A Principled Approach to the Knowledge Discovery in Databases: Part II- Modelling Association Queries by Formal Concept Analysis

Abstract

In this study we utilize formal concept analysis to model association rules. Formal concept analysis provides a topological structure for a universe of objects and attributes. By exploiting the relationship between objects and attributes, formal concept analysis then introduces an entity called a concept. A concept is a set of attributes and objects. The attributes are maximally possessed by the set of objects and similarly the objects are the maximal set which all possess the set of attributes. Formal concept analysis deals with formal mathematical tools and techniques to develop and analyze relationship between concepts and to develop concept structures. We propose and develop a connection between association rule mining and formal concept analysis. We show that dependencies found by an association query can be derived from a concept structure. We have extended formal concept analysis framework to the association rule mining. We use analysis of market-basket problem, a specific case of association rule mining, to achieve this extension. This extension provides a natural basis for complexity analysis of the association rule mining. This extension can also help in developing a unified framework for common data mining problems.