Exploring the Disjunctive Search Space towards Discovering New Exact Concise Representations for Frequent Patterns T. Hamrouni 1,2 , I. Denden 1 , S. Ben Yahia 1 and E. Mephu Nguifo 2,3 1 Department of Computer Sciences, Faculty of Sciences of Tunis University Campus, 1060 Tunis, Tunisia {tarek.hamrouni, sadok.benyahia}@fst.rnu.tn 2 CRIL-CNRS, Artois University Rue de l’universit´ e, 62307 Lens cedex, France {hamrouni, mephu@cril.univ-artois.fr} 3 LIMOS-CNRS, Blaise Pascal Clermont 2 University Campus des c´ ezeaux, 63173 Aubi` ere cedex, France engelbert.mephu nguifo@univ-bpclermont.fr October 2007 Abstract. Extracting concise representations seems to be a milestone towards the emerging knowledge extraction field. In fact, it is a quite survival reflex towards providing a manageably-sized and reliable knowledge. Thus, we bash- fully witness the emergence of a trend towards extracting concise representations, e.g., closed patterns, non-derivable patterns and essential patterns. The essential pattern-based concise representation presents very interesting properties since it also allows the direct derivation of the disjunctive and negative supports of a pat- tern, in contrast with almost all known concise representations. In addition, it offers a respectable compactness rates. However, these properties are shadowed by the burden of a positive border maintained in the sake of preserving the ex- actness property. In this technical report, we introduce a new exact concise rep- resentation standing at the crossroads of closure operators and essential patterns. The introduced concise representation required the definition of a new closure operator. Since the latter operator makes possible mapping many elements to a unique one, the new representation permits to drastically reduce the number of handled patterns while avoiding the use of the positive border. It also maintains the interesting properties of essential patterns. Furthermore, this representation makes it possible to bridge the gap with various association rule forms. Carried out experiments show an important lossless reduction of the number of extracted patterns vs. those performed by the concise representations based on frequent closed, (closed) non-derivable and essential patterns, respectively. Keywords: Frequent pattern, Concise representation, Disjunctive closure opera- tor, Disjunctive closed pattern, Generalized association rule, Itemset. 1 Introduction and motivations Within the traditional framework for extracting association rules, the conjunctive op- erator – linking items – got the monopoly. To palliate a hardly manageable number