1. Link Prediction & Content
Seminar Social Media Mining
University UC3M
Date May 2017
Lecturer Carlos Castillo
Sources:
Lilian Weng, Jacob Ratkiewicz, Nicola Perra, Bruno Gonçalves, Carlos Castillo, Francesco Bonchi, Rossano Schifanella, Filippo Menczer, Alessandro Flammini: The Role of Information Diffusion in the Evolution of Social Networks. In KDD 2013 [doi]
Nicola Barbieri, Francesco Bonchi, and Giuseppe Manco Who to follow and why: link prediction with explanations. In KDD 2014 [doi]
Seth A. Myers and Jure Leskovec The bursty dynamics of the Twitter information network. In WWW 2014 [doi]

2. Extension: links and traces, with data from Y! Meme (2009-2010)
Lilian Weng, Jacob Ratkiewicz, Nicola Perra, Bruno Gonçalves, Carlos Castillo, Francesco Bonchi, Rossano Schifanella, Filippo Menczer, Alessandro Flammini: The Role of Information Diffusion in the Evolution of Social Networks. In KDD 2013

3. Y! Meme Dataset ~128k users ~3.5M links ~7M posts
Entire history available!
Lilian Weng, Jacob Ratkiewicz, Nicola Perra, Bruno Gonçalves, Carlos Castillo, Francesco Bonchi, Rossano Schifanella, Filippo Menczer, Alessandro Flammini: The Role of Information Diffusion in the Evolution of Social Networks. In KDD 2013

4. Most slides on this section from talk by F
Most slides on this section from talk by F. Menczer:

5. Triadic closure with grandparent
Triadic closure with original poster
Triadic closure with someone else

7. Many traffic shortcuts … can this happen by chance?
Let's take for instance grandparent links G
Links labeled in creation order
Probability of link being a “grandparent” link by chance:
Where NG is the number of grandparents of the link at creation time, φ(.) the set of people followed by the creator of the link at link creation time

8. Expected and actual number of links
Expected number of links and variance if process is random
Actual number of grandparent links SG
By central limit theorem, the following should be normally distributed with mean 0 and variance 1:

9. z computed for different degrees
Notice z is in general a large number, very unlikely to come from a normal with mean 0 and variance 1. Observe also that at about 75 links, triadic closure starts taking a secondary role.

10. Effect of repeated exposure
The more posts we see from someone, the more likely we are of following her/him next
This is consistent with previous observations regarding repeated exposure to online content

11. Link efficiency (Usage of link after creation)
Average number of posts seen through that link per unit of time after the link is created
Each box shows data within lower and upper quartile. Whiskers represent the 99th percentile. The triangle and line in a box represent the median and mean, respectively. Note that the mean can fall outside the shown quantiles for skewed distributions. The gray area and the black line across the entire figure mark the interquartile range and the median of the measure across all links, respectively.

12. Link creations might happen by a mixture of reasons
How do we determine the relative weights of each element in the mixture? E.g. grandparent vs. random
Likelihood of link being created if we're using strategy Ψ and the state of the graph is Θ
Combined strategy: link to grandparent with probability p, random with probability (1-p):

13. Log likelihood For numerical stability, the log likelihood is computed
For instance for grandparent links, it is:
To plot the log likelihood as a function of p, we exhaustively use several values of p and calculate this numerically

14. Link creations happen through a mixture of reasons

15. Assume all users create links using a mix of triadic closure and G+O, max likelihood estimate of params

16. Per-user assignments
Assume you have p = <ptraffic, pstructure, prandom> (traffic=G+O, structure=Δ)
Assume you have p' = <p'traffic, p'structure, p'random>
Could you determine if a particular user is more likely to be using strategy p than p'?

17. Behavioral clusters Expectation-Maximization algorithm for clustering:
Assume there are k centroids
Each centroid is a vector of three probabilities: <ptraffic, pstructure, prandom> (traffic=G+O, structure=Δ)
Repeat:
Assign person to most likely centroid
Recompute centroids
Number k can be determined by cross-validation

18. Clusters found Info: preference for traffic-related linking
>0.50
>0.05
Info: preference for traffic-related linking
Cfrd: preference for friends but also random
Random: preference for random

19. Clusters of users by most likely link creation strategy
Random
Mixture
Information oriented
Casual friendship
Friendship

21. In general ...
In general, active, popular, influential users make an information network more efficient by creating “shortcuts” for information diffusion.

22. Link prediction with explanations

23. Link prediction with explanations
Nicola Barbieri, Francesco Bonchi, and Giuseppe Manco Who to follow and why: link prediction with explanations. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD '14)

24. Key idea Common identity and common bond theory:
Identity-based attachment holds when people join a community based on their interest in a well-defined common topic;
Bond-based attachment is driven by personal social relations with other specific individuals.

25. Example network
Sets next to nodes indicate interests (products purchased, hashtags used, keywords, etc.)
Which links are identity-based and which ones are bond-based?

26. Example network (3 communities)
Blue links are bond-based
Bond-based communities tend to have high density and reciprocal links
Green and orange links are identity-based
Identity-based communities tend to exhibit a clear directionality (leaders and followers)

27. Factors governing link behavior
Authority (influence held)
Susceptibility (influence received)
Social attitude (propensity to reciprocate links)
Features adopted

28. Factors governing link behavior

29. Inference of generative model
Gray circles are observed (u,v) links, (u,f) features
Dirichlet distributions are used for sparsity

30. Parameters

31. Once a model has been fitted ...
Recommend social link (u,v) if both are members of the same social community
Recommend topical link (u,v) if u is interested in the topic and v is an authority in the topic

32. Experimental results: baselines
JSVD (joint-SVD): approx. matrix X'≈X=[E F]
E contains (user, user) pairs for links
F contains (user, feature) pairs for interests
CNF (common neighbors and features)
Adamic/Adar

33. Results (two datasets)
Twitter (n=81K, m=1.7M)
Flickr (n=80K, m=14M)

34. Temporal dimension

35. Temporal dimension
“Bursty” dynamic in which cascades of information create new links
Communities become more dense
Communities become more topically cohesive
Myers & Leskovec: The bursty dynamics of the Twitter information network. WWW 2014

36. Followers gained, followers lost, number of retweets, and number of tweets all scale with the indegree (number of followers) of a user.
E.g.: in a given month a user of degree 100 tends to gain 10 and lose 3 followers.

37. For users with 1000-2000 followers
Got retweeted? => will get followers
Tweet too little or too much => lose followers

38. Three case studies
266K followers: burst in retweets => burst in followers
218K followers: burst in retweets => nothing
112K followers: no tweets, but followed/unfollowed

39. Observations of ego-networks
Users with 2K or more followers
Instances in which a retweet burst was followed by a follow burst (or unfollow burst)
Measure properties in their ego network:
Tweet similarity: average content similarity of (v,u) for all v such that follows(v,u)
Tweet coherence: average content similarity across all (v,w) pairs such that follows(v,u) and follows(w,u)
Connected components
Edge density

40. Results in ego-nets
Content similarity (to leader) and coherence (among followers) increases.
Weakly connected components increase; edge density increases slightly.

41. What causes a large follower burst?
The perfect scenario for a large follower burst is that a person's content reaches a large, new, and compatible audience

42. What does it mean a compatible audience? What is the scale?
# Followers
Probability
Different users have different characteristic scales
sim(v,u) is lognormal-distributed for follows(v,u)

43. Normalized similarity of v as a potential follower of u

44. Yuv helps predict followers
Probability that v follows u
Probability increases exponentially with normalized similarity

45. Building a predictor
Basic building block, estimates prob. of following given similarity
Set of nodes who have seen content by u
Set of nodes that are followers of followers of u

46. Experimental results Task: given a retweet burst (cascade)
Predict whether there will be a follower burst
Method
AUC
Myers & Leskovec 2014
0.52
Number of retweet exposures
0.38
Number of retweets
0.33
Number of followers
0.22
Random
0.21

47. Conclusions Link formation is a complex process
Driven by triadic closure
Driven by shortcut formation
Driven by topical communities
Tends to occur in bursts