关联规则的Redestion、Deduction Schemes和最小基
Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules
摘要：
关联规则是数据采掘中应用最广泛的数据分析方法之一。关联规则是两组二元变量之间部分蕴涵的一种形式。在最常见的方法中，关联规则通过其置信度下限（即给定前件的后件的经验条件概率）和/或通过一些其他参数界限（例如“支持度”或独立性偏差）进行参数化。我们在这里研究的概念之间的关联规则的冗余从一个基本的角度来看。我们将数据集中的每个事务视为命题逻辑意义上的解释（或模型），并考虑现有的冗余概念，即关联规则中的逻辑蕴涵，其形式为“任何第一规则成立的数据集也必须遵守第二规则，因此第二规则是冗余的”。我们讨论了现有的几种替代定义之间的关联规则的冗余，并提供新的刻画和它们之间的关系。我们表明，我们讨论的主要替代品实际上对应于两个变量，这两个变量在处理完全置信度的影响方面有所不同。对于这两个概念的冗余，我们提供了一个健全的和完整的演绎演算，我们展示了如何构建完整的基础（即公理化）的绝对最小大小的规则的数量。最后，我们探讨了一种方法，冗余多个关联规则，并充分表征其最简单的情况下，两个部分前提。
英文摘要：
Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.
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