An integer programming approach for frequent itemset hiding

1
An integer programming approach for frequent
itemset hiding

• Aris Gkoulalas-Divanis
• Vassilos S. Verykios
• CIKM06

2
outline

• Introduction
• Basic definitions
• Methodology
• Experimental results
• Conclusions

3
introduction

• It based on the notion of distance between
  original database and the sanitized database
• goal minimized the distance based on the integer
  programming while hiding the sensitive itemsets
  and minimally affecting non-sensitive itemsets

4
Basic definitions

• the support count of itemsets in bitmap
  representation

a b c
1 0 1
1 1 1
Maximizing the number of 1 left in D
non-sensitive itemsets should satisfy this rule
in D
sensitive itemsets should satisfy this rule in D
5
(cont.)

• Solving this problem is NP-hard ,there are 2m-1
  inequalities (mtransactions lists)

6
(cont.)

• SIe,ae,bc (sensitive itemsets)
• Se,bc (minimal sensitive itemsets)
• SSe,ae,bc,ce,abc, set of all sensitive
  itemsets and their supersets
• Ideal case FF-SS ,santized database D to
  contain all the frequent itemsets of D expect
  from the sensitive ones

7
(cont.)

• Negative border
• Positive border

8
Border revision
null
A
B
C
D
BC
AD
AC
AB
BD
CD
ABC
BCD
ACD
ABD
ABCD
9
Problem size minimization

• Cthe total set of affected itemsets
• Lc the set of solutions of the corresponding
  inequalities
• remove the inequality of C2
  without affecting the global solution of the
  system then C2 covers C1

10
(cont.)

• Corollary any itemset belonging in the positive
  border of F-SS covers all its subsets
• gtB(F) cover all itemset of F
• B-(F) cover all itemsets of
• Ideal solution Lc

11
(cont.)
12
example

• FA,B,C,D,AB,AC,AD,CD,ACD
• SIAB,SAB
• FA,B,C,D,AC,AD,CD,ACD
• B(F)B,ACD

Bfrequent
ACDfrequent
ABinfrequent
13
Constraint satisfaction problem

• A solution of a CSP is a complete assignment of
  values to the variables that satisfies all the
  constraints
• In CSP we usually wish to maximize or minimize an
  objective function subject to a number of
  constraints
• To solve this problem we use binary integer
  programming (BIP) that transform the CSP to an
  optimization problem

14
Binary integer problem
15
Experimental results

• 10,000 transactions,10items,msup0.1

16
conclusions

• Defined a new metric to quantify the distance of
  the initial database D and its sanitized version
  D
• It has benefit of being exact when ideal solution
  can be identified

17
Exact knowledge hiding through database extension

• Aris Gkoulalas-Divanis
• Vassilos S. Verykios
• TKDE08

18
introduction

• The goal of the hiding algorithm is to create a
  minimal extension DX to the original database DO

D
19
(cont.)

• Se,ae,bc

20
methodology

• PD NDo QDx
• ex e4,ae3,bc4

21
(cont.)

• The distance between Do and D is measured based
  on the extension Dx

(minimize)
22
(cont.)

• Optimal solution set c
• Se,ae,bc mfreq0.3 Q4
• Ce,f,bc,bd,ab,acd

23
Safety margin

• The lower bound of Q under certain circumstances
  be insufficient to allow for the identification
  of an exact solution
• Safety margin(SM) Expand the size of Q of Dx, it
  can be predefined or be computed dynamically
• Exsabc
• only 1 transaction is insufficient to
• provide an exact solution

24
(cont.)

• Null transaction
• (i) an unnecessarily large safety
• margin
• Should be removed from Dx
• (ii) a large value of Q essential for
• proper hiding
• Need to be validated ,since Q denotes the
  
• lower bound in the number of
  transactions to
• ensure proper hiding

25
(cont.)

• To ensure minimum size of Dx, the hiding
  algorithm keeps only k null transactions
• Qinvnull transaction
• VQSM-Qinv
• Ex sabc ,Q1 ,SM3
• Kmax(1-3,0)1

Null transaction
26
Experimental results
27
(cont.)
28
conclusions

• Use a minimal extension to the original database
• It has benefit of being exact when ideal solution
  can be identified