Constraint-Based Rule Mining

In practice, users may only be interested in subsets of associations containing attributes satisfying given Boolean conditions also called Boolean constraints. This chapter, which builds upon the previous chapter, deals with solving the problem of mining for association rules in the presence of such constraints. Taxonomies may be present and constraints may contain both terminal and nonterminal attributes. A set of Boolean constraints can be identified with a Boolean function. In the first section, we define the syntax and semantics of Boolean functions. In the second section we review the notion of prime implicant. The prime implicants are the basic building blocks of Boolean functions. Any Boolean function can be identified with the set of its prime implicants (often, only identified with a subset of it, since the set of prime implicants is, in general, redundant). Each prime implicant defines a sublattice in 2A. In the last section, we take advantage of the sublattices attached to the prime implicants to devise a sequential and a parallel algorithm solving the problem of mining for association rules under Boolean constraints. The algorithms derive from the ones developed in Chapter 4. Cas enumeration takes advantage of the sublattices to discard all those cass that do not meet the given constraints or cannot be expected to lead to cass meeting these constraints.