A Novel Framework for Unification of Association Rule Mining, Online Analytical Processing and Statistical Reasoning

Statistical reasoning was one of the earliest methods to draw insights from data. However, over the last three decades, association rule mining and online analytical processing have gained massive ground in practice and theory. Logically, both association rule mining and online analytical processing have some common objectives, but they have been introduced with their own set of mathematical formalizations and have developed their specific terminologies. Therefore, it is difficult to reuse results from one domain in another. Furthermore, it is not easy to unlock the potential of statistical results in their application scenarios. The target of this paper is to bridge the artificial gaps between association rule mining, online analytical processing and statistical reasoning. We first provide an elaboration of the semantic correspondences between their foundations, i.e., itemset apparatus, relational algebra and probability theory. Subsequently, we propose a novel framework for the unification of association rule mining, online analytical processing and statistical reasoning. Additionally, an instance of the proposed framework is developed by implementing a sample decision support tool. The tool is compared with a state-of-the-art decision support tool and evaluated by a series of experiments using two real data sets and one synthetic data set. The results of the tool validate the framework for the unified usage of association rule mining, online analytical processing, and statistical reasoning. The tool clarifies in how far the operations of association rule mining and online analytical processing can complement each other in understanding data, data visualization and decision making.