Findingthe&Most&Appropriate&Auxiliary&Data&& …...ThetruenodeOverlap(isthefractionofthe nodesinF...
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The true node Overlap is the fraction of the nodes in F aux that appear in F anon Finding the Most Appropriate Auxiliary Data for Social Graph Deanonymization Priya Govindan* Sucheta Soundarajan Tina EliassiRad * [email protected] • Selecting the most appropriate auxiliary data for deanonymization of F anon reduces to the problem of predicting the amount of node overlap between F anon and F aux • Given no additional info, an adversary can identify graphs with low Overlap with F anon • Given labels for some of the nodes, an adversary can predict the Overlap quite well. If also given some seed matches, an adversary can estimate the Lookalikes for the given graph pair • Given labels for one graph, an adversary can learn to predict Overlap in another graph. 1. No link structure 2. Nodes have many lookalikes (i.e., similar structural features) 3. DifNicult to distinguish between nodes in F anon that are present in F aux and those that are absent in F aux How can an adversary select the most appropriate auxiliary graph to breach the privacy of individuals in an anonymized graph? The features for each node in F anon are: 1. Node’s degree 2. Avg. degree of node’s neighbors 3. Node’s clustering coefNicient 4. Avg. clustering coefNicient of node’s neighbors 5. # of edges between node’s neighbors 6. # of nodes adjacent to node’s neighbors 7. # of edges outgoing from the node’s neighbors Given: F anon , F aux , matches for m% nodes Predicted Overlap = ratio of predicted ‘present’ labels, by learning a classiNier on labeled nodes Predicted Lookalikes = Average lookalikes of seed matches Given: F anon , F1 aux , F2 aux , labels on all nodes of F1 aux A classiNier is trained on the labels of F1 aux ; is used to predict labels on the nodes of F2 aux Predicted Overlap between F anon and F2 aux = ratio of predicted ‘present’ labels, by the classiNier Lookalikes for a node x in F aux is the number of nodes in F anon that are at least as similar to x, as its matching node x’ in F anon Goal of the adversary Find an auxiliary graph G aux , whose structural feature matrix (F aux ) has high Overlap and low Lookalikes with F anon Lookalikes for a graphpair is the average lookalikes of nodes in F aux , normalized by size of F anon Given: F anon , F aux , and labels (present/absent) for k nodes selected uniformly at random Predicted Overlap = ratio of `present’ labels in k seeds Given: F anon and F aux Predicted !"#$%&' = !"#$%&% !"#$%&' × 1 − !"#$%&&" !"#$%&'( ! !"#" , !"#$%&'( ! !"# Case 2: Adversary has labels/ matches for some nodes Case 3: Adversary has labels on another auxiliary graph Case 1: Adversary has no side info DADNANEEOEENE1 2 3 n Nodes Local and Egonet based Features Structural Feature Matrix of the Anonymized Graph Organization Owns Releases Social Graph Anonymize Anonymized graph F anon When the predicted nodeoverlap is low (< 0.5), then the true nodeoverlap is also low (< 0.2) Given 10 seedlabels chosen uniformly at random, overlap can be predicted quite well (MAE = 0.03 ) Given 10% seedmatches, overlap can be predicted very accurately (~100%) when the predicted lookalikes is < 0.1 Most values lie on the diagonal (with RMSE = 0.14 from the 45degree line), thus transferlearning predictions are deemed good estimates of the true overlap where the Maximum Overlap is the minimum of |F anon | and |F aux |, divided by |F aux |
Transcript of Findingthe&Most&Appropriate&Auxiliary&Data&& …...ThetruenodeOverlap(isthefractionofthe nodesinF...
The true node Overlap is the fraction of the nodes in Faux that appear in Fanon
Finding the Most Appropriate Auxiliary Data for Social Graph Deanonymization Priya Govindan* Sucheta Soundarajan Tina Eliassi-‐Rad
• Selecting the most appropriate auxiliary data for deanonymization of Fanon reduces to the problem of predicting the amount of node-‐overlap between Fanon and Faux
• Given no additional info, an adversary can identify graphs with low Overlap with Fanon
• Given labels for some of the nodes, an adversary can predict the Overlap quite well. If also given some seed matches, an adversary can estimate the Lookalikes for the given graph pair
• Given labels for one graph, an adversary can learn to predict Overlap in another graph.
1. No link structure
2. Nodes have many lookalikes (i.e., similar structural features)
3. DifNicult to distinguish between nodes in Fanon that are present in Faux and those that are absent in Faux
How can an adversary select the most appropriate auxiliary graph to breach the privacy of individuals in an anonymized graph?
The features for each node in Fanon are: 1. Node’s degree 2. Avg. degree of node’s neighbors 3. Node’s clustering coefNicient 4. Avg. clustering coefNicient of node’s neighbors
5. # of edges between node’s neighbors 6. # of nodes adjacent to node’s neighbors 7. # of edges outgoing from the node’s neighbors
Given: Fanon , Faux , matches for m% nodes
Predicted Overlap = ratio of predicted ‘present’ labels, by learning a classiNier on labeled nodes
Predicted Lookalikes = Average lookalikes of seed matches
Given: Fanon , F1aux , F2aux , labels on all nodes of F1aux A classiNier is trained on the labels of F1aux; is used to predict labels on the nodes of F2aux
Predicted Overlap between Fanon and F2aux = ratio of predicted ‘present’ labels, by the classiNier
Lookalikes for a node x in Faux is the number of nodes in Fanon that are at least as similar to x, as its matching node x’ in Fanon
Goal of the adversary Find an auxiliary graph Gaux, whose structural feature matrix (Faux) has high Overlap and low Lookalikes with Fanon
Lookalikes for a graph-‐pair is the average lookalikes of nodes in Faux, normalized by size of Fanon
Given: Fanon , Faux , and labels (present/absent) for k nodes selected uniformly at random
Predicted Overlap = ratio of `present’ labels in k seeds
Given: Fanon and Faux
Predicted!!"#$%&' = !"#$%&%!!"#$%&'!×!1− !"#$%&&"! !"#$%&'( !!"#" ,!"#$%&'( !!"# !
Case 2: Adversary has labels/matches for some nodes
Case 3: Adversary has labels on another auxiliary graph
Case 1: Adversary has no side info D egree Clust. Coeff.
Avg Degree of N brs
Avg Clust. Coeff. of N brs
# Edges in E gonet
# Outgoing Edges from E gonet
# Nbrs of E gonet
1 2 3 … … … … … … … … … … … … … … … … … … … … … … … … … n
Structural Feature Table, F
Nodes
Local and Egonet based Features
Structural Feature Matrix of the Anonymized Graph
Organization
Owns
Releases
Social Graph
Anonym
ize
Anonymized graph
Fanon
When the predicted node-‐overlap is low (< 0.5), then the true node-‐overlap is also low (< 0.2)
Given 10 seed-‐labels chosen uniformly at random, overlap can be predicted quite well (MAE = 0.03 )
Given 10% seed-‐matches, overlap can be predicted very accurately (~100%) when the predicted lookalikes is < 0.1
Most values lie on the diagonal (with RMSE = 0.14 from the 45-‐degree line), thus transfer-‐learning predictions are deemed good estimates of the true overlap
where the Maximum Overlap is the minimum of |Fanon| and |Faux|, divided by |Faux|
