Q.8 What are multidimensional association rules ? Mention few approaches to mining multilevel association rule.

Ans. **Association rules **that involve two or more dimensions or predicates can be referred to as multidimensional association rules. For instance, the rule

age(X, “20.....29') ^ occupation(X, "student”) = buys(X, "laptop”)

contains three predicates (age, occupation, and buys), each of which occurs only once in the rule. Hence, we say that it has no repeated predicates. Multidimensional association rules with no repeated predicates are called inter dimensional association rules. We can also mine multidimensional association rules with repeated predicates, which contain multiple occurrences of some predicates. These rules are called hybrid-dimensional association rules.

An example of such a rule is the following, where the predicate buys is repeated -

age(X, “20.....29") ^ buys(X, “laptop”) => buys(X, “HP printer”)

Database attributes can be categorical or quantitative. Categorical attributes have a finite number of possible values, with no ordering among the values. Quantitative attributes are numeric and have an implict ordering among values. Techniques for mining multidimensional association rules can be categorized into two basic approaches regarding the treatment of quantitative attributes -

**(i) Static Discretization of Quantitative Attributes –** In the first approach, quantitative attributes are discretized using predefined concept hierarchies. This discretization occurs before mining. For instance, a concept hierarchy for income may be used to replace the original numeric values of this attribute by interval labels, such as “0.......20K”, “21 K........30K”, “31K........40K”, and so on. Here, discretization is static and predetermined. The discretized numeric attributes, with their interval labels, can then be treated as categorical attributes (where each interval is considered a category). We refer to this as mining multidimensional association rules using static discretization of quantitative attributes.

**(ii) Dynamic Quantitative Association Rules –** In the second approach, quantitative attributes are discretized or clustered into "bins” based on the distribution of the data. These bins may be further combined during the mining process. The discretization process is dynamic and established so as to satisfy some mining criteria, such as maximizing the confidence of the rules mined. Because this strategy treats the numeric attribute values as quantities rather than as predefined ranges or categories, association rules mined from this approach are also referred to as (dynamic) quantitative association rules.

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