Anonymized social networks

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Anonymized social networks

• Wherefore Art Thou R3579X? Anonymized Social
  Networks, Hidden Patterns, and Structural
  Stenography

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What is a social network?

• A social network occurs anywhere there is social
  interaction between people.
• Examples include Email, instant messaging,
  Facebook, blogging trackbacks, coauthor networks

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Coauthor Network
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Uses of mining social networks

• The structure of social networks can be
  interesting

How are friendships usually structured? Are there
hubs, such as Heather, who connect separate
networks? How many degrees of Kevin Bacon? We
can investigate these questions if we have the
data to mine.
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Email

• For our examples, we will use a network of emails
  sent between users.
• How do we protect users privacy while still
  releasing the data for research?

John
Mary
Vertex
Vertex
Directed edge
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Anonymization Techniques

• Remove any identifiable information, such as name
  and other attributes.
• Randomly rename the vertices

R3579X
R73313
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Anonymization Techniques

• Convert directed edges to undirected edges. This
  increases the complexity and makes it harder to
  attack.

R3579X
R73313
Undirected edge
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Compromising privacy

• Lets say you want to know if two vertices are
  connected onthe graph.
• All the identifying info has beenremoved, so how
  do we do it?

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Active Attacks!

• An active attack involves the adversary creating
  vertices in the graph before the graph is
  released
• The adversary will create edges between the
  vertices in a fashion that it can then recognize
  later on in when the graph is released

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Walk-Based Attack

• We create k new vertices around 2(log n) where n
  is the total number of vertices
• We create new do d1 edges between these new
  vertices and the other ones in the graph
• Then, we randomly create edges between these new
  nodes with independent probability of 1/2

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Algorithm

• Given the graph, how do we find the subgraph that
  we created?
• Create a search tree, pruning the tree based on
  the properties of our subgraph, such as the
  number of degrees of our new vertices

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Are Mary and John connected?
John
Mike
Mary
Zoe
Tom
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Are Mary and John connected?
John
Mike
k1
k5
k2
Mary
k4
k3
Zoe
Tom
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Are Mary and John connected?
John
Mike
k1
k5
k2
Mary
k4
k3
Zoe
Tom
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Are Mary and John connected?
John
Mike
k1
k5
k2
Mary
k4
k3
Zoe
Tom
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Graph is released
ZXCV
ASDF
WER
DFG
UYT
QWER
ASD
HGF
BNM
JKL
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We identify our subgraph
ZXCV
ASDF
k1
k5
k2
QWER
k4
k3
BNM
JKL
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Yes, theyre connected
John
ASDF
k1
k5
k2
Mary
k4
k3
BNM
JKL
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Analysis

• The paper proves that the search tree does not
  grow too large and that the algorithm displays
  good performance
• Also, it proves that the subgraph is unique so
  that we dont identify the wrong subgraph

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Experimental attack

• They simulate an attack on LiveJournal friendship
  links. They create the accounts on the website,
  make the connections, and then crawl the site and
  anonymize the data
• The network has 4.4 million nodes and 77 million
  edges

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Results
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Cut-Based Attack

• Only needs sqrt(log(n)) new nodes to attack the
  graph
• However, its much more computationally intensive
  and less practical in the real world, although it
  takes less nodes

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Cut-based Results
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Passive Attack

• Its a lot like an active attack, except you
  dont create new nodes, instead you collaborate
  with your friends and find yourselves in the
  graph
• However, because you did not specifically target
  certain people, you may not be able to identify
  other people when you find yourself

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Conclusion

• We cannot rely on anonymization to ensure privacy
  in social networks
• Possible improvements add noise to the data by
  adding/removing random edges