1 / 32

Analysis of Social Media MLD 10-802, LTI 11-772

Analysis of Social Media MLD 10-802, LTI 11-772. William Cohen 1-25-010. Recap: What are we trying to do?. Like the normal curve: Fit real-world data Find an underlying process that “explains” the data Enable mathematical understandingl (closed-form?)

aira
Download Presentation

Analysis of Social Media MLD 10-802, LTI 11-772

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Analysis of Social MediaMLD 10-802, LTI 11-772 William Cohen 1-25-010

  2. Recap: What are we trying to do? • Like the normal curve: • Fit real-world data • Find an underlying process that “explains” the data • Enable mathematical understandingl (closed-form?) • Modelssome small but interesting part of the data

  3. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Connected components • … • Some types of graphs to consider: • Real graphs (social & otherwise) • Generated graphs: • Erdos-Renyi“Bernoulli” or “Poisson” • Watts-Strogatz “small world” graphs • Barbosi-Albert “preferential attachment” • …

  4. Graphs • Some types of graphs to consider: • Real graphs (social & otherwise) • Generated graphs: • Erdos-Renyi“Bernoulli” or “Poisson” • Watts-Strogatz “small world” graphs • Barbosi-Albert “preferential attachment” • … All pairs connected with probability p

  5. Graphs • Some types of graphs to consider: • Real graphs (social & otherwise) • Generated graphs: • Erdos-Renyi“Bernoulli” or “Poisson” • Watts-Strogatz “small world” graphs • Barbosi-Albert “preferential attachment” • … Regular, high-homophily lattice Plus random “shortcut” links

  6. Graphs • Some types of graphs to consider: • Real graphs (social & otherwise) • Generated graphs: • Erdos-Renyi“Bernoulli” or “Poisson” • Watts-Strogatz “small world” graphs • Barbosi-Albert “preferential attachment” • … New nodes have m neighbors High-degree nodes are preferred “Rich get richer”

  7. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Connected components • … • Some types of graphs to consider: • Real graphs (social & otherwise) • Generated graphs: • Erdos-Renyi“Bernoulli” or “Poisson” • Watts-Strogatz “small world” graphs • Barbosi-Albert “preferential attachment” • …

  8. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Connected components • …

  9. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Connected components • … • In a big Erdos-Renyi graph this is very small (1/n) • In social graphs, not so much • More later…

  10. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Mean diameter • Connected components • … • In a big Erdos-Renyi graph this is small (logn/logz) • In social graphs, it is also small (“6 degrees”)

  11. Graphs • Some common properties of graphs: • Distribution of node degrees • Distribution of cliques (e.g., triangles) • Distribution of paths • Diameter (max shortest-path) • Effective diameter (90th percentile) • Mean diameter • Connected components • … • In a big Erdos-Renyi graph there is one “giant connected component”… • … because two giant connected components cannot co-exist for long.

  12. n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Poor fit

  13. More terms • Centrality and betweenness: how does your position in a network affect what you do and how you do it? • And how can we define these precisely? • High centrality: ringleaders? • High betweenness: go-between, conduit between different groups? • “Structural hole” • Group cohesiveness: number of edges within a (sub)group

  14. More terms

  15. More terms • Association network: bipartite network where nodes are people or organizations

  16. A larger association network

  17. Triads and clustering coefficients • In a random Erdos-Renyi graph: • In natural graphs two of your mutual friends might well be friends: • Like you they are both in the same class (club, field of CS, …) • You introduced them

  18. Watts-Strogatz model • Start with a ring • Connect each node to k nearest neighbors •  homophily • Add some random shortcuts from one point to another •  small diameter • Degree distribution not scale-free • Generalizes to d dimensions

  19. Even more terms • Homophily: tendency for connected nodes to have similar properties • Social contagion: connected nodes become similar over time • Associative sorting: similar nodes tend to connect • Disassociative sorting: vice-versa • Association network: bipartite network where nodes are people or organizations

  20. A big question • Homophily: similar nodes ~= connected nodes • Which is cause and which is effect? • Do birds of a feather flock together? • Do you change your behavior based on the behavior of your peers? • Do both happen in different graphs? Can there be a combination of associative sorting and social contagion in the same graph?

  21. A big question about homophily • Which is cause and which is effect? • Do birds of a feather flock together? • Do you change your behavior based on the behavior of your peers? • How can you tell? • Look at when links are added and see what patterns emerge (triadic closure): Pr(new link btwnu and v | #common friends)

  22. Triadic closure T(k) = 1 – (1-p)^k T(k) = 1 – (1-p)^(k-1) • Pr(new link btwnu and v | #common friends)

  23. Changing behavior

  24. Final example: spatial segregation • How picky do people have to be about their neighbors for homophily to arise? • Imagine a grid world where • Agents are red or blue • Agents move to a random location if they are unhappy • Agents are happy unless <k neighbors are the same color they are (k= • i.e., they prefer not to be in a small minority • What’s the result over time? • http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/

More Related