A step toward the foundations of data mining

This paper addresses some fundamental issues related to the foundations of data mining. It is argued that there is an urgent need for formal and mathematical modeling of data mining. A formal framework provides a solid basis for a systematic study of many fundamental issues, such as representations and interpretations of primitive notions of data mining, data mining algorithms, explanations and applications of data mining results. A multi-level framework is proposed for modeling data mining based on results from many related fields. Formal concepts are adopted as the primitive notion. A concept is jointly defined as a pair consisting of the intension and the extension of the concept, namely, a formula in a certain language and a subset of the universe. An object satisfies the formula of a concept if the object has the properties as specified by the formula, and the object belongs to the extension of the concept. Rules are used to describe relationships between concepts. A rule is expressed in terms of the intensions of the two concepts and is interpreted in terms of the extensions of the concepts. Several different types of rules are investigated. The usefulness and meaningfulness of discovered knowledge are examined using a utility model and an explanation model.