Pattern ordering is an important task in data mining because the number of patterns extracted by standard data mining algorithms often exceeds our capacity to manually analyze them. A standard approach for handling this problem is to rank the patterns according to an evaluation metric and then presents only the highest ranked patterns to the users. This approach may not be trivial due to the wide variety of metrics available, some of which may lead to conflicting ranking results. In this paper, we present an effective approach to address the pattern ordering problem by combining the rank information gathered from multiple sources. Although rank aggregation techniques have been developed for applications such as meta-search engines, they are not directly applicable to pattern ordering for two reasons. First, the techniques are mostly supervised, i.e., they require a sufficient amount of labeled data. Second, the objects to be ranked are assumed to be independent and identically distributed (i.i.d), an assumption that seldom holds in pattern ordering. The method proposed in this paper is an adaptation of the original Hedge algorithm, modified to work in an unsupervised learning setting. Techniques for addressing the i.i.d. violation in pattern ordering are also presented. Experimental results demonstrate that our unsupervised Hedge algorithm outperforms many alternative techniques such as those based on weighted average ranking and singular value decomposition.

Abstract. In this paper we introduce distribution rules, a kind of association rules with a distribution on the consequent. Distribution rules are related to quantitative association rules but can be seen as a more fundamental concept, useful for learning distributions. We formalize the main concepts and indicate applications to tasks such as frequent pattern discovery, sub group discovery and forecasting. An efficient algorithm for the generation of distribution rules is described. We also provide interest measures, visualization techniques and evaluation. 1