Mining concise representations of frequent patterns through conjunctive and disjunctive search spaces

Abstract

The last years witnessed an explosive progress in networking, storage, and processing technologies resulting in an unprecedented amount of digitalization of data. There is hence a considerable need for tools or techniques to delve and efficiently discover valuable, non-obvious information from large databases. In this situation, Knowledge Discovery in Databases offers a complete process for the non-trivial extraction of implicit, previously unknown, and potentially useful knowledge from data. Amongst its steps, data mining offers tools and techniques for such an extraction. Much research in data mining from large databases has focused on the discovery of association rules which are used to identify relationships between sets of items in a database. The discovered association rules can be used in various tasks, such as depicting purchase dependencies, classification, medical data analysis, etc. In practice however, the number of frequently occurring itemsets, used as a basis for rule derivation, is very large, hampering their effective exploitation by the end-users. In this situation, a determined effort focused on defining manageably-sized sets of patterns, called concise representations, from which redundant patterns can be regenerated. The purpose of such representations is to reduce the number of mined patterns to make them manageable by the end-users while preserving as much as possible the hidden and interesting information about data. Many concise representations for frequent patterns were so far proposed in the literature, mainly exploring the conjunctive search space. In this space, itemsets are characterized by the frequency of their co-occurrence. A detailed study proposed in this thesis 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. A closed itemset includes the most specific expression describing the associated transactions, while a minimal generator includes one of the most general expressions. However, an intra-class combinatorial redundancy would logically results from the inherent absence of a unique minimal generator associated to a given closed itemset. This motivated us to carry out an in-depth study aiming at only retaining irreducible minimal generators in each equivalence class, and pruning the remaining ones. In this respect, we propose lossless reductions of the minimal generator set thanks to a new substitution-based process. We then carry out a thorough study of the associated properties of the obtained families. Our theoretical results will then be 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. In order to validate our approach, computing means for the new pattern families are presented together with empirical evidences about their relative sizes w.r.t. the entire sets of patterns. 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. Thus, an itemset verifies a portion of data if at least one of its items belongs to it. Disjunctive itemsets thus convey knowledge about complementary occurrences of items in a dataset. This exploration is motivated by the fact that, in some applications, such information -- conveyed through disjunctive support -- brings richer knowledge to the end-users. In order 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 introduce 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. Dedicated tools were then designed and implemented for extracting disjunctive itemsets and generalized association rules. Our experiments showed the usefulness of our exploration and highlighted interesting compactness rates.