CFI-Stream: Mining Closed Frequent Itemsets in Data Streams

1. CFI-Stream: Mining Closed Frequent Itemsets in DataStreams Nan Jiang,Le Gruenwald SIGKDD’06 報告者：林靜怡 2006/10/04

2. Introduction • mining Closed frequent itemsets • computes and maintains closed itemsets online and incrementally • perform the closure checking • output the current closed frequent itemsets in real time based on users’ specified thresholds

3. Definition • D：data stream • I = { , , …, } :a set of n elements, called items • T： subsets of all the transactions • X： subsets of all the items appearing in a data stream

4. Definition • C(X)：the smallest closed set containing X • Definition 1 An itemset X is said to be closed if and only if C(X)= f(g(X)) = f•g(X) = X

5. Algorithm • CFI-Stream algorithm • DIrect Update (DIU) tree • perform the closure checking online over a data stream sliding window • Conditions need to check for closed itemsets • check when performing addition and deletion operations on the DIU tree

6. DIU tree • maintain the current closed itemsets • k levels in the DIU tree, each level i stores the closed i-itemsets

7. DIU tree • Each node in the DIU tree stores • a closed itemset • its current support information • links to its parent and children nodes

8. Add a Transaction to the DIU Tree T1：original transaction set t：new arrived transaction • Conditions to Check for Closed Itemsets (1) t is in the T1, if the largest itemset X it contains is not currently in the DIU tree ->check for all X’s subsets Y, which are in T1

9. (2) when t is not in T1, for each its subset Y, if Y is in T1, we need to check

10. Closure Checking for Addition

11. 2 1 C 3 3 CD CD 1 ABC • C,D 2 A,B 3 A,B,C 4 A,B,C 2 1 1 AB 2

12. Delete a Transaction in DIU Tree • Conditions to Check for Closed Itemsets • When the number of the transactions with same itemset of X is equal to zero, if Y is a subset of X, and Y is a closed itemset in the original transaction set

13. Closure Checking for Deletion

14. 2 2 • C,D 2 A,B 3 A,B,C 4 A,B,C 3 C 3 1 CD AB 2 ABC

15. Experiment • Synthetic datasets T10.I6.D100K and T5.I4.D100K

16. Experiment

17. Experiment