  The problem of selecting small groups of itemsets that represent the data
well has recently gained a lot of attention. We approach the problem by
searching for the itemsets that compress the data efficiently. As a compression
technique we use decision trees combined with a refined version of MDL. More
formally, assuming that the items are ordered, we create a decision tree for
each item that may only depend on the previous items. Our approach allows us to
find complex interactions between the attributes, not just co-occurrences of
1s. Further, we present a link between the itemsets and the decision trees and
use this link to export the itemsets from the decision trees. In this paper we
present two algorithms. The first one is a simple greedy approach that builds a
family of itemsets directly from data. The second one, given a collection of
candidate itemsets, selects a small subset of these itemsets. Our experiments
show that these approaches result in compact and high quality descriptions of
the data.
