Efficient intensional redefinition of aggregation hierarchies in multidimensional databases

Abstract

Enhancing multidimensional database models with aggregation hierarchies allows viewing data at different levels of aggregation. Usually, hierarchy instances are represented by means of so-called rollup functions. Rollup between adjacent levels in the hierarchy are given extensionally, while rollups between connected nonadjacent levels are obtained by means of function composition. In many real-life cases, this model cannot capture accurately the meaning of common situations, particularly when exceptions arise. Exceptions may appear due to corporate policies, unreliable data or uncertainty, and their presence may turn the notion of rollup composition unsuitable for representing real relationships in the aggregation hierarchies. In this paper we present a language allowing augmenting traditional extensional rollup functions with intensional knowledge. We denote this language IRAH (Intensional Redefinition for Aggregation Hierarchies). Programs in IRAH consist of intensional rules, which can be regarded as patterns for: (a) overriding natural composition between rollup functions on adjacent levels in the concept hierarchy, (b) canceling the effect of rollup functions for specific values. Our proposal is presented as a stratified default theory. We show that a unique model for the underlying theory always exists, and can be computed in a bottom-up fashion. Finally, we present an algorithm that computes the revised dimension in polynomial time, although under more realistic assumptions, complexity becomes linear on the number of paths in the hierarchy of the dimension instance.

Enhancing flexibility and expressivity of contextual hierarchies

“…Here is an extract of these works. In [14], definitions of rules enhance the flexibility of the navigation since they can express exception in the aggregation process. In [15], the user knowledge allows the creation of new levels in dimension hierarchies.…”

Gestion et analyse personnalisées des demandes marketing. Cas de LCL-Le Crédit Lyonnais

“…Enfin, afin de pouvoir rendre l'analyse plus flexible, un langage à base de règles a été développé dans (Espil et al, 2001). Le langage IRAH (Intensional Redefinition of Aggregation Hierarchies) permet de redéfinir des chemins d'agrégation pour exprimer des exceptions dans les hiérarchies de dimensions prévues par le modèle.…”

MAT, un outil d'aide et d'accompagnement des enseignants dans la conception de scénario pour un EIAH

“…Enfin, mentionnons qu'afin de pouvoir rendre l'analyse plus flexible, un langage à base de règles a été développé dans (Espil et al, 2001) pour la gestion des exceptions dans le processus d'agrégation. Le langage IRAH (Intensional Redefinition of Aggregation Hierarchies) permet de redéfinir des chemins d'agrégation pour exprimer des exceptions dans les hiérarchies de dimensions prévues par le modèle.…”