Synonyms
Definition
Consider an n × m binary matrix D. Each row of D corresponds to a transaction t and each column of D corresponds to an item i. The (t, i)-element of D, denoted D(t, i), is 1 if transaction t contains item i, and 0 otherwise. Let T 0 = {t 1, t 2,…,t n } and I 0 = {i 1, i 2,…,i m } be the set of transactions and items associated with D, respectively.
Let D be as above, and let ε r , ε c ∈ [0, 1]. An itemset I ⊆ I 0 is an approximate frequent itemset AFI(ε r , ε c ), if there exists a set of transactions T ⊆ T 0 with | T |  ≥ minsup | T 0 | such that the following two conditions hold:
- 1.
\( \forall i\in T,\frac{1}{\mid I\mid}\sum_{j\in I}D\left(i,j\right)\ge \left(1-{\upepsilon}_r\right); \)
- 2.
\( \forall j\in I,\frac{1}{\mid T\mid}\sum_{i\in T}D\left(i,j\right)\ge \left(1-{\upepsilon}_c\right); \)
Recommended Reading
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Creighton C, Hanash S. Mining gene expression databases for association rules. Bioinformatics. 2003;19(1):79–86.
Yang C, Fayyad U, Bradley PS. Efficient discovery of error-tolerant frequent itemsets in high dimensions. In: Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining; 2001. p. 194–203.
Liu J, Paulsen S, Wang W, Nobel A, Prins J. Mining approximate frequent itemset from noisy data. In: Proceedings of the 2005 IEEE International Conference on Data Mining; 2005. p. 721–4.
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Liu, J. (2017). Approximation of Frequent Itemsets. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_22-2
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DOI: https://doi.org/10.1007/978-1-4899-7993-3_22-2
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