Influence Evolution and Competition via a Social Network User’s Timeline Anurag Kumar Joint work with Srinivasan Venkatramanan and Eitan Altman ECE Department, Indian Institute of Science, Bangalore 16 January, 2014 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 1 / 51
Overview Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 2 / 51
Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 3 / 51
Social Networks to Content Networks Popular Online Social Networks (OSN): Facebook, Twitter, Google+ Massive userbase: Facebook ( > 1 billion), Google+ (500million), Twitter (300million) Most OSNs are becoming content-centric Tool for sharing and discovery of new content on the Internet Content: news articles, photos, videos, etc. Users need not own the content Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 4 / 51
Towards Social Advertising Advertising: the main revenue stream for OSNs Traditional online ads: sponsored search slots, featured links, banner ads Consumers are becoming more immune to traditional advertising Ads cannot be shared to our social circle Advertising on online social networks Customized suggestions based on personal/social history Brands have their own pages/accounts on the social network Consumers can share or retweet the promotional content Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 5 / 51
Timelines on Social Networks Facebook, Twitter use a Timeline based social feed Reverse chronological - latest entries pushing out older entries Similar to an email inbox Google+, So.cl(Microsoft) employ parallel timelines Recently, OSNs also sort the entries according to user preference Priority Inbox, Facebook’s EdgeRank, etc. Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 6 / 51
Limited User Attention 80 % of the users’ viewing time is spent on the contents above the fold True for most web experience Timeline: User attention is limited to the top few items Source: http://www.nngroup.com/articles/scrolling-and-attention/ Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 7 / 51
Literature Survey Several studies of information flow in online social networks (OSN) and the “dynamics of collective attention” Wu, Huberman (PNAS 2007): Mutual reinforcement; competition; boredom; show a lognormal distribution for eventual attention Lerman, Ghosh (ICWSM 2010): Empirical study; Twitter and Digg; interpretation in terms of the different network structures Myers, Leskovec (ICDM 2012): Mutual reinforcement or suppression between information cascades Weng, et al. (2012) OSN structure; users’ limited attention; influence of information spreaders; the intrinsic quality of the information Model a limited “screen” and “user memory;” probabilistic model for new information arrival, user focus, and information sharing Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 8 / 51
Literature Survey Several studies of information flow in online social networks (OSN) and the “dynamics of collective attention” Wu, Huberman (PNAS 2007): Mutual reinforcement; competition; boredom; show a lognormal distribution for eventual attention Lerman, Ghosh (ICWSM 2010): Empirical study; Twitter and Digg; interpretation in terms of the different network structures Myers, Leskovec (ICDM 2012): Mutual reinforcement or suppression between information cascades Weng, et al. (2012) OSN structure; users’ limited attention; influence of information spreaders; the intrinsic quality of the information Model a limited “screen” and “user memory;” probabilistic model for new information arrival, user focus, and information sharing We focus on modeling the interaction between publishers on a user’s “timeline” Incorporating issues such as rates of content arrival, influence of content from different sources, decay of influence with time Performance analysis and competition analysis Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 8 / 51
Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 9 / 51
Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 10 / 51
Publisher-Subscriber Model Bipartite graph between C I C content creators and I users Content creators do not consume or share competing ν c content Simplifying assumptions � � c � � i All users follow/subscribe to � � � � M c all content creators N i Absence of content sharing among users: publish-subscribe framework Sufficient to restrict attention Consumers Creators to an isolated user’s timeline Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 11 / 51
User’s Timeline Reverse chronological timeline of size K ( i ) Items of content c generated at points of a Poisson process of rate ν c ν := � c ν c , ν − c := � c ′ � = c ν c ′ N i c |C| 1 � � � � � � � � � � � � � � � � � � � � � � � � λ 1 λ c λ |C| c K ( i ) c K ( i ) − 1 �� �� �� �� �� �� c 2 c 1 User i 's timeline Timeline of a single user i Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 12 / 51
Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 13 / 51
Occupancy Distribution of the Timeline Timeline state, c K ( i ) C ( t ): vector of c K ( i ) − 1 ν − c ν c contents of c K ( i ) � = c c K ( i ) = c c k = c timeline at time t c K ( i ) − 1 c K ( i ) − 1 c 1 c k − 1 = c c k − 1 = c Continuous time Markov chain c new = c old c new = c old 1 2 1 2 (CTMC) Evolution of a single user’s timeline Theorem The stationary probability distribution for the CTMC C ( t ) is given by, ν c k π c = Π K ( i ) k =1 ν where c k is the content at the kth position on the timeline. Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 14 / 51
Expected ic -Busy Period ic-busy period: The duration for which at least one item of c ’s content is present in user i ’s timeline after first entering the head of the timeline α c := ν − c ν Theorem The expected ic-busy period is given by � 1 − α − K ( i ) � E [ T ic ( K ( i ))] = 1 c 1 − α − 1 ν c c Proof sketch: Recursive equation for E [ T ic ( k )], the duration for which content c stays on user i ’s timeline, starting at position k . E [ T ic (0)] = 0 , E [ T ic ( k + 1)] = 1 ν + ν c ν E [ T ic ( K ( i ))] + ν − c ν E [ T ic ( k )] Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 15 / 51
Probability of Finding Content c on a User’s Timeline p ic := The probability of finding content c in user i ’s timeline (fraction of time) A measure of effectiveness in getting the user’s attention Using the expected ic busy period (recalling: α c = ν − c ν ) E [ T ic ( K ( i ))] p ic = E [ T ic ( K ( i ))] + 1 /ν c 1 − α K ( i ) = c Can also be obtained from the occupancy distribution Note that for K ( i ) = 1, p ic = ν c /ν Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 16 / 51
Problem Motivation 1 Finite Timeline Model 2 System Model Analysis of Timeline Occupancy Competition for User Attention Numerical Study Infinite Timeline Model 3 System Model Analysis of Influence Evolution Computation of Expected Influence Competition on the Timeline Conclusion 4 Anurag Kumar (ECE, IISc, Bangalore) Competition over Timeline 16 January, 2014 17 / 51
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