Mining Closed Gradual Patterns

With the steady development of the computing tools, we attended last three decades a considerable increase of the quantity of data stored in databases. So, extracting knowledge from this data is of paramount importance. Data mining is becoming an inescapable tool to reach this goal. Association rule extraction is one of the important tasks in data mining. This powerful technique has a wide range of applications in many areas of business practice and also research. A scrutiny of the related work shows that another type of rules called gradual rules also paid attention within the data mining community. Gradual rules of the form −“the more A, the more B”− mainly grasped the interest within recommendation and command system fields [2]. Several approaches and semantics dealing with this kind of rules have been proposed in literature. However, the relevance and the usefulness of the mined knowledge seems no to be the main concern in these approaches. In fact, it is expected that an overwhelming quantity of gradual rules will be drawn even from low sized contexts. The main thrust of this paper is to address to lossless reduction of the mined knowledge. To reach this goal, a possible solution consists in using results of Formal Concept Analysis that has been shown to provide useful seeds to tackle such knowledge extraction problem. However, no work has addressed the use of the FCA framework for gradual patterns. Hence, we introduce a novel Galois connection that is a sine qua non issue for extracting closed gradual patterns. These latter patterns will act as a lossless reduced-size nucleus of patterns. The remainder of the paper is organized as follows. Section 2 reviews the related work focused on mining gradual rules and some basic notions of the FCA framework. Section 3 introduces our novel Galois connection definition and shows its validity and soundness. Section 4 validates the importance of our approach at reducing the hudge number of the extracted gradual closed patterns through experiments carried out over synthetic datasets. Section 5 sketches our future perspectives and presents concluding remarks.