SECURED OUTSOURCING OF FREQUENT ITEMSET MINING

Hana Chih-Hua Tai

Dept. of CSIE, National Taipei University

OUTLINE

Preliminary – Frequent ItemSet Mining Motivation Privacy Model – K-Support Anonymity Algorithm Performance Studies Conclusion

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OUTLINE

Preliminary – Frequent ItemSet Mining Motivation

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FREQUENT ITEMSET MINING (FIM)

Discover what happened frequently

4

Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

When threshold set as 3 (=60%), {wine} and {cigar} are frequent.

When threshold set as 2 (=40%),{wine}, {cigar}, {tea}, {beer}, {wine, cigar}, and {wine, beer} are frequent.

FREQUENT ITEMSET MINING (FIM)

Discover what happened frequently

Frequent itemset mining (FIM)

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

When threshold set as 3 (=60%), {wine} and {cigar} are frequent.

When threshold set as 2 (=40%),{wine}, {cigar}, {tea}, {beer}, {wine, cigar}, and {wine, beer} are frequent.

THE NEEDS OF OUTSOURCING FIM

For those who lack of expertise in FIM and/or computing resources, they have the need of outsourcing the mining tasks to a professional third party.

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Data Owner

Mining Services Provider(Cloud Computing)

THE NEEDS OF OUTSOURCING FIM

For those who lack of expertise in FIM and/or computing resources, they have the need of outsourcing the mining tasks to a professional third party.

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Data Owner

Mining Services Provider(Cloud Computing)

Privacy?

!

THE RISKS OF OUTSOURCING FIM

Encryption/decryption method is believed as the possible solution.

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Mining Services Provider(Cloud Computing)

Data Owner

THE RISKS OF OUTSOURCING FIM

Encryption/decryption method is believed as the possible solution.

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Mining Services Provider(Cloud Computing)

Data OwnerHow to achieve the encryption and decryption?

Privacy protected

Correct mining results

Reasonable overhead

THE RISKS OF OUTSOURCING FIM

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Trans. ID Items

1 a

2 a, c

3 c, d

4 a, b, c

5 a, b, d

Encrypt

THE RISKS OF OUTSOURCING FIM

Top frequency attack Wine is the most frequent item ‘a’ is ‘wine’

Approximate support attack The support of cigar is about 55%~60% ‘c’ is

‘cigar’

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Trans. ID Items

1 a

2 a, c

3 c, d

4 a, b, c

5 a, b, d

Encrypt

THE RISKS OF OUTSOURCING FIM

Top frequency attack Wine is the most frequent item ‘a’ is ‘wine’

Approximate support attack The support of cigar is about 55%~60% ‘c’ is

‘cigar’

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Trans. ID Items

1 a

2 a, c

3 c, d

4 a, b, c

5 a, b, d

Encrypt

The Risks of Outsourcing FIM

The support information about the frequent itemsets can be utilized to effectively reveal the raw data as well as the sensitive information from the anonymized transactions.

T. Mielik¨ainen. Privacy problems with anonymized transaction databases. In Proc. of Discovery Science, 2004.

RELATED WORKS

Encrypt each real items by a one-many mapping function.

Wong, W. K., Cheung, D. W., Hung, E., Kao, B., Mamoulis, N.: Security in Outsourcing of Association Rule Mining. In: Proc. of VLDB, 2007.

However, it does not try to anonymize the support information.

Recently it is cracked.

Molloy, I., Li, N., Li, T.: On the (In)Security and (Im)Practicality of Outsourcing Precise Association Rule Mining. In: Proc. of ICDM, 2009.

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OUTLINE

Preliminary – Frequent ItemSet Mining Motivation Privacy Model – K-Support Anonymity

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K-SUPPORT ANONYMITY & ANONYMIZATION For every sensitive item, there are at least k-1

other items of the same support. The probability of an item being correctly re-identified

is limited to 1/k, even when the precise support information is known.

Given a transactional database T, encrypt T into E(T) such that There exist a decryption function D such that

MiningResult(T, Δ)= D(MiningResult(E(T), Δ)), for any minimal support Δ.

E(T) is k-support anonymous.

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SOLUTION 1: A NAÏVE APPROACH

For each set of real items of the same support, add enough fake items randomly into transactions to make the fake items as frequent as real ones.

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Trans. ID

Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

For k = 3, 16 additional items are required.4 x 2 = 8 (e, f) for wine 3 x 2 = 6 (g, h) for cigar 2 x 1 = 2 (i) for beer and tea

Items

a, e, g, h, i

a, c, e, f, h, i

c, d, e, f, g

a, b, c, f, h

a, b, d, e, f, g

A NAÏVE SOLUTION

For each set of real items of the same support, add enough fake items randomly into transactions to make the fake items as frequent as real ones.

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Trans. ID

Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

For k = 3, 16 additional items are required.4 x 2 = 8 (e, f) for wine 3 x 2 = 6 (g, h) for cigar 2 x 1 = 2 (i) for beer and tea

Items

a, e, g, h, i

a, c, e, f, h, i

c, d, e, f, g

a, b, c, f, h

a, b, d, e, f, g

There could be too large storage overhead when k is large.

GENERALIZED FIM

Discover all frequent items across concept levels, given a taxonomy indicating the hierarchical concepts between items

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

beer

teaalcoholic

wine

beverage

all prod.

cigar

When threshold set as 3 (=60%), {wine}, {cigar}, {alcoholic}, {beverage} and {all prod.} are frequent.{beverage, cigar} are also frequent.

GENERALIZED FIM

Discover all frequent items across concept levels, given a taxonomy indicating the hierarchical concepts between items

19

Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

beer

teaalcoholic

wine

beverage

all prod.

cigar

When threshold set as 3 (=60%), {wine}, {cigar}, {alcoholic}, {beverage} and {all prod.} are frequent.{beverage, cigar} are also frequent.

1. The support of a parent node comes from the supports of it child nodes. 2. Only lead nodes need to appear in the transactions.

OUTLINE

Preliminary – Frequent ItemSet Mining Motivation Privacy Model – K-Support Anonymity Algorithm

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ANONYMIZATION: OVERVIEW

For storage efficiency, we suggest to convert FIM to GFIM.

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Pseudo Taxonomy Generation in the Encryption

Encrypt Transaction Data

Frequent Itemsets

Pseudo Taxonomy

Transaction

Data

Encrypted

Decrypt Frequent Itemsets

Data Owner Third Party

Generalized Frequent Itemset Mining

wine {e, f, j}cigar {b, c, d}beer and tea {a, g, h}

ANONYMIZATION: STORAGE EFFICIENCY

In GFIM, items can be at multiple levels of a taxonomy and only the items at leaf level need to appear in the database.

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Encrypt with k=3

4 additional items required

a

f

beer

wine

j

cigar

e

b

i

k

c d

g htea

Trans. ID

Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h

2

1

1

In GFIM, items can be at multiple levels of a taxonomy and only the items at leaf level need to appear in the database.

wine {e, f, j}cigar {b, c, d}beer and tea {a, g, h}

ANONYMIZATION: STORAGE EFFICIENCY

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Encrypt with k=3

4 additional items required

a

f

beer

wine

j

cigar

e

b

i

k

c d

g htea

Trans. ID

Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h

2

1

1

Small storage overhead compared to the naïve method.

ANONYMIZATION: EASY DECRYPTION

The real frequent itemsets can be obtained by filtering out patterns containing any fake item in 1 scan of the returned results.

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, winemin_sup = 2

a

f

beer

wine

j

cigar

e

b

i

k

c d

g htea

Trans. ID Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h Results ={{beer}, {cigar}, {wine}, {tea}, {beer, wine}, {cigar, wine}}

Results ={a, b, c, d, e, f, g, h, i, j, k, ac, af, bf, ce, …}

a

f

beer

wine

j

cigar

e

b

i

k

c d

g htea

ANONYMIZATION: EASY DECRYPTION

The real frequent itemsets can be obtained by filtering out patterns containing any fake item in 1 scan of the returned results.

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, winemin_sup = 2

Trans. ID Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h Results ={{beer}, {cigar}, {wine}, {tea}, {beer, wine}, {cigar, wine}}

Results ={a, b, c, d, e, f, g, h, i, j, k, ac, af, bf, ce, …}

The data owner can obtain the real results in 1 scan of the returned itemsets.

ANONYMIZATION: ENCRYPTION

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

Encrypt with k=3

a

f

beer

wine

j

cigar

e

b

i

k

c d

g htea

Trans. ID

Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h

The problem is how to build the taxonomy and encrypt T for k-support anonymity.

ANONYMIZATION: ENCRYPTION

1: Generalization of the Mining Task To generate a pseudo taxonomy that can

(a) conserve the correct and complete mining results, (b) facilitate k-support anonymization.

2: Anonymization with Taxonomy Tree To encrypt T for k-support anonymity with the

help of the constructed taxonomy tree.

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1: GENERALIZATION OF THE MINING TASK

Build a k-bud tree of T All real items at the leaf level The number of nodes in three categories is equal

to or greater than kLet xM denote the most frequent real item in T A> = { v | sup(v) > sup(xM) and v is leaf}, A= = { v | sup(v) = sup(xM)}, and A< = { v | sup(v) < sup(xM) < sup(u), where u is the

parent node of v }.

2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3-bud tree

Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

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1: GENERALIZATION OF THE MINING TASK

29beerciga

rwine tea

3 groupsTrans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

1: GENERALIZATION OF THE MINING TASK

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

2 4(beer) (wine)

2(cigar)

4

3

3 subtrees

(tea)

1: GENERALIZATION OF THE MINING TASK

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine 2(tea)(beer)

2

4(wine)

(cigar)

4

3

5

Iteratively connect a subtree which sup(root) ≧ sup(wine) with the other subtree

1: GENERALIZATION OF THE MINING TASK

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Trans. ID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3 bud-tree

2: ANONYMIZATION WITH TAXONOMY TREE

Alternate k-bud tree and modify T simultaneously to achieve k-support anonymity Insertion Split Increase

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2: ANONYMIZATION WITH TAXONOMY TREE

Alternate k-bud tree and modify T simultaneously to achieve k-support anonymity Insertion (Ex.) Split Increase

34

u

p

vq

u

vv

p: the node with target supportq: randomly select sup(p) – sup(v) transactions from T(u) – T(v)

T(x) is the set of transactions containing the item x.

sup(v) < target-sup < sup(u)

sup(u) and sup(v) should not be changed.

TID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3-bud tree

4

5

2 2

(tea)

insertion

Items

wine, p1

cigar, wine, p1

cigar, tea

beer, cigar, wine

beer, tea, wine

p1

x

y

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2: ANONYMIZATION WITH TAXONOMY TREE

For wine

2: ANONYMIZATION WITH TAXONOMY TREE

Alternate k-bud tree and modify T simultaneously to achieve k-support anonymity Insertion Split (Ex.) Increase

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v

qpv

p: randomly select target-sup transactions from T(v)q: T(p) = T(v) – T(q)

T(x) is the set of transactions containing the item x.

target-sup < sup(v)

sup(v) should not be change.

Split operation can raise up leaf nodes to internal nodes!

TID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3-bud tree

4

5

2 2

(tea)

4(wine)

5

5

3 1

insertion

split

Items

wine, p1

cigar, wine, p1

cigar, tea

beer, cigar, wine

beer, tea, wine

Items

p1, p2

cigar, p1, p3

cigar, tea

beer, cigar, p2

beer, tea, p2

p1

p2 p3

x

y

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2: ANONYMIZATION WITH TAXONOMY TREE

For wine For cigar

2: ANONYMIZATION WITH TAXONOMY TREE

Alternate k-bud tree and modify T simultaneously to achieve k-support anonymity Insertion Split Increase (Ex.)

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u

v

u

v

sup(v) < target-sup randomly select target-sup – sup(v) transactions from T(u) – T(v)

sup(v) should not be changed. So, Increase operation is applicable only on node that does not belong to any anonymous group!

TID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3-bud tree

4

5

2 2

(tea)

4(wine)

5

5

3 1

insertion

4(wine)

5

5

3

split increase

Items

wine, p1

cigar, wine, p1

cigar, tea

beer, cigar, wine

beer, tea, wine

Items

p1, p2

cigar, p1, p3

cigar, tea

beer, cigar, p2

beer, tea, p2

Items

p1, p2, p3

cigar, p1, p3

cigar, tea

beer, cigar, p2

beer, tea, p2, p3

p1

p2 p3 p3

x

y

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2: ANONYMIZATION WITH TAXONOMY TREE

For wine For cigar For cigar

TID Items

1 wine

2 cigar, wine

3 cigar, tea

4 beer, cigar, wine

5 beer, tea, wine

2

4

(beer)

(wine)

2

(cigar)

4

3

5

5

(tea)

3-bud tree

TID Items

1 c, d, g

2 b, d, g

3 b, h

4 a, b, c

5 a, c, d, h

3-support anonymity

4

5

2 2

(tea)

4(wine)

5

5

3 1

insertion

2

4

a(beer

)

f(wine)

4

b(cigar

)

4

3

5

5

3 3

2 2

h(tea

)

c d

ge

i j

k

4(wine)

5

5

3

split increase

Items

wine, p1

cigar, wine, p1

cigar, tea

beer, cigar, wine

beer, tea, wine

Items

p1, p2

cigar, p1, p3

cigar, tea

beer, cigar, p2

beer, tea, p2

Items

p1, p2, p3

cigar, p1, p3

cigar, tea

beer, cigar, p2

beer, tea, p2, p3

p1

p2 p3 p3

x

y

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2: ANONYMIZATION WITH TAXONOMY TREE

For wine For cigar For cigar

OUTLINE

Preliminary – Frequent ItemSet Mining Motivation Privacy Model – K-Support Anonymity Algorithm Performance Studies Conclusion

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PERFORMANCE STUDIES

Data sets Retail dataset

88162 transactions with 2117 different items T10I1kD100k dataset

100k transactions with 1000 different items

Security Against precise item support attacks Against precise itemset support attacks

Storage overhead Execution efficiency

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SECURITY

Against precise item support attacks Item accuracy: The ratio of items being re-identified DB accuracy: The avg. ratio of items in a

transaction being re-identified

4343

(a) Retail dataset (b) T10I1kD100k dataset

SECURITY

Against precise itemset support attacks Item accuracy: The ratio of items being re-identified DB accuracy: The avg. ratio of items in a

transaction being re-identified

4444

(a) Retail dataset (b) T10I1kD100k dataset

STORAGE OVERHEAD & EXECUTION EFFICIENCY

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(a) Retail dataset (b) T10I1kD100k dataset

(a) Retail dataset (b) T10I1kD100k dataset

SUMMARY We proposed k-support anonymity to

enhance the privacy protection in outsourcing of frequent itemset mining (FIM).

For storage efficiency, we transformed FIM to GFIM, and proposed a taxonomy-based anonymization algorithm.

Our method allows the data owner to obtain the real frequent itemsets in 1 scan of the returned results.

Experimental results on both real and synthetic data sets showed that our method can achieve very good privacy protection with moderate storage overhead. 46

Q & A