Database Reference
In-Depth Information
Fig. 2.13
Frequent, maximal and closed itemsets
5
Maximal and Closed Frequent Itemsets
One of the major challenges of frequent itemset mining is that, most of the itemsets
mined are subset of the set of single length frequent items. Therefore, a signifi-
cant amount of time is spent on counting redundant itemsets. One solution to this
problem is to discover condensed representations of the frequent itemsets. It will be
such representations that synopsizes the property of the set of itemsets completely
or partially. The compact representation not only save computational and memory
resource but also paved a much easier way towards knowledge discovery stage after
mining. Another interesting observation by [
53
] was that, instead of mining the com-
plete set of frequent itemsets and their associations, association mining only needs
to find frequent closed itemsets and their corresponding rules. So, mining frequent
closed itemset can fulfill the objectives of mining all frequent itemsets but with less
redundancy and better efficiency and effectiveness in mining. In this section, we
will discuss two types of condensed representation of itemset: maximal and closed
frequent itemset.
5.1
Definitions
Maximal Frequent Itemset
Suppose,
T
is the transaction database,
I
is the set of
all items in the database and
F
is the set of all frequent itemsets. A frequent itemset
P
∈
F
is called maximal if it has no frequent superset. let
M
be the set of all frequent
maximal itemsets, which is denoted by
M
={
P
|
P
∈
F
and
Q
⊃
P
,
such that Q
∈
F
}
