1 research outputs found
Contributions to the Formalization and Extraction of Generic Bases of Association Rules
In this thesis, a detailed study shows that closed itemsets and minimal
generators play a key role for concisely representing both frequent itemsets
and association rules. These itemsets structure the search space into
equivalence classes such that each class gathers the itemsets appearing in the
same subset aka objects or transactions of the given data. In this respect, we
proposed lossless reductions of the minimal generator set thanks to a new
substitution-based process. Our theoretical results are extended to the
association rule framework in order to reduce as much as possible the number of
retained rules without information loss. We then give a thorough formal study
of the related inference mechanism allowing to derive all redundant association
rules, starting from the retained ones. We also lead a thorough exploration of
the disjunctive search space, where itemsets are characterized by their
respective disjunctive supports, instead of the conjunctive ones. This
exploration is motivated by the fact that, in some applications, such
information brings richer knowledge to the end-users. To obtain a redundancy
free representation of the disjunctive search space, an interesting solution
consists in selecting a unique element to represent itemsets covering the same
set of data. Two itemsets are equivalent if their respective items cover the
same set of data. In this regard, we introduced a new operator dedicated to
this task. In each induced equivalence class, minimal elements are called
essential itemsets, while the largest one is called disjunctive closed itemset.
The introduced operator is then at the roots of new concise representations of
frequent itemsets. We also exploit the disjunctive search space to derive
generalized association rules. These latter rules generalize classic ones to
also offer disjunction and negation connectors between items, in addition to
the conjunctive one.Comment: in French, HDR thesi