Given a set $I$ of $n$ items, and a collection $D$ of $m<2^n$ subsets of $I$, a closed itemset is a subset $A$ of $I$ that is contained in strictly more elements of $D$ than any of its proper supersets. Closed itemsets are important in data mining because they provide a compact representation of the dataset. I'm trying to find some non-trivial upper bound to the number of closed itemsets. It seems a natural combinatorial question and I'm surprised I can't find anything non-trivial. Any suggestion/reference? Thank you.
Upper bound to number of closed itemsets
co.combinatorics;upper bounds;data mining