Mining for Rules with Categorical and Metric Attributes

Abstract

This chapter focuses on mining for association rules with categorical and metric attributes. Categorical attributes are similar to Boolean ones except that they can take on several discrete values instead of two. A categorical attribute can easily be transformed into a set of Boolean attributes. For instance, the categorical attribute (a, {1, 2, 3, 4}) can be transformed into the following set of pseudo-Boolean attributes: {(a_1, {0, 1}), (a_2, {0, 1}), (a_3, {0, 1}), (a_4, {0, 1})} such that a_i = 0 if §Ñ ≠ i and a_i = 1 if a = i. A metric attribute is one whose domain of values is a metric space, that is (see [B48], p. X for instance), a set M endowed with a distance δ satisfying the properties:

• 1. δ(e, e) = 0 for any e in M,

• 2. δ(e1, e2) > 0 for any pair (e1, e2) such that e1 ≠ e2,

• 3. δ(e1, e2) = δ(e2, e1) for any pair (e1, e2),

• 4. δ(e1, e2) + δ(e2, e3) ≥ δ(e1, e3) for any triple (e1, e2, e3).