单调性约束与反单调性约束的区别 monotonicity and anti-monotonicity constraint

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已于 2022-06-25 00:35:57 修改 · 1.5k 阅读

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#反/单调性约束 #monotonicity

于 2022-06-25 00:28:38 首次发布

本文介绍了数据挖掘中两种重要的约束类型：单调性约束和反单调性约束。单调性约束（如最低价格不超过30美元）确保如果一个项集违反约束，其所有超集也会违反。反单调性约束（如最低价格至少20美元）则指出如果一个项集满足约束，其所有子集也同样满足。这些性质在减少频繁项集挖掘的计算量和剪枝不频繁项集时非常有用。通过利用这些约束，可以更有效地进行挖掘操作。

▚ 01 Monotone Constraints 单调性约束

1.1 Definitions 定义

【Monotone Constraints | SpringerLink 】

A constraint C is monotone if and only if for all itemsets S and S′:
if S ⊇ S′ and S violates C, then S′ violates C.

1.2 Key Points 要点

Monotone constraints possess the following property. If an itemset S violates a monotone constraint C, then any of its subsets also violates C. Equivalently, all supersets of an itemset satisfying a monotone constraint C also satisfy C (i.e., C is upward closed). By exploiting this property, monotone constraints can be used for reducing computation in frequent itemset mining with constraints. As frequent itemset mining with constraints aims to find frequent itemsets that satisfy the constraints, if an itemset S satisfies a monotone constraint C, no further constraint checking needs to be applied to any superset of S because all su