PRIVACY-PRESERVING RELEASES OF SOCIAL NETWORKS

Chih-Hua Tai

Dept. of CSIE, National Taipei University, New Taipei City, Taiwan

DATA MINING

The primary task in data mining: development of models about aggregated data. Finding frequent patterns Finding rules

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FINDING PATTERNS

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FINDING RULES

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DATA MINING VS. PRIVACY

The primary task in data mining: development of models about aggregated data. Finding frequent patterns Finding rules

Can we develop accurate models without access to precise information in individual data records? Why?

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PRIVACY ISSUES IN DATA

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PRIVACY ISSUES IN DATA

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PRIVACY ISSUES IN DATA

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DATA MINING AND PRIVACY

The primary task in data mining: development of models about aggregated data.

Can we develop accurate models without access to precise information in individual data records?

Answer: yes, by randomization. R. Agrawal, R. Srikant “Privacy Preserving Data

Mining,” SIGMOD 2000 How about the data utility?

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DATA MINING VS. SOCIAL NETWORKS

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Attributes: Name, Salary, …

Links: Friends, Neighborhood, …

Communities: Interests, Activities, …

PRIVACY ISSUES ON SOCIAL NETWORKS

Personal information leaked, even if the vertex identifies are hidden…

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Many information can be used to re-associate the vertex with its identity.

Vertex degree: k-degree anonymity , …

Neighborhood configuration: k-neighborhood anonymity, k-automorphism anonymity, k-isomorphism anonymity, grouping-and- collapsing, …

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C.-H. Tai, P. S. Yu, D.-N. Yang and M.-S. Chen, "Privacy-preserving Social Network Publication Against Friendship Attacks," In KDD, 2011.

FRIENDSHIP ATTACK

Still there are another type of information for vertex re-identification – friendship attack

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FRIENDSHIP ATTACK

Given a target individual A and the degree pair information D2 = (d1,d2), a friendship attack (D2,A) exploits D2 to identify a vertex v1 corresponding to A in a published social network where v1 connects to another vertex v2 with the degree pair (dv1

,dv2) = (d1,d2).

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10

1 2 3

4 5

Alice

6 7

9

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Ex 1. Assume that an attacker knows that Alice has 3 connections, Bob has 2 connections, and Alice and Bob are friends. The attacker identifies v9 as Alice with 100% confidence.

FRIENDSHIP ATTACK

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In DBLP data set, the percentages of vertices that can be re-identified with a probability larger than 1/k by degree and friendship attacks.

Original Social Network

k-degree anonymized Social Network

kDegree Attack Friendship Attack Friendship Attack

5 0.28% 5.37% 2.89%

10 0.53% 10.69% 4.65%

15 0.73% 14.71% 5.82%

20 0.93% 18.44% 7.23%

NEW PRIVACY MODEL AGAINST FRIENDSHIP ATTACK

k2-degree AnonymityA social network is k2-degree anonymous

if, for every vertex with an incident edge of degree pair (d1,d2), there exist at least k − 1 other vertices, each of which also has an incident edge of the same degree pair.

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10

1 2 3

4 5

6 7

9

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Ex 2. Even with the knowledge (D2,A)=((3,2),Alice), the probability that an attacker can re-identify Alice in the 22-degree anonymous social network is limited to ½.

THE ANONYMIZATION

Problem formulation: Given a graph G(V, E) and an integer k, the problem is to

anonymize G to satisfy k2-degree anonymity such that information distortion is minimized.

The challenges: Any alteration on an edge will affect the degrees of

two vertices.

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GRAPH ANONYMIZATION ALGORITHMS

Integer Programming formulation Obtain the optimal solution with bad scalability

DEgree SEqence ANonymization (DESEAN) Step1. Degree Sequence Anonymization.

- determine the groups of vertices protecting each others

Step2. Privacy Constraint Satisfaction.- eliminate the advantage of knowing friendship information

Step3. Anonymous Degree Realization.- have the vertices in the same group share the same vertex degree 19

Step1. Degree Sequence Anonymization. Cluster vertices with similar degrees and select a

target degree dx for each cluster x s. t. each cluster contains at least k vertices and the weighted degree difference ω Σvϵx (dx - d v) + (1 − ω) Σvϵx (d v - dx) is as small as possible.

ALGORITHM DESEAN

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10

1 2 3

4 5

6 7

9

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Ex 3. Given k = 2 and ω = 0.5.

ALGORITHM DESEAN

Step1. Degree Sequence Anonymization. Cluster vertices with similar degrees and select a

target degree dx for each cluster x s. t. each cluster contains at least k vertices and the weighted degree difference ω Σvϵx (dx - d v) + (1 − ω) Σvϵx (d v - dx) is as small as possible.

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1 2 3

4 5

6 7

9

8

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1 2 3

4 5

6 7

9

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Ex 3. Given k = 2 and ω = 0.5.

Step2. Privacy Constraint Satisfaction. Add or delete edges between clusters to ensure

that, for each pair of clusters (x,y), the number of vertices in x directly connected to the vertices in y is either zero or not less than k.

ALGORITHM DESEAN

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10

1 2 3

4 5

6 7

9

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Ex 3. Given k = 2 and ω = 0.5.

Step2. Privacy Constraint Satisfaction. Add or delete edges between clusters to ensure

that, for each pair of clusters (x,y), the number of vertices in x directly connected to the vertices in y is either zero or not less than k.

ALGORITHM DESEAN

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10

1 2 3

4 5

6 7

9

8

10

1 2 3

4 5

6 7

9

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Ex 3. Given k = 2 and ω = 0.5.

Step3. Anonymous Degree Realization. Adjust edges in G s. t. the vertices in each

cluster x meet the target degree dx selected in Step 1.

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1 2 3

4 5

6 7

9

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ALGORITHM DESEAN

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Ex 3. Given k = 2 and ω = 0.5.

Step3. Anonymous Degree Realization. Adjust edges in G s. t. the vertices in each

cluster x meet the target degree dx selected in Step 1.

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1 2 3

4 5

6 7

9

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1 2 3

4 5

6 7

9

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ALGORITHM DESEAN

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Ex 3. Given k = 2 and ω = 0.5.

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C.-H. Tai, P. S. Yu, D.-N. Yang, and M.-S. Chen, ”Structural diversity for privacy in publishing social networks,” In SDM, 2011.

COMMUNITY IDENTIFICATION

Vertex identification is considered to be an important privacy issue in publishing social networks. ◦ k-degree anonymity, k-neighborhood anonymity, …

In addition to a vertex identity, each individual is also associated with a community identity. ◦ Could be used to infer the political party affiliation or disease

information sensitive to the public.◦ Is a kind of structural information

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COMMUNITY IDENTIFICATION

Community information is explicitly given:

Ex.

Alice knows recently… Bob is sick Bob participates in this social network Bob makes 5 friends. (vertex degree attack)

Bob has AIDS!

AIDS Com. SLE Com.

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COMMUNITY IDENTIFICATION

Community information is not given:

Ex.

Alice knows Bob participates in this social network and has 5 friends. (vertex degree attack)

Alice can know the approximation of Bob’s neighborhood.

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COMMUNITY IDENTIFICATION

% of vertices violating k-structural diversity◦ (a) DBLP◦ (b) ca-CondMat

k-degree anonymization is insufficient 30

COMMUNITY IDENTIFICATION

structural diversity◦ (a) original DBLP◦ (b) 10-degree anonymized DBLP

Vertices with large degrees appear in a small set of communities 31

NEW PRIVACY MODEL AGAINST COMMUNITY IDENTIFICATION

k-Structural Diversity To protect against vertex degree attack, for each vertex, there

should be other vertices with the same degree located in at least k-1 other communities.

If a graph satisfies k-structural diversity, then it also satisfies k-degree anonymity.

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THE ANONYMIZATION

Problem formulation: Given a graph G(V, E, C) and an integer k, 1 k |C|, the ≦ ≦

problem is to anonymize G to satisfy k-structural diversity such that information distortion is minimized.

The challenges: How to preserve community structures, even in

the implicit cases, while preserving privacy.

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PROBLEM FORMULATION

Operation Adding Edge ◦ Connect two vertices belonging to the same community.◦ Can avoid destroying the communities.

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PROCEDURE MERGENCE

◦ To protect a vertex v in an existing anonymous group, in which all the vertices have the same degree d

Com. 1

v

Com. 2

Com. 335

PROCEDURE MERGENCE

◦ To protect a vertex v in an existing anonymous group, in which all the vertices have the same degree d

Com. 1

v

Com. 2

Com. 336

PROCEDURE CREATION

To create a new anonymous group for a vertex v, such that all the vertices in the group locate in at least k difference communities and have the same degree as v

Com. 1 Com. 2 Com. 3

v

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PROCEDURE CREATION

To create a new anonymous group for a vertex v, such that all the vertices in the group locate in at least k difference communities and have the same degree as v

Com. 1 Com. 2 Com. 3

v

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THE EDGE-REDITECTION MECHANISM

◦ Is defined on w, v, x in the same community w: an anonymized vertex v and x : two not-yet-anonymized vertices

◦ Is to replace the edge (w, v) with the edge (w, x)

v w

v w

x

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THE EDGE-REDITECTION MECHANISM

By mergence

v w

Com. 1 Com. 2

Com. 3

Q. Why needs the Edge-Reditection mechanism?

By mergence

v w

Com. 1 Com. 2

Com. 3

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THE EDGE-REDITECTION MECHANISM

By creation

Com. 1

Com. 2 Com. 3

v w

Q. Why needs the Edge-Reditection mechanism?

By creation

Com. 1

Com. 2 Com. 3

v w

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ALGORITHM EDGECONNECT (EC)

Procedures Mergence and Creation◦ Let Rv be the set of edges that could be redirected away from v

The Edge-Reditection mechanism

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PROBLEM FORMULATION

Operation Adding Edge ◦ Connect two vertices belonging to the same community.◦ Can avoid destroying the communities.

Operation Splitting Vertex◦ Replace a vertex v with a set of substitute vertices, such that

each substitute vertex is connected with at least one edge incident to v originally.

◦ Each substitute vertex presents partial truth of the vertex v.

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PROCEDURE CREATIONBYSPLIT

Split a set of vertices, including v, to create a new anonymous group

Com. 1 Com. 2

Com. 3

v

Com. 1 Com. 2

Com. 3

v1v2

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PROCEDURE MERGEBYSPLIT

Split v into a set of substitute vertices s.t. each substitute vertex is protected in some existing anonymous group

Com. 1 Com. 2

Com. 3 v

v1

v2

v3

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C.-H. Tai, P.-J. Tseng, P. S. Yu and M.-S. Chen, "Identities Anonymization in Dynamic Social Networks," In ICDM-11, 2011.

THE PROBLEM IN DYNAMIC SCENARIOS…

A dynamic social network will be sequentially released.

An attacker can monitor a victim for a period w.

Therefore, the adversary knowledge includes: The releases G t-w+1,

G t-w+2, …, G t during w A degree sequence Δv

w=(dvt-

w+1, dv

t-w+2, …, dvt) of a victim v

during w47

G2G1

Ex. John has two friends at time 1, and three friends at time 2.

PRIVACY MODEL: KW-STRUCTURAL DIVERSITY ANONYMITY

Base case of w=1 A group θd, consisting of all

vertices of degree d, is a k-shielding group if there is a vertex subset θ ⊆ θd s. t. (1) |θ |≥ k, and (2) any two vertices u and v in θ,

Cv ∩ Cv = ø, where C is the community identity.

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The adversary knowledge includes: 1. The release

social network G t 2. A degree

sequence Δv

1=(dvt) of a

victim v

Ex. Mary has four friends.

???

G

PRIVACY MODEL: KW-STRUCTURAL DIVERSITY ANONYMITY

Dynamic scenarios of w>1 A consistent group ΘΔ is the set of vertices

that always share the same degree during w.

A consistent group ΘΔ is a k-shielding if

at each time instant t in w, there is a vertex subset Θ t

⊆ ΘΔ s. t. (1) |Θ t |≥ k, and (2) any two vertices u and v in Θ t, Cv

t ∩ Cv t = ø, where

C t is the community identity at time t.

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The adversary knowledge of includes: 1. The releases G t-

w+1, G t-w+2, …, G t during w

2. A degree sequence Δv

w=(dvt-w+1, dv

t-

w+2, …, dvt) of a

victim v during w

…

THE ANONYMIZATION

Problem formulation: Suppose that every vertex in a series of sequential

releases G t-w+1, G t-w+2, …, G t-1 is protected. Given G t-w+1, G t-w+2, …, G t-1 and k, anonymize the

current social network Gt s. t. every vertex is protected in a k-shielding consistent group.

The challenges: The anonymization is depended on not only the

current social network but also previous w-1 releases.

Searching through all the w-1 releases to eliminate privacy leak is time consuming.

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ANONYMIZATION ALGORITHM

Construct CS (Clustering Sequence) -Table to prevent the search through w graphs.

CS-Table Summary the vertex information in w-1 previous

releases. Fetch v’ info. in w graphs without scanning the graphs.

According to the degree sequence during w, sort the vertices in hierarchical clustering manner. Vertices in the same k-consistent shielding group are close in CS-Table. CS-Table can be incrementally updated.

According to the vertex ranking in CS-Table, anonymize each vertex to be protected.

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THANK YOU~!