Association rules are among the most popular and widely used data mining
techniques. Often, associations are sought between items forming a taxonomy.
Patterns discovered between items from different levels of a taxonomy provide
aggregated view over the data and allow to discover trends and regularities
that are not apparent in the raw transactional data. Generalized association
rule mining, i.e. mining in presence of a taxonomy of items, is an important
augmentation to the original association rule mining framework. Unfortunately,
currently available algorithms do not allow to efficiently discover
generalized association rules. 

In this paper we present the state-of-the-art in generalized association rule
mining. We describe the hierarchical bitmap index, an efficient physical
structure optimized for set processing. Next, we modify the Prutax algorithm
by incorporating the hierarchical bitmap index as the crucial internal
structure, resulting in the advent of the PrutaxHBI algorithm. An experimental
evaluation and comparison of the proposed solution with currently available
algorithms clearly shows that the proposed algorithm outperforms current
algorithms under all circumstances.