Mining High Order Decision Rules

We introduce the notion of high order decision rules. While a standard decision rule expresses connections between attribute values of the same object, a high order decision rule expresses connections of different objects in terms of their attribute values. An example of high order decision rules may state that “if an object x is related to another object y with respect to an attribute a, then x is related to y with respect to another attribute b.” The problem of mining high order decision rules is formulated as a process of finding connections of objects as expressed in terms of their attribute values. In order to mine high order decision rules, we use relationships between values of attributes. Various types of relationships can be used, such as ordering relations, closeness relations, similarity relations, and neighborhood systems on attribute values. The introduction of semantics information on attribute values leads to information tables with added semantics. Depending on the decision rules to be mined, one can transform the original table into another information table, in which each new entity is a pair of objects. Any standard data mining algorithm can then be used. As an example to illustrate the basic idea, we discuss in detail the mining of ordering rules.