A complementary method of reducing the large amount of frequent patterns is to use so-called condensed representations. Two important examples of condensed representations for frequent itemsets are maximal frequent itemsets and closed frequent itemsets. Maximal frequent itemsets are frequent itemsets for which none of their supersets is also frequent. Clearly, each frequent itemset is a subset of a maximal frequent itemset. Closed frequent itemsets are itemsets that completely characterize their associated set of transactions. That is, a frequent itemset X is closed if it contains all items that occur in every transaction in which X is bought. The closed frequent itemsets form a basis for all frequent sets; The underlying idea of both concepts is that the set of all maximal/closed frequent itemsets represents all frequent itemsets but is far smaller.
