Mining Closed Frequent Itemsets
In Section 5.1.2 we saw how frequent itemset mining may generate a huge number of
frequent itemsets, especially when the min sup threshold is set low or when there exist
long patterns in the data set. Example 5.2 showed that closed frequent itemsets9 can
substantially reduce the number of patterns generated in frequent itemset mining while
preserving the complete information regarding the set of frequent itemsets. That is, from
the set of closed frequent itemsets, we can easily derive the set of frequent itemsets and
their support. Thus in practice, it is more desirable to mine the set of closed frequent
itemsets rather than the set of all frequent itemsets in most cases.
“How can we mine closed frequent itemsets?” A naïve approach would be to first mine
the complete set of frequent itemsets and then remove every frequent itemset that is a
proper subset of, and carries the same support as, an existing frequent itemset. However,
this is quite costly. As shown in Example 5.2, this method would have to first derive
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