OPTIMONOTONE MEASURES FOR OPTIMAL RULE DISCOVERY
Article first published online: 2 MAY 2012
© 2012 Wiley Periodicals, Inc.
Volume 28, Issue 4, pages 475–504, November 2012
How to Cite
Le Bras, Y., Lenca, P. and Lallich, S. (2012), OPTIMONOTONE MEASURES FOR OPTIMAL RULE DISCOVERY. Computational Intelligence, 28: 475–504. doi: 10.1111/j.1467-8640.2012.00422.x
- Issue published online: 30 OCT 2012
- Article first published online: 2 MAY 2012
- Received 13 July 2010; Revised 24 February 2011; Accepted 8 May 2011; Published online 3 May 2012
- rule discovery;
- optimal rule set;
- interestingness measures;
- optimonotone measures
Many studies have shown the limits of the support/confidence framework used in Apriori -like algorithms to mine association rules. There are a lot of efficient implementations based on the antimonotony property of the support, but candidate set generation (e.g., frequent item set mining) is still costly. In addition, many rules are uninteresting or redundant and one can miss interesting rules like nuggets. We are thus facing a complexity issue and a quality issue. One solution is to not use frequent itemset mining and to focus as soon as possible on interesting rules using additional interestingness measures. We present here a formal framework that allows us to make a link between analytic and algorithmic properties of interestingness measures. We introduce the notion of optimonotony in relation with the optimal rule discovery framework. We then demonstrate a necessary and sufficient condition for the existence of optimonotony. This result can thus be applied to classify the measures. We study the case of 39 classical measures and show that 31 of them are optimonotone. These optimonotone measures can thus be used with an underlying pruning strategy. Empirical evaluations show that the pruning strategy is efficient and leads to the discovery of nuggets using an optimonotone measure and without the support constraint.