Exploring the Disjunctive Search Space towards Discovering New Exact Concise Representations for Frequent Patterns

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 bashfully 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 pattern, 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 exactness property. In this technical report, we introduce a new exact concise representation 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.