Mathematical Foundation of Association Rules - Mining Associations by Solving Integral Linear Inequalities

Informally, data mining is derivation of patterns from data. The mathematical mechanics of association mining (AM) is carefully examined from this point. The data is table of symbols, and a pattern is any algebraic/logic expressions derived from this table that have high supports. Based on this view, we have the following theorem: A pattern (generalized associations) of a relational table can be found by solving a finite set of linear inequalities within a polynomial time of the table size. The main results are derived from few key notions that observed previously: (1) Isomorphism: Isomorphic relations have isomorphic patterns. (2) Canonical Representations: In each isomorphic class, there is a unique bitmap based model, called granular data model