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Strategic Network Formation
in a Location-Based Social Network:
A Topic Modeling Approach
Gene Moo LeePh.D. Candidate
University of Texas at Austin
Joint work with Liangfei Qiu and Andrew Whinston
Workshop on Information Technology and Systems (WITS)
December 18, 2014
WITS 2014, Auckland, New Zealand
Social networks shape behaviours
• Social networks shape individual behaviours
• Product adoption, media consumption, etc.
• Social networks are going mobile
• Facebook 68%, Twitter 86%, Instagram 98%
• Location-based social network (LBSN)
• Sharing locations with friends
2
WITS 2014, Auckland, New Zealand
Network formation in LBSN
3
• RQ1: How mobile users form friendship?
• Structural model of strategic network formation
• RQ2: How to measure mobile user similarity?
• Novel dyadic user similarity with topic models
• RQ3: How each factor plays role empirically?
• Empirical analysis with large-scale LBSN data
WITS 2014, Auckland, New Zealand
Roadmap
1. Model
2. User similarity
3. Data
4. Empirical analysis
5. Conclusion and future directions
4
WITS 2014, Auckland, New Zealand
Structural model of network formation
• Network formation procedure
1. A pair of users meet for linking opportunity
2. Each party checks the marginal utility by forming the link
3. If both parties see positive utilities, then a link is formed
• User i’s utility of forming a link with j
5
Individual characteristics
Dyadic similarity
WITS 2014, Auckland, New Zealand
User similarity in LBSN
1. User profiles: unstructured text
2. Tweets: unstructured text
3. Geography: distance between home locations
4. Common mobility: normalized co-check-in
• Challenge: how to extract similarity from unstructured texts
• Latent Dirichlet allocation (LDA) to extract “topics”
6
WITS 2014, Auckland, New Zealand 7
Business topic modelPer-word
topic
assignment
Observed
biography,
tweets
Bio/tweet
topicsPer-user
topics distribution
Topic
parameter
Proportions
parameter
K: # topics
D: # users
N: # words
WITS 2014, Auckland, New Zealand
LDA and user similarity
• Inputs: LBSN users’ text info (bio and tweets)
• LDA outputs:
• (1) topics in the whole corpus
• (2) topic vectors for each user
• Dyadic user similarity based on topic vectors
• Cosine similarity, Kullback–Leibler divergence
8
WITS 2014, Auckland, New Zealand
Gowalla data• #2 location-based social network in 2010~2011
• Acquired by Facebook in 2012
• Data
• Time: Jan 2009 ~ Jan 2012 (3 years)
• 285,306 users
• 3,101,620 spots
• 35,691,059 check-ins
• Social network snapshot in May 2011
• Tweets
• 100,946 users with Twitter
• 200 tweets from 79,979 users
9
WITS 2014, Auckland, New Zealand
Gowalla data
10
Check-in locations
Individual user’s
mobility trajectory
We are here!
WITS 2014, Auckland, New Zealand
Topic models from bio and tweets
11
Biography
Tweet
Mobile
Family
Life
Social
Texas
Bitcoin
Music
WITS 2014, Auckland, New Zealand
Topic model and friendship
12
Biography topic #187:
open, source, advocate, software
Tweet topic #17:
code, web, javascript
WITS 2014, Auckland, New Zealand
Model estimation
• User sampling by hometowns
• Utility function of each match
• Maximum Likelihood Estimation (MLE)
• Given the observed social graph G
13
Formed links Unrealized links
WITS 2014, Auckland, New Zealand
Empirical analysis: Main results
14
• Each similarity variable has expected effects
• (+): co_checkin, bio_topic_sim
• (-) : hometown_distance
WITS 2014, Auckland, New Zealand 15
Empirical analysis: Robust check
WITS 2014, Auckland, New Zealand
Counterfactual analysis
• Structural model enables counterfactual analysis
• No homophily
• 20% decrease in link formation
16
WITS 2014, Auckland, New Zealand
Summary and future directions
1. Structural model for strategic network formation in LBSN
2. Propose TM-based user similarity measures
3. Find an evidence on homophily effect
• Directions:
• Consider network structure for linking opportunity
(meeting) sequence
• Multiple social network snapshots
• Simultaneous effects between check-ins and
friendships
17
WITS 2014, Auckland, New Zealand
Social networks going mobile
• Mobile usages: Facebook 68%, Twitter 86%, Instagram 98%,
LinkedIn 26%, Snapchat 100%
• Location is an important factor in mobile social networks (LBSN)
• In this work, we study network formation in LBSN
19
WITS 2014, Auckland, New Zealand
Literature
• Matching theory (CS, Math, Econ)
• matching in graph [MS, FoCS’04]
• Link prediction in complex networks (CS, Physics)
• social networks [LK, CIKM’03], biological networks [Yu+, Science’08]
• Empirical matching (Econ)
• kidney exchange [Roth+, QJE’04], medical interns [Roth, JPE’84]
• M&A analysis (Finance)
• 12 deals [GE, ASQ’04], geography [E+, JF’12] [KL, AEJ’13], social
networks [H+, JF’07] [C+, JF’10]
20
WITS 2014, Auckland, New Zealand
References• M&A analysis
• M. Graebner, K. Eisenhardt, The Seller’s Side of the Story: Acquisition as Courtship and Governance as Syndicate in
Entrepreneurial Firms, Administrative Science Quarterly, 2004
• Link prediction
• D. Liben-Nowell, J. Kleinberg., The Link Prediction Problem for Social Networks. Proc. 12th International Conference on
Information and Knowledge Management (CIKM), 2003.
• H. Yu, et al., High-Quality Binary Protein Interaction Map of the Yeast Interactome Network, Science, 2008
• Matching problem
• M. Mucha, P. Sankowski, Maximum Matchings via Gaussian Elimination, Proc. of Foundations of Computer Science
(FOCS), 2004
• A. Roth, T. Sonmez, M Unver, Kidney Exchange, Quarterly Journal of Economics, 2004
• A. E. Roth, The college admissions problem is not equivalent to the marriage problem, Journal of Economic Theory, 1985
• A. E. Roth, The evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory, Journal
of Political Economy, 1984
• Innovation and entrepreneurship
a. W. Kerr, Breakthrough inventions and migrating clusters of innovation, Journal of Urban Economics, 2010
2. Topic modeling
a. D. Blei, A. Ng, M. Jordan, Latent Dirichlet allocation, Journal of Machine Learning Research, 2003
21
WITS 2014, Auckland, New Zealand
References• Random graph
• P. Erdos, A. Renyi, On random graphs, Publicationes Mathematicae, 1959
• M. Newman, The structure and function of complex networks, SIAM Reviews, 2003
• G. Robins, P. Pattison, Y. Kalish, D. Lusher, An introduction to exponential random graph models for social networks, Social
Networks, 2007
• Business
• A. Haigu, D. Yoffie, The New Patent Intermediaries: Platforms, Defensive Aggregators, and Super-Aggregators, Journal of
Economic Perspectives, 2003
• Geography
• I. Erel, R. Liao, M. Weisbach, Determinants of Cross-Border Mergers and Acquisitions, Journal of Finance, 2012
• A. Kalnins, F. Lafontaine, Too Far Away? The Effect of Distance to Headquarters on Business Establishment Performance,
American Economic Journal: Microeconomics, 2013
• Social links
• L. Cohen, A. Frazzini, C. Malloy, Sell-Side School Ties, Journal of Finance, 2010
• Y. Hochberg, A. Ljungqvist, Y. Liu, Whom You Know Matters: Venture Capital Networks and Investment Performance, Journal
of Finance, 2007
• M. Conyon, M. Muldoon, The Small World of Corporate Boards, Journal of Business Finance & Accounting, 2006
• Two-sided markets
• G. Weyl, A Price Theory of Multi-Sided Platforms, American Economic Review, 2010
• A. Haigu, Two-Sided Platforms: Product Variety and Pricing Structures, Journal of Economics & Management Strategy, 200922