Romantic Partnerships and the Dispersion of Social Ties

Transcription

1 Introduction Embeddedness and Evaluation Combining Features Romantic Partnerships and the of Social Ties Lars Backstrom Jon Kleinberg presented by Yehonatan Cohen

2 Introduction Embeddedness and Evaluation Combining Features 1 Introduction Problem Statement Dataset 2 Embeddedness and Embeddedness 3 Evaluation Take 1 Take 2 Time and Space 4 Combining Features Machine Learning Performance Over Time

3 Introduction Embeddedness and Evaluation Combining Problem Features Statement Problem Statement Dataset Consider a social network user, a

4 Introduction Embeddedness and Evaluation Combining Problem Features Statement Problem Statement Dataset Consider a social network user, a, and its neighborhood...

5 Introduction Embeddedness and Evaluation Combining Problem Features Statement Problem Statement Dataset Consider a social network user, a, and its neighborhood... Also, let us assume that a is married. Can we identify his wife?

6 Introduction Embeddedness and Evaluation Combining Problem Features Statement Problem Statement Dataset Formally, our problem is defined as follows: Spouse Detection Let a an ego Facebook node and denote by G a its set of all friends and the links among them. Given a declared a relationship partner ( married, engaged or in a relationship ). Can we identify a s spouse?

7 Introduction Embeddedness and Evaluation Combining Problem Features Statement Motivation Dataset Such relationships detection is important for several reasons: Romantic relationships are singular type of social ties that play powerful roles in social processes over a person s whole life course. They also form an important aspect of the everyday practices and uses of social media. They are among the very strongest ties, but is has not been clear whether standard structural features are sufficient to characterize them.

8 Introduction Embeddedness and Evaluation Combining Problem Features Statement Facebook Semantcis Dataset Facebook is the most popular on-line social network.

9 Introduction Embeddedness and Evaluation Combining Problem Features Statement Facebook Semantcis Dataset Facebook is the most popular on-line social network. A user is represented by a node.

10 Introduction Embeddedness and Evaluation Combining Problem Features Statement Facebook Semantcis Dataset Facebook is the most popular on-line social network. A user is represented by a node. Facebook s friendship relation is undirected.

11 Introduction Embeddedness and Evaluation Combining Problem Features Statement Facebook Semantcis Dataset Facebook is the most popular on-line social network. A user is represented by a node. Facebook s friendship relation is undirected. An edge between two nodes represents a friendship between the corresponding users.

12 Introduction Embeddedness and Evaluation Combining Problem Features Statement Facebook Semantics Dataset

13 Introduction Embeddedness and Evaluation Combining Problem Features Statement Datasets Description Dataset Two datasets were used by the authors: The first consists of the network neighborhoods of approximately 1.3 million Facebook users. Users were selected uniformly at random from among: Users of age at least 20. Users with between 50 and 2000 friends. Users who list a spouse or relationship partner in their profile.

14 Introduction Embeddedness and Evaluation Combining Problem Features Statement Datasets Description Dataset The second is a sample of approximately 73,000 neighborhoods from the first dataset selected uniformly at random from among all neighborhoods with at most 25,000 links.

15 Introduction Embeddedness and Evaluation Combining Problem Features Statement Datasets Dimensions Dataset The datasets contains 379 million nodes. Overall there are 8.6 billion links. An average of 291 nodes and 6652 links per node s neighborhood.

16 Introduction Embeddedness and Evaluation Combining Problem Features Statement Dataset 1 Introduction Problem Statement Dataset 2 Embeddedness and Embeddedness 3 Evaluation Take 1 Take 2 Time and Space 4 Combining Features Machine Learning Performance Over Time

17 Introduction Embeddedness and Evaluation Combining Embeddedness Features Embeddedness Embeddedness Given an edge (u, v), its embeddedness is the number of mutual friends shared by its endpoints. Traditionally, embeddedness is associated with tie strength, and will be used as a baseline predictor.

18 Introduction Embeddedness and Evaluation Combining Embeddedness Features Embeddedness What is the embeddedness of (b, c)?

19 Introduction Embeddedness and Evaluation Combining Embeddedness Features Embeddedness What is the embeddedness of (b, c)?

20 Introduction Embeddedness and Evaluation Combining Embeddedness Features Embeddedness Can you determine the strongest tie in the network below?

21 Introduction Embeddedness and Evaluation Combining Embeddedness Features Embeddedness Can you determine the strongest tie in the network below?

22 Introduction Embeddedness and Evaluation Combining Embeddedness Features Many individuals have large clusters of friends corresponding to well-defined foci of interaction in their lives: Co-workers. People with whom they attended college. Family members. Etc. Since many people within these clusters know each other, the clusters contain links of very high embeddedness even though they do not necessarily correspond to particularly strong ties.

23 Introduction Embeddedness and Evaluation Combining Embeddedness Features In contrast, the links to a person s relationship partner may have lower embeddedness, but they will often involve mutual neighbors from several different foci, reflecting the fact that the social orbits of these friends are not bounded within any one focus.

24 Introduction Embeddedness and Evaluation Combining Embeddedness Features Consider the following example: A husband who knows several of his wife s co-workers, family members, and former classmates, even though these people belong to different foci and do not know each other.

25 Introduction Embeddedness and Evaluation Combining Embeddedness Features The mutual neighbors of a married couple are not well-connected to one another.

26 Introduction Embeddedness and Evaluation Combining Embeddedness Features We take the subgraph G u induced on u and all neighbors of u, and for a node v in G u we define C uv to be the set of common neighbors of u and v. Then disp(u, v) = Σ s,t Cuv d v (s, t)

27 Introduction Embeddedness and Evaluation Combining Embeddedness Features We take the subgraph G u induced on u and all neighbors of u, and for a node v in G u we define C uv to be the set of common neighbors of u and v. Then disp(u, v) = Σ s,t Cuv d v (s, t) d v is a distance function on the nodes of C uv.

28 Introduction Embeddedness and Evaluation Combining Embeddedness Features We take the subgraph G u induced on u and all neighbors of u, and for a node v in G u we define C uv to be the set of common neighbors of u and v. Then disp(u, v) = Σ s,t Cuv d v (s, t) d v is a distance function on the nodes of C uv. We do not consider the two-step paths through u and v themselves.

29 Introduction Embeddedness and Evaluation Combining Embeddedness Features The function d v need not be the standard graph-theoretic distance.

30 Introduction Embeddedness and Evaluation Combining Embeddedness Features The function d v need not be the standard graph-theoretic distance. A function equal to 1 when s and t are not directly linked and also have no common neighbors in G u other than u and v.

31 Introduction Embeddedness and Evaluation Combining Embeddedness Features The function d v need not be the standard graph-theoretic distance. A function equal to 1 when s and t are not directly linked and also have no common neighbors in G u other than u and v. A function equal to 1 when the distance between s and t is greater than a pre-defined threshold T.

32 Introduction Embeddedness and Evaluation Combining Embeddedness Features The function d v need not be the standard graph-theoretic distance. A function equal to 1 when s and t are not directly linked and also have no common neighbors in G u other than u and v. A function equal to 1 when the distance between s and t is greater than a pre-defined threshold T. A function equal to 1 when there are less than T disjoint paths between s and t.

33 Introduction Embeddedness and Evaluation Combining Embeddedness Features Let us practice dispersion under the assumption that d v (s, t) equal to 1 when s and t are not directly linked and also have no common neighbors in G u...

34 Introduction Embeddedness and Evaluation Combining Embeddedness Features disp(u, b) =?

35 Introduction Embeddedness and Evaluation Combining Embeddedness Features disp(u, b) =?

36 Introduction Embeddedness and Evaluation Combining Embeddedness Features disp(u, b) =?

37 Introduction Embeddedness and Evaluation Combining Embeddedness Features disp(u, h) =?

38 Introduction Embeddedness and Evaluation Combining Embeddedness Features disp(u, h) =?

39 Introduction Embeddedness and Evaluation Combining Embeddedness Features Strengthenings of We can detect a s romantic partner based of the two functions (dispersion and embeddedness). It has been empirically found that performance is highest for functions that are monotonically increasing in dispersion and monotonically decreasing in embeddedness. E.g. disp(u, v)/emb(u, v). Can you find the logic behind this finding?

40 Introduction Embeddedness and Evaluation Combining Embeddedness Features One can strengthen performance by applying the idea of dispersion recursively as follows: We initially define X v = 1 for all neighbors v of u, and then iteratively update each X v to be: Recursive X v = Xw 2 +2 d v (s,t)x sx t w Cuv s,t Cuv emb(u,v) The authors found that the highest performance is achieved when they rank nodes by the values of X v after the third iteration.

41 Introduction Embeddedness and Evaluation Combining Embeddedness Features 1 Introduction Problem Statement Dataset 2 Embeddedness and Embeddedness 3 Evaluation Take 1 Take 2 Time and Space 4 Combining Features Machine Learning Performance Over Time

42 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 1 Accuracy is defined as the fraction of instances on which the highest-ranked node under the examined measure is in fact the partner. Results can be compared to other standard measures: The number of photos in which u appear with v. The total number of times that u has viewed v s profile page in the previous 90 days.

43 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 1

44 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 1 When the user v who scores highest under one of these measures is not the partner of u, what role does v play among u s network neighbors?

45 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 1 When the user v who scores highest under one of these measures is not the partner of u, what role does v play among u s network neighbors? v is often a family member of u.

46 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 2 Let us consider dispersion measures based on other definitions of d v : d v (s, t) = 1 when s and t are at least r hops apart in G u \ {u, v}, and d v (s, t) = 0 otherwise.

47 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 2 Let us consider dispersion measures based on other definitions of d v : d v (s, t) = 1 when s and t are at least r hops apart in G u \ {u, v}, and d v (s, t) = 0 otherwise. d v (s, t) = 1 if s and t belong to different connected components of G u \ {u, v}, and d v (s, t) = 0 otherwise.

48 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 2 Let us consider dispersion measures based on other definitions of d v : d v (s, t) = 1 when s and t are at least r hops apart in G u \ {u, v}, and d v (s, t) = 0 otherwise. d v (s, t) = 1 if s and t belong to different connected components of G u \ {u, v}, and d v (s, t) = 0 otherwise. d v (s, t) = 1 if and only if s and t belong to different communities based on Louvain method.

49 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Take 2

50 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Time and Space An important source of variation among users is in the size of their network neighborhoods and the amount of time since they joined Facebook. Time effects: The neighborhood s complexity. The extent to which the network reflects the user s off-line relationships.

51 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Time and Space

52 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space Evaluation - Time and Space Why the interaction features performance increases as a function of neighborhood size?

53 Introduction Embeddedness and Evaluation Combining TakeFeatures 1 2 Time and Space 1 Introduction Problem Statement Dataset 2 Embeddedness and Embeddedness 3 Evaluation Take 1 Take 2 Time and Space 4 Combining Features Machine Learning Performance Over Time

54 Introduction Embeddedness and Evaluation Combining Machine Features Learning Machine Learning Performance Over Time Why focus on one aspect of the user s neighborhood? Let s combine information! Structural features: Absolute and normalized dispersion based on six distinct distance functions. Recursive versions using iterations 2 through 7. Interaction features: Number of common photos. Number of profile views over the last 30, 60 and 90 days. Number of messages sent. Etc.

55 Introduction Embeddedness and Evaluation Combining Machine Features Learning Machine Learning Performance Over Time The combination of structural and interaction features improves the accuracy.

56 Introduction Embeddedness and Evaluation Combining Machine Features Learning Machine Learning Performance Over Time Recall our focus is on partner detection, given the user is in a romantic relation. Can we determine whether or not a user is single? Learn demographic features (age, gender and country). Include structural features. Train a classifier.

57 Introduction Embeddedness and Evaluation Combining Machine Features Learning Time Dependency Performance Over Time Notice the decrease of profile viewing...

58 Introduction Embeddedness and Evaluation Combining Machine Features Learning Time Dependency Performance Over Time Say a s romantic partner is b. Is the dispersion of their link correlated with their transition probability over a 60 day period?

59 Introduction Embeddedness and Evaluation Combining Machine Features Learning Time Dependency Performance Over Time Relationships on which recursive dispersion fails to correctly identify the partner are significantly more likely to transition to single status over a 60 day period.

60 Introduction Embeddedness and Evaluation Combining Machine Features Learning Conclusions Performance Over Time Understanding the structural roles of significant people in on-line social network neighborhoods is a broad question that requires a combination of different approaches.

61 Introduction Embeddedness and Evaluation Combining Machine Features Learning Conclusions Performance Over Time Understanding the structural roles of significant people in on-line social network neighborhoods is a broad question that requires a combination of different approaches. provides a powerful method for recognizing the structural positions occupied by romantic partners from network data alone.

62 Introduction Embeddedness and Evaluation Combining Machine Features Learning Conclusions Performance Over Time Understanding the structural roles of significant people in on-line social network neighborhoods is a broad question that requires a combination of different approaches. provides a powerful method for recognizing the structural positions occupied by romantic partners from network data alone. Romantic relations connect us to people who belong to multiple parts of our social neighborhood, producing a set of shared friends that is not simply large but also diverse.

63 Introduction Embeddedness and Evaluation Combining Machine Features Learning Performance Over Time