Xiaowei Ying, Xintao Wu

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On Link Privacy in Randomizing Social Networks

• Xiaowei Ying, Xintao Wu
• Univ. of North Carolina at Charlotte
• PAKDD-09 April 28, Bangkok, Thailand

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Motivation

• Privacy Preserving Social Network Publishing
• node-anonymization
• cannot guarantee identity/link privacy due to
  subgraph queries.
• Backstrom et al. WWW07, Hay et al. UMass TR07
• edge randomization
• Random Add/Del
• Random Switch
• K-anonymity
• Hay et al. VLDB08, LiuTerzi SIGMOD08, ZhouPei
  ICDE08
• Utility preserving randomization
• Spectral feature preserving YingWu SDM08
  
• Real space feature preserving YingWu SDM09

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Problem Formalization
Add k then del k edges
Prior belief
vs. Posterior belief
YingWu SDM08
This paper
similarity measure value between node i and j
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Polbooks network
Network of US political books (105 nodes, 441
edges, r8) Books about US politics sold by
Amazon.com. Edges represent frequent
co-purchasing of books by the same buyers. Nodes
have been given colors of blue, white, or red to
indicate whether they are "liberal", "neutral",
or "conservative". http//www-personal.umich.edu
/mejn/netdata/
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Proportion of true edges vs. similarity
After randomly add/delete 200 edges (totally 441
edges)
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Similarity measures vs. Link prediction

• Similarity measures
• The number of common neighbors
• Adamic/Adar, the weighted number of common
  neighbors
• Katz, a weighted sum of the number of paths
  connecting two nodes
• Commute time, the expected steps of random walks
  from node i to j and back to i.
• Similarity measures have been exploited in the
  classic link prediction problem.
  Liben-NowellKleinberg CIKM03

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Proportion of true edges vs. similarity
After randomly add/delete 200 edges (totally 441
edges)
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Calculating Posterior belief
Applying Bayes theorem
The attacker does not know this value, what he
can do?
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MLE estimation

• Estimate based on randomized graph

Posterior belief can be calculated by attackers
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Comparison
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Comparison
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Empirical Evaluation

• Attackers Prediction Strategy
• Calculate posterior probability of all node pairs
  
• Choose top t node pairs (with highest post.
  Prob.) as predicted candidate links

For each t, the precision of predictions (k0.5m)
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Empirical Evaluation
The posteriori beliefs with similarity measures
achieve higher precision than that without
exploiting similarity measures. One measure that
is best for one data is not necessarily best for
another data.
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Determining k to guarantee privacy
Data Owner
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Conclusion Future Work

• We have shown that node proximity measures can be
  exploited by attackers to breach link privacy in
  edge add/del randomized networks

• How about other topological properties?

• How about other randomization strategies?
• Privacy vs. utility tradeoff

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Thank You!

• Questions?
• Acknowledgments
• This work was supported in part by U.S. National
  Science Foundation IIS-0546027 and CNS-0831204.

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Utility preserving randomization

• Graph space
• G with the given degree seq.
• Examining proportion of sample graphs with
  existence a link between node i and j
• YingWu,SDM09

Attackers confidence on link (i,j)