Two–Phase Iterative Algorithm - Association Rule Hiding for Data Mining - page 80

(ACE) : u 15 +u 31 u 35 +u 41 u 43 +u 53 +u 61 u 63 +
u 71 u 75 +u 83 u 85 +u 95 +u 101 u 105 1 (15.5)

(AB) : u 41 < 1 ) u 41 = 0 (15.6)

(BC) : u 43 +u 83 < 2 ) u 43 = 0_u 83 = 0 (15.7)

(BE) : u 85 < 1 ) u 85 = 0 (15.8)

(CD) : u 53 +u 63 < 1 ) u 53 = u 63 = 0 (15.9)

Notice that no inequality is produced from itemset BD since this itemset is foreign
to set I H . The produced set of inequalities is solvable, yielding two exact solutions,
each of which requires only one binary variable to become '1': either u 15 or u 95 .
These two solutions are actually the same, since the involved transactions (1st or
9th) do not differ from one another and both solutions apply the same modification
to either of them. Table 15.5 presents the solution where u 15 = 1.

Table 15.5: Database D produced by the two-phase iterative approach.

A B C D E

1 0 1 0 1

1 0 1 1 1

0 0 1 0 0

0 1 0 0 1

1 0 0 1 1

0 0 0 1 1

0 0 1 0 0

1 1 0 0 0

1 0 1 0 0

0 0 1 0 0

Figure 15.3 shows the original borderline along with the borderlines of the
databases produced as an output of the two phases of the algorithm. Notice that
the output of the second phase in the first iteration of the algorithm yields an exact
solution. Thus, for ` = 1 the two-phase iterative algorithm has provided an exact
solution that was missed by the inline algorithm of [23].

15.4 Experimental Evaluation

In this section, we provide some experimental results that test the two-phase itera-
tive approach against the inline algorithm. The two algorithms were tested in [27]
on three real world datasets using different parameters such as minimum support
threshold and number/size of sensitive itemsets to hide. All these datasets are pub-
licly available through the FIMI repository [30] and are summarized in Table 14.4.