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

London, April 11-12 2015 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

We want to... ● Study propagation models and social networks • Compare the propagation models • Use graph rewriting techniques to represent models and run propagation simulations • Perform visual analysis 2

Defjnitjons A social network: G =( V , E ) Described as a graph with • a set of nodes V  called “individuals” • a set of edges E ∈ V × V  to represent “relatjons” W. W. Zachary , An informatjon fmow model for confmict 3 and fjssion in small groups, Journal of Anthropological Research 33, (1977).

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 4

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 5

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 6

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 7

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 8

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 9

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 10

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 11

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 12

Probabilistjc cascade model simulatjon Linear threshold model simulatjon 13

Defjnitjons Selected references: • 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)... 14

Model translatjon and rewrite rules Propagatjon in a network from a graph theoretjc perspectjve • 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 15

Model translatjon and rewrite rules Propagatjon in a network as a Graph Rewritjng System • 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)] 16

Model translatjon and rewrite rules Defjnitjon: Port graph with propertjes [Fernandez et al. (2014)] ● G =( N , P, E ) ● Ports are used as connectjon points ● Edges connect nodes through ports ● Each element possess a set of propertjes 17

Model translatjon and rewrite rules Defjnitjon: Port graph rewrite rule ● Symbolically writuen as L ⇒ R ● LHS/RHS expressed as port graphs ● is a special node whose ports ⇒ encode rewiring conditjons to perform in rewritjng (through red edges) 18

Model translatjon and rewrite rules Example: Independent cascade model [Kempe et al. (2003)] • 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 19

Model translatjon and rewrite rules Rule 1: infmuence from a neighbour 20

Model translatjon and rewrite rules Active = true Marked = false Active = false Visited = ? Rule 1: infmuence from a neighbour 21

Model translatjon and rewrite rules Active = true Active = true Marked = false Marked = true Active = false Active = false Visited = ? Visited = true Rule 1: infmuence from a neighbour 22

Model translatjon and rewrite rules Active = true Active = true Marked = false Marked = true [Probability = X] [Probability = X] Active = false Active = false Visited = true Visited = ? [Sigma = f(X, Y)] [Sigma = Y] Rule 1: infmuence from a neighbour 23

Model translatjon and rewrite rules Active = false Active = true Visited = true Rule 2: node actjvatjon 24

Model translatjon and rewrite rules Defjnitjon: Strategy • Manage the rules' applicatjon order • Express control ( repeat, if-then-else, while-do, … ) • Use a located graph with P ositjon and B anned subgraphs:  Positjon represents the subgraph where rewritjng may take place  Banned represents the subgraph where rewritjng is forbidden 25

Model translatjon and rewrite rules 26

Model translatjon and rewrite rules Step 1 Step 2 Step 3 27

Model translatjon and rewrite rules Step 4 Step 5 Step 6 28

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)] 29

Analytjc visualizatjon and model comparison Metrics: used to measure the propagatjon evolutjon • 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 30

Propagatjon speed Number of actjve nodes Number of actjve nodes Propagatjon step Propagatjon step 31 Linear threshold model Independent cascade

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Propagatjon speed Number of actjve nodes Propagatjon step Propagatjon step Propagatjon step Independent cascade Linear threshold model Linear threshold model (reinforced infmuences) 33

Acknowledgment speed Number of visited nodes Propagatjon step Propagatjon step Propagatjon step Independent cascade Linear threshold model Linear threshold model (reinforced infmuences) 34

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 35

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) 36

References • Goyal, A., F. Bonchi, and L. V. Lakshmanan (2010). Learning infmuence probabilitjes in social networks. In 3 rd 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 9 th 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. 37

Thanks for your attention.