AC-Close: Efficiently Mining Approximate Closed Itemsets by Core Pattern Recovery

1. AC-Close: Efficiently Mining Approximate Closed Itemsets by Core Pattern Recovery H.Cheng, P.S. Yu, and J.Han ICDM’06 報告者：林靜怡 2007/01/17

2. Introduction • In real applications, a database contains random noise or measurement error • some interesting patterns would previously be fragmented • discover approximate frequent itemsets in the presence of random noise

3. Definition • D：a transaction database take the form of an n x m binary matrix • I = be a set of all items • T：the set of transactions in D

4. Definition • ：The exact support of an itemset x • ： The exact supporting transactions of x • ：the support of an approximate itemset x • ： The supporting transactions of an approximate itemset x

5. Definition

6. Definition

7. approximate closed frequent itemset mining • The problem of approximate closed frequent itemset mining from core patternsis the mining of all itemsets which are (1) core patterns w.r.t.α (2) approximate frequent itemsets w.r.t. , and min sup (3) closed.

8. Approximate Closed Itemset Mining • Mine the set of core patterns with min_sup = αs • Treat core patterns as the initial seeds for possible further extension to approximate frequent itemsets • C：the set of core patterns • L：A lattice whichis built over C

9. Candidate Approximate Itemset Generation

10. Example • For core pattern ,the number of 0s allowed in a supporting transaction is • extension space for ： traverse upward in the lattice for 2 levels (i.e., levels 2 and 3)

12. for a core itemset yand each sub-pattern , any transaction supporting x also approximately supports y • is the unionof the transaction set • Ex: is the union of the transaction sets of all itemsets at levels 2 and 3

13. identify candidate approximateitemsets • steps to identify candidate approximate itemsets include

14. Pruning by

15. Topdown Mining and Pruning by Closeness • effective pruning by the closeness definition and the min_sup threshold • starts with the largest pattern in L and proceeds level by level, in the size decreasing order of core patterns.

16. {0,2,4} {0,2,5} {2,5} {0,2,6} {2,6} {2,3,5,6} {0,2} {2} {2,5} {2,6}

17. Example • = {0,2,3,4,5,6} The number of 0s allowed in a transaction is => extension space includes its sub- patterns at level 2.

18. => • prune{a,b,c} without actual computation: (1) if {a,b,c,d} satisfies the min_sup threshold and the constraint, then no matter whether it is closed or non-closed {a,b,c} can be pruned (2) if {a,b,c,d}does not satisfy the min_sup, then {a,b,c}can be pruned

19. Forward pruning

20. Backward pruning

22. Experiment • The IBM synthetic data generator • A dataset T10.I100.D20K is generated with 20K transactions, 100 distinct items and an average of 10 items per transaction