In this chapter, we design an online environment for mining inter-dimensional association rules from data cubes as a part of a platform called CubeMining. We use a guided rule mining facility, which allows users to limit the mining process to a specific context defined by a particular portion in the mined data cube. We also provide a computation of the support and the confidence of association rules when a SUM-based measure is used. This issue is quite interesting since it expresses associations which do not restrict users’ analysis to associations driven only by the traditional COUNT measure. The support and the confidence may lead to the generation of large number of association rules. Therefore, we propose to evaluate interestingness of mined rules according to two additional descriptive criteria (lift and loevinger). These criteria can express the relevance of rules in a more precise way than what is offered by the support and the confidence. Our association rule mining procedure is an adaptation of the traditional level-wise apriori algorithm to multidimensional data. In order to make extracted knowledge easier to interpret and exploit, we provide a graphical representation for the visualization of inter-dimensional association rules in the multiinter-dimensional space of the mined data cube. Empirical analysis showed the efficiency of our proposal and the acceptable runtime of our algorithm.
In the current development of our mining solution, we integrate SUM-based mea-sures in the computation of interestingness criteria of extracted association rules.
However, this choice assumes that the selected measure is additive and has only positive values. In the suspicious regions data cube, the surface of regions is an appropriate measure for the computation of the revisited criteria. Nevertheless, the total boundary length of regions can not be used for that computation since the SUM of boundary lengths does not make concrete sense. In some cases, an OLAP context may be expressed by facts with non-additive or negative measures. For instance, in the traditional example of a sales data cube, the average of sales is typically a non-additive measure. Furthermore, the profit of sales is also an OLAP measure that can have negative values. In such situations, we obviously need a more appropriate interestingness estimation of association rule to handle a wider spectrum of measure types and aggregate functions (e.g., AVG, MAX).
Our proposal provides inter-dimensional association rules with non-repetitive predicates. Such rules consist of a set of predicate instances where each one repre-sents a modality coming from a distinct dimension. This kind of association rules helps explain a value of a dimension by other values drawn from other dimensions.
Nevertheless, an inter-dimensional association rule does not explain a modality by other ones from the same dimension. For instance, the latter type of rules is not able to explain the sales of a product by those of other products or even other product categories. In order to cope with this issue, we also need to extend our proposal in order to cover the mining of inter-dimensional association rules with repetitive predicates as well as intra-dimensional association rules. In addition, these new kinds of associations should profit from dimension hierarchies and allow modalities from multiple granularity levels.
The association rule mining process in our environment is based on an adaptation of the traditional level-wise apriori algorithm to multidimensional data. The anti-monotony property (Agrawal et al., 1993) allows a fast search of frequent itemsets, and the guided mining of association rules we express as a meta-rule limits the search space according to the analysis objectives of users. However, some recent studies have shown the limitations of Apriori and privileged the notion of frequent closed itemsets like in close (Pasquier, Bastide, Taouil, & Lakhal, 1999), pascal (Bastide, Taouil, Pasquier, Stumme, & Lakhal, 2000), closet (Pei, Han, & Mao, 2000), Charm (Zaki & Hsiao, 2002), and galicia (Valtchev, Missaoui & Godin, 2004).
Finally, measures are used in our environment for computing interestingness criteria.
We plan to study the semantics of association rules when measures appear in the expression of rules.
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