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algorithm we move top-down in the lattice to identify infrequent itemsets whose all
proper subsets are frequent in F 0 D . First, we examine all 1-itemsets (i.e., items).
If any of these itemsets is infrequent, it should be included in the revised negative
border. Then, we examine all 2-itemsets by properly joining (symbol ./ denotes a
join) the frequent 1-itemsets. Again, if the produced 2-itemset does not exist in F 0 D
we include it in Bd (F 0 D ). To examine k-itemsets (where k > 3), we first construct
them by properly joining frequent (k-1)-itemsets (as in Apriori) and then check to
see if the produced itemset is frequent inF 0 D . If the itemset is reported as infrequent,
we then examine all its (k-1) proper subsets. If none of these is infrequent, then the
itemset belongs to the revised negative border, so we include it in Bd (F 0 D ).
Algorithm 9.4 Hiding of all the sensitive itemsets and their supersets.
1: procedure H IDE SS(F D O , S max )
2:
for each s 2S max do
. for all sensitive itemsets
3:
for each f 2F D O do
. for all large itemsets
4:
if s f then
. the large itemset is sensitive
5:
F D O F D O f
. remove itemset f
6: end if
7: end for
8: end for
9: Return: F 0 D F D O
10: end procedure
Last, Algorithm 9.4 presents the hiding process in which we identify F 0 D by
removing from F D O all the sensitive itemsets and their supersets. To do so, we
iterate over all the sensitive itemsets and their supersets (i.e., set S max ), and the large
itemsets in F D O , and we identify all those large itemsets that are supersets of the
sensitive. Then, we remove these itemsets from the list of frequent itemsets, thus
construct a new set F 0 D with the remaining large itemsets in F D O .
 
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