A Pragmatic Approach to Summarize Association Rules in Business Analytics Projects - Technologies and Applications of Artificial Intelligence - page 324

Property 1: Consequent Frequency Indicates the Importance of a Rule Summary
Consequent Frequency indicates the importance of an RS as it denotes the number of
rules that have been summarized in the RS . The higher the Consequent Frequency, the
more important the RS is. In Example 1, the rule summary has a Consequent
Frequency of 2.

Property 2: Antecedent Frequency Indicates Antecedent Importance within a
Rule Summary
Antecdent Frequency indicates the relative importance of an antecedent as compared
to other antecedents within the same RS . The higher the Antecedent Frequency, the
more important the antecedent is. In Example 1, antecedent A is less important than B
because it has a lower antecedent frequency compared to B.

Property 3: Upper Bound of Interestingness Metric in a Rule Summary
Let the interestingness metric range (i.e., f_range ) of a rule summary be [ f min , f max ]. As
long as the other metrics' thresholds are fixed, f max is invariant when different values
of f (i.e., support thresholds) are used. This implies that no association rules exist with
an f value greater than f max . Hence setting f > f max is meaningless because it will yield
no rule.

Property 4: No Rule Exists in the Range of [ f , f min ] within a Rule Summary
Let the interestingness metric range (i.e., f_range ) of a rule summary be [ f min , f max ]. As
long as the other metric thresholds are fixed, there are no association rules in the range of
[ f , f min ]. This implies that there is no point in setting any new interestingness thresholds
within the range of [ f , f min ] because it will not generate a different set of rules.
Here, we give an example of Property 3 using the support-and-confidence
framework. Let the Antecedent Support Range of a rule summary be [ S min , S max ]. As
long as the confidence threshold y is fixed, S max is invariant when different values of x
(i.e., support thresholds) are used. Property 3 implies that no association rules exist
with a support greater than S max . Hence setting x > S max is meaningless because it will
yield no rule. In Example 1, with y being fixed at 80%, we know that setting x > 45%
will not yield any rule for the rule summary with consequent C.
Similarly, Property 4 states that no association rules exist in the range of [ x , S min ].
This implies that there is no point in setting any new support thresholds in the range
of [ x , S min ] because it will not generate a different set of rules with consequent C. In
Example 1, with y being fixed at 80%, we know that setting x in the range of [35%,
42%] will not change the rule summary with consequent C.
Note that Properties 3 and 4 are also applicable to rule confidence. If the end-user
varies the confidence threshold while leaving the support threshold fixed, the same
behavior can be expected about rule confidence.

4 Experimental Setup and Results

This section first presents the experimental data and setup, and then it discusses the
usage and interpretations of rule summaries.