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We propose a formal definition of the robustness of association rules for interestingness measures. It is a central concept in the evaluation of the rules and has only been studied unsatisfactorily up to now. It is crucial because a good rule (according to a given quality measure) might turn out as a very fragile rule with respect to small variations in the data. The robustness measure that we propose here is based on a model we proposed in a previous work. It depends on the selected quality measure, the value taken by the rule and the minimal acceptance threshold chosen by the user. We present a few properties of this robustness, detail its use in practice and show the outcomes of various experiments. Furthermore, we compare our results to classical tools of statistical analysis of association rules. All in all, we present a new perspective on the evaluation of association rules. [ABSTRACT FROM AUTHOR]

Many studies have shown the limits of 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 is still costly and many rules are uninteresting or redundant. In addition one can miss interesting rules like nuggets. We are thus facing a complexity issue and a quality issue. One solution is to get rid of frequent itemset mining and to focus as soon as possible on interesting rules. For that purpose algorithmic properties were first studied, especially for the confidence. They allow to find all confident rules without a preliminary support pruning. Recently, in the case of class association rules, the universal existential upward closure property of confidence has been exploited in an efficient manner. Indeed, it allows to use a pruning strategy for an Apriori-like but top-down associative classification rules algorithm. We present a new formal framework which allows us to make the link between analytic and algorithmic properties of the measures. We then apply this framework to propose a general universal existential upward closure. We demonstrate a necessary condition and a sufficient condition of existence for this property. These results are then applied to 32 measures and we show that 13 of them do have the GUEUC property. [ABSTRACT FROM AUTHOR]

Many studies have shown the limits of 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 is still costly. In addition many rules are uninteresting or redundant and one can miss interesting rules like nuggets. One solution is to get rid of frequent itemset mining and to focus as soon as possible on interesting rules. For that purpose algorithmic properties were first studied, especially for the confidence. They allow all confidence rules to be found without a preliminary support pruning. More recently, in the case of class association rules, the concept of optimal rules gave a pruning strategy compatible with more measures. However, all these properties have been demonstrated for a limited number of interestingness measures. We present a new formal framework which allows us to make the link between analytic and algorithmic properties of the measures. We apply this framework to optimal rules, and we demonstrate a necessary and sufficient condition of existence for this pruning strategy, which can be applied to any measure. [ABSTRACT FROM AUTHOR]