 11-12 2015

We want to...

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• Study propagation models and social networks
• Compare the propagation models
• Use graph rewriting techniques to represent models and run

propagation simulations

• Perform visual analysis

Defjnitjons

Described as a graph with

• a set of nodes
• called “individuals”
• a set of edges
• to represent “relatjons”

A social network:

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• W. W. Zachary, An informatjon fmow model for confmict

and fjssion in small groups, Journal of Anthropological Research 33, (1977).

G=(V , E)

E∈V ×V V

Defjnitjons

Propagatjon in a network – as a social process

• An individual performs an actjon
• Her/his neighbours are informed and

choose to perform the same actjon

• The process repeats itself
• Decisions can depend on infmuences,

vulnerabilitjes or resistances between neighbours

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Probabilistjc cascade model simulatjon Linear threshold model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

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Linear threshold model simulatjon Probabilistjc cascade model simulatjon

Defjnitjons

Selected references:

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• Threshold models

Bertuzzo et al. (2010), Dodds et al. (2005), Goyal et al. (2012), Granovetuer (1978), Watus (2002)…

• Cascade models

Chen W. et al. (2011), Gomez-Rodriguez et al. (2010), Payne et al. (2011), Richardson et al. (2002), Wonyeol et al. (2012)...

Model translatjon and rewrite rules

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• Social state (actjvated, infmuent) are encoded as node atuributes
• The process acts locally, is asynchronous, distributed and follows

some conditjons

• This is where graph rewritjng comes into play

Propagatjon in a network from a graph theoretjc perspectjve

Model translatjon and rewrite rules

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• Rules as a common paradigm to express the propagatjon models
• Each propagatjon paradigm (threshold, cascade) has its own ruleset

and a strategy managing their applicatjon

• Modelling through Strategic Rewritjng [Fernandez et al. (2014)]

Propagatjon in a network as a Graph Rewritjng System

• Ports are used as connectjon points
• Edges connect nodes through ports
• Each element possess a set of propertjes

Defjnitjon: Port graph with propertjes

[Fernandez et al. (2014)]

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Model translatjon and rewrite rules

G=(N , P, E)

Model translatjon and rewrite rules

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Defjnitjon: Port graph rewrite rule

• Symbolically writuen as
• LHS/RHS expressed as port graphs
• is a special node whose ports

encode rewiring conditjons to perform in rewritjng (through red edges)

L⇒ R ⇒

• Start with a set of infmuencers
• Infmuencers try (according to some

probability) to infmuence their neighbours and recruit them as new infmuencers

• The process repeats untjl no more

infmuencer can be recruited

Example: Independent cascade model [Kempe et al. (2003)]

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Model translatjon and rewrite rules

Model translatjon and rewrite rules

Rule 1: infmuence from a neighbour

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Model translatjon and rewrite rules

Rule 1: infmuence from a neighbour

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Active = true Active = false Visited = ? Marked = false

Model translatjon and rewrite rules

Rule 1: infmuence from a neighbour

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Active = true Active = false Visited = ? Active = false Visited = true Active = true Marked = false Marked = true

Model translatjon and rewrite rules

Rule 1: infmuence from a neighbour

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Active = true Active = false Visited = ? [Sigma = Y] Active = false Visited = true [Sigma = f(X, Y)] Active = true Marked = false [Probability = X] Marked = true [Probability = X]

Model translatjon and rewrite rules

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Active = false Visited = true Active = true

Rule 2: node actjvatjon

• Manage the rules' applicatjon order
• Express control (repeat, if-then-else, while-do, …)
• Use a located graph with Positjon and Banned subgraphs:

 Positjon represents the subgraph where rewritjng may take place  Banned represents the subgraph where rewritjng is forbidden

Defjnitjon: Strategy

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Model translatjon and rewrite rules

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Model translatjon and rewrite rules

Model translatjon and rewrite rules

Step 1 Step 2 Step 3

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Model translatjon and rewrite rules

Step 4 Step 5 Step 6

Analytjc visualizatjon and model comparison

• Successive applicatjons of rules
• Keep track of the previously computed

simulatjons

• Use the derivatjon tree during

comparatjve analysis

[Pinaud et al. (2012)]

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Analytjc visualizatjon and model comparison

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• Propagatjon speed: estjmated by the number of actjve nodes at a

given step

• Acknowledgment speed: estjmated by the number of visited nodes

at a given step

• Propagatjon effjciency: ratjo of actjvated nodes at step t against

those visited at t-1

Metrics: used to measure the propagatjon evolutjon

Independent cascade Linear threshold model

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Number of actjve nodes Number of actjve nodes

Propagatjon speed

Propagatjon step Propagatjon step

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Propagatjon speed

Propagatjon step

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Independent cascade Linear threshold model

Number of actjve nodes Propagatjon step Propagatjon step

Linear threshold model (reinforced infmuences)

Acknowledgment speed

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Independent cascade Linear threshold model

Number of visited nodes

Linear threshold model (reinforced infmuences)

Propagatjon step Propagatjon step Propagatjon step

To conclude

• We have used graph rewritjng as a common language to express

propagatjon models

• Analyze and compare the models precisely by storing the

propagatjon evolutjon

• Results can be visually investjgated to help enforce infmuence

maximizatjon

• Several metrics available to perform analysis

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Future work

• Extend to additjonal models
• Explore other visual encodings for scalability (Matrix views...)
• Management of tjme-dependent atuributes evolving along the

propagatjon (infmuence exhaustjon, media induced fashion...)

• Joint use of propagatjon and topological modifjcatjons
• Applicatjon to difgerent domains (power distributjon, network

security, epidemiology, fjnancial crisis)

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References

• Goyal, A., F. Bonchi, and L. V. Lakshmanan (2010). Learning infmuence probabilitjes in social
• networks. In 3rd ACM Int. Conf. on Web Search and Data Mining, WSDM ’10, pp. 241–250
• Kempe, D., J. Kleinberg, and É. Tardos (2003). Maximizing the spread of infmuence through a

social network. In Proc. of the 9th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD ’03, pp. 137–146

• Fernandez, M., H. Kirchner, and B. Pinaud (2014). Strategic Port Graph Rewritjng : An

Interactjve Modelling and Analysis Framework. In D. Bošnački, S. Edelkamp, A. L. Lafuente, et

• A. Wijs (Eds.), GRAPHITE 2014, Volume 159 of EPTCS, pp. 15–29
• Pinaud, B., G. Melançon, and J. Dubois (2012). Porgy : A visual graph rewritjng environment

for complex systems. Computer Graphics Forum 31(3), 1265–1274.

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Thanks for your attention.