Synonyms
Anti-monotonic constraints
Definition
A constraint C is anti-monotone if and only if for all itemsets S and S′:
Key Points
Anti-monotone constraints [1, 2] possess the following nice property. If an itemset S satisfies an anti-monotone constraint C, then all of its subsets also satisfy C (i.e., C is downward closed). Equivalently, any superset of an itemset violating an anti-monotone constraint C also violates C. By exploiting this property, anti-monotone constraints can be used for pruning in frequent itemset mining with constraints. As frequent itemset mining with constraints aims to find itemsets that are frequent and satisfy the constraints, if an itemset violates an anti-monotone constraint C, all its supersets (which would also violate C) can be pruned away and their frequencies do not need to be counted. Examples of anti-monotone...
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Recommended Reading
Lakshmanan LVS, Leung CK-S, Ng RT. Efficient dynamic mining of constrained frequent sets. ACM Trans Database Syst. 2003;28(4):337–89. https://doi.org/10.1145/958942.958944.
Ng RT, Lakshmanan LVS, Han J, Pang A. Exploratory mining and pruning optimizations of constrained associations rules. In: Proceedings of the ACM SIGMOD International Conference on Management of Data; 1998. p. 13–24.
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Leung, C.KS. (2018). Anti-monotone Constraints. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_5046
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