关联规则挖掘中闭频繁项集的理解与探索

Understanding and Exploration of Closed Frequent Itemsets in Association Rule Mining

摘要: 关联规则挖掘，通过数据挖掘事务之间的关联关系，被广泛应用到各个领域，主要是通过频繁项集产生关联规则，而频繁项集的挖掘又归结到闭频繁项集的挖掘，由此可见闭频繁项集在关联规则挖掘种的重要作用。本文以购物篮关联规则分析为场景，对闭频繁项集的理论进行了梳理，针对闭包算子定义中的函数i和t进行了单调性证明；对闭包算子定义满足的三条性质进行了证明；对频繁项集和其闭包的支持度进行了探讨；对封闭频繁项集和其超集之间的支持度进行了关系讨论。最后，按照频繁项集及其闭包所形成的等价类的性质进行了研究，给出了有关定理和证明，以及结论等。

Abstract: Association rule mining, is widely used in various fields by mining the association relationships between transactions through data mining, in which, association rules are mainly generated through frequent itemsets, and the mining of frequent itemsets is reduced to the mining of closed frequent itemsets, and this shows the important role of closed frequent itemsets in association rule mining. This article takes the analysis of shopping basket association rules as a scenario to sort out the theory of closed frequent itemsets, and proves the monotonicity of functions i and t in the defi-nition of closure operators; proves three properties that the closure operator definition satisfies; explores the support of frequent itemsets and their closures; discusses the relationship between the support of closed frequent itemsets and their supersets. Finally, the properties of the equiva-lence class formed by the frequent itemsets and their closure are studied, and relevant theorems, proofs, and conclusions are provided.