SNAMS-2019

Slides for SNAMS 2019

Transcript

1. Simmelian ties on Twitter: empirical analysis and prediction IsaInuwa-Dutse· MarkLiptrott· YannisKorkontzelos Department of Computer Science March ,
2. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Outline Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion /
3. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion The eccentricity of Twitter connections challenges mining tasks e.g. communitydetection & contentveracity (a) dyads (b) RT and hashtag (c) @mention /
4. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion The eccentricity of Twitter connections challenges mining tasks e.g. communitydetection & contentveracity (a) dyads (b) RT and hashtag (c) @mention (d) Relative proportion Figure: Connection types on Twitter /
5. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Di ficult to keep track of socially cohesive groups on Twitter ... the large network size a fects user’s ability to maintain a cohesive social relationship Twitter: ≈ M daily users & ≈ M content items www.omnicoreagency.com/twitter-statistics /
6. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Di ficult to keep track of socially cohesive groups on Twitter ... the large network size a fects user’s ability to maintain a cohesive social relationship Twitter: ≈ M daily users & ≈ M content items ... inverse relationship between socialcohesion and networksize [ ] Figure: Classification of social groups and the degree of cohesiveness www.omnicoreagency.com/twitter-statistics /
7. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Level of trust is stronger among cliques[ ] a group of nodes with reciprocal ties will be more helpful in mining tasks /
8. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Level of trust is stronger among cliques[ ] a group of nodes with reciprocal ties will be more helpful in mining tasks cognitivebalancetheory: strong ties in a small group prevent unethical behaviour[ ] /
9. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Level of trust is stronger among cliques[ ] a group of nodes with reciprocal ties will be more helpful in mining tasks cognitivebalancetheory: strong ties in a small group prevent unethical behaviour[ ] ... and socialhomophily [ ] /
10. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Level of trust is stronger among cliques[ ] a group of nodes with reciprocal ties will be more helpful in mining tasks cognitivebalancetheory: strong ties in a small group prevent unethical behaviour[ ] ... and socialhomophily [ ] focus: Simmeliantie [ ], a strong social relationship within groupsofthreeormore synonymous to transitivity: people become friends with a friend-of-a-friend more easily[ ] /
11. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Basic units of structural relationships – dyadic and transitive ties given the sets of nodes a, b, c, ...., n ∈ V and edges e , e , ...en ∈ E V, E ∈ D our target is to find the likelihood of reciprocity p(Ra,b ) between any pair of nodes /
12. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Basic units of structural relationships – dyadic and transitive ties given the sets of nodes a, b, c, ...., n ∈ V and edges e , e , ...en ∈ E V, E ∈ D our target is to find the likelihood of reciprocity p(Ra,b ) between any pair of nodes we collected and analysed user profiles from m accounts (Table ) Table: Dataset Summary. C: Category; S: Seed Size; V: Visited users; P: Pairwise ties; T: Transitive ties; D: Search duration C S V P T D (min.) :verified , , , – , :verified , , , , – , :verified , , , , , :unverified , , , – , :unverified , , , , – , :unverified , , , , , ego-Twitter , – – – – /
13. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion User-centric attributes to estimate likelihood of reciprocity propose a model to predict ties between users /
14. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion User-centric attributes to estimate likelihood of reciprocity propose a model to predict ties between users modelled as functions of easily accessible features f ∈ X Figure: (a) Possible triads and (b) relevant features /
15. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Distribution of ties and relevant metrics in the data For each user a followed by m users: a b = , if there is a reciprocal tie, , between a and b ∈ m a b = , otherwise /
16. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Distribution of ties and relevant metrics in the data For each user a followed by m users: a b = , if there is a reciprocal tie, , between a and b ∈ m a b = , otherwise Usercategory: a higher proportion of reciprocal ties exists in the unverified users category /
17. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion ECDF of relevant ties x axis: the measuredquantity y axis: a fraction of the data (%) Figure: ECDF of relevant ties /
18. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Observations on the likelihood of reciprocity a user’s network size is likely to grow if the user: is verified has manyfollowers /
19. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Observations on the likelihood of reciprocity a user’s network size is likely to grow if the user: is verified has manyfollowers the likelihoodofreciprocity is high if: /
20. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Observations on the likelihood of reciprocity a user’s network size is likely to grow if the user: is verified has manyfollowers the likelihoodofreciprocity is high if: the user is unverified has a relatively large network /
21. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Observations on the likelihood of reciprocity a user’s network size is likely to grow if the user: is verified has manyfollowers the likelihoodofreciprocity is high if: the user is unverified has a relatively large network unverifiedusers are more likely to reciprocate a followership /
22. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Observations on the likelihood of reciprocity a user’s network size is likely to grow if the user: is verified has manyfollowers the likelihoodofreciprocity is high if: the user is unverified has a relatively large network unverifiedusers are more likely to reciprocate a followership users with large networks (> K) have a low proportion of reciprocated ties /
23. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Likelihood of reciprocity and profile attributes Figure: The e fect of user’s attributes in enabling reciprocal ties /
24. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Bayesian process of simulating the real data and making inference why? Due to the rarity of transitiveties /
25. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Bayesian process of simulating the real data and making inference why? Due to the rarity of transitiveties Given a set of nodes X, Bayesian analysis is useful to estimate: mean reciprocity, mean values for features such as indegree,outdegree in the ground-truth data /
26. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Bayesian process of simulating the real data and making inference why? Due to the rarity of transitiveties Given a set of nodes X, Bayesian analysis is useful to estimate: mean reciprocity, mean values for features such as indegree,outdegree in the ground-truth data we use the information represented into features to propose a prediction model reciprocitye fect: to understand why some users have reciprocated ties, and some not ... we propose a generative model to improve the prediction of reciprocal ties /
27. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion A Log-linearmodel as a linear combination of the user’s attributes (Eq. ) the model enables the simulation of the observed data D and generate a synthetic version ˆ D indistinguishable from the observed information D yi = βui + γcui + ui ( ) where βui, γcui and ui denote meanreciprocityamongusers, meanreciprocitybetweenusers’ categories and errorterm respectively parameters in Eq. are treated as random variables specified by probability distribution functions p(·) Priorθ andlikelihoodf(y|θ, x)– represent set of variables that are likely to characterise the data informed by previous knowledge about the data we assume θi comes from a probability distribution that describes the individual di ference among users posteriorp(θ|D)orp(θ|y, x) is given as a function of the likelihood and the prior which is simply the evidence in the data based on Bayes’rule. The rule entails updating beliefs about θ given the observed data D /
28. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Likelihood maximisation given the observed data Data sampling and posterior distribution Figure: Sampling results showing the errorterm,indegree and outdegree. Some of the samples are unstable, as evidenced by the perturbations in the results in the second column. /
29. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Reciprocity Prediction: doessimilaritybetweenusers’attributesinducereciprocity? we use attributes of nodes to predict reciprocal tie we focus on easily accessible attributes: Xf , networksize,indegree(ind),outdegree(out), category(cat), thus: {ind, out, cat} ⊂ Xf for a pair of nodes vi, vj, their corresponding features are given by: Xfvi = {indvi , outvi , catvi }, Xfvj = {indvj , outvj , catvj } /
30. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Reciprocity Prediction: doessimilaritybetweenusers’attributesinducereciprocity? we use attributes of nodes to predict reciprocal tie we focus on easily accessible attributes: Xf , networksize,indegree(ind),outdegree(out), category(cat), thus: {ind, out, cat} ⊂ Xf for a pair of nodes vi, vj, their corresponding features are given by: Xfvi = {indvi , outvi , catvi }, Xfvj = {indvj , outvj , catvj } ... ratio of corresponding attributes, e.g.indvi indvj ∈ R ∀f ∈ Xfvi,vj ... if the ration lies [ . , . ], return similarity ( ), else dissimilarity ( ) ... the resulting binaries are used to compute the overall similarity between pairs using JaccardSimilarityCoe ficient,J (Eq. ): J(Xfvi , Xfvj ) = |Xfvi ∩ Xfvj | |Xfvi ∪ Xfvj | ( ) /
31. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Each prediction is associated with a decision error ... modelled using a probabilisticpreferencemodel or responseprobability response probability capture various scenarios in which an actor is o fered a set of features ... and the decision process is associated with a constant probability of making an error in the choice, tremblinghanderror [ ] thus, the error term vi,vj (Eq. ) is given as a function of the similarity index J(vi, vj ) (Eq. ), between pairs: vi,vj = ζ × ( + log(J(vi, vj ) + ζ)) ( ) ζ corresponds to the constanterrorterm and the final relation is given by: (Eq. ): p(Rvi,vj ) = + exp ϕ ( ) where: ϕ = − log( vi,vj + J(vi, vj )) × ( vi,vj + J(vi, vj )) we use ζ ≥ . and each item in the predicted ties, κ, satisfies (Eq. ) /
32. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Eq. enables the computation of the probability of reciprocity we can identify as many nodes with a high likelihood of establishing reciprocal ties as required adding a layer of social cohesion related to community detection /
33. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Eq. enables the computation of the probability of reciprocity we can identify as many nodes with a high likelihood of establishing reciprocal ties as required adding a layer of social cohesion related to community detection The likelihood of a reciprocal tie between any pair of users: L(Rvi,vj ) = − f∈χs ( − p(Rvi,vj )) ( ) Defines a generative process where p(Rvi,vj ) is the marginal reciprocity e fect of each feature f ∈ Xf /
34. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Utility of Simmelian ties Content veracity: Simmelian ties represent strong relationships, vital in preventing unethical behaviours [ , ] using Simmelian ties allows to enhance the quality of interactions on Twitter We use the term hop-skippers á la [ ] /
35. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Utility of Simmelian ties Content veracity: Simmelian ties represent strong relationships, vital in preventing unethical behaviours [ , ] using Simmelian ties allows to enhance the quality of interactions on Twitter information di fusion: ... some nodes act as hop-skippers , i.e. users with many reciprocal ties they connecting disparate community parts We use the term hop-skippers á la [ ] /
36. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Hop-skippers are helpful in community detection Figure: An Example of users with reciprocated ties /
37. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Enhancing community detection clustering using a collection of nodes with Simmelian ties – ground-truth vs. predicted we use two state-of-the-art community detection algorithms: Girvan-Newman(G-N) [ ] and LabelPropagation(LP) [ ] /
38. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Community detection result Table: Community detection on three di ferent datasets using two di ferent algorithms: G–N and LP: Girvan–Neuman and Label Propagation #DC: Number of Detected Communities G–N LP Dataset Metric #DC Metric #DC Q NMI Q NMI Ground-truth . . . . ego-Twitter . . . . Predicted . . . . /
39. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Simelian ties empirically quantify and evaluate social relationships challenging mining-relatedtasks – e.g., clustering, information di fusion & content veracity https://github.com/ijdutse/simmelian_ties_on_Twitter /
40. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Simelian ties empirically quantify and evaluate social relationships challenging mining-relatedtasks – e.g., clustering, information di fusion & content veracity Simmelianties exhibit useful behaviour such as: connecting large groups of users we demonstrated how Simmelianties can be leveraged to improve such tasks https://github.com/ijdutse/simmelian_ties_on_Twitter /
41. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Simelian ties empirically quantify and evaluate social relationships challenging mining-relatedtasks – e.g., clustering, information di fusion & content veracity Simmelianties exhibit useful behaviour such as: connecting large groups of users we demonstrated how Simmelianties can be leveraged to improve such tasks we proposed a way to identify Simmelianties on Twitter the data is freely available for further analysis https://github.com/ijdutse/simmelian_ties_on_Twitter /
42. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Reference See the full paper for further information and details about the references: Inuwa-Dutse, I., Liptrott, M. and Korkontzelos, Y., . Simmelian ties on Twitter: empirical analysis and prediction. SixthInternationalConferenceonSocialNetworks Analysis,ManagementandSecurity(SNAMS). IEEE. /
43. Introduction Our Approach Prediction Framework Usefulness of Simmelian ties Conclusion Thank you /