An Efficient Algorithm for Mining Frequent Itemests over the Entire History of Data Streams

1. An Efficient Algorithm for Mining Frequent Itemestsover the Entire History of Data Streams Hua-Fu Li, Suh-Yin Lee, and Man-Kwan Shan. Accepted for publication in the Proceedings of First International Workshop on Knowledge Discovery in Data Streams, to be held in conjunction with the 15th European Conference on Machine Learning (ECML 2004). Adviser: Jia-Ling Koh Speaker: Shu-Ning Shin Date: 2005.3.4

2. Introduction • This paper proposes a single-pass algorithm, called DSMFI(Data Stream Mining for Frequent Itemsets), has three major features: • single streaming data scan for counting itemsets’ frequency information. • extended prefix-tree-based compact pattern representation. • top-down frequent itemset discovery scheme.

3. Problem Definition (1) • Item: Ψ={i1, i2, …, im} • Data Stream: DS=B1, B2, …,BN • Block: B=[tsi, T1, T2, …, Tk] • Current Length of Data Stream: CL=|B1|+|B2|+ …+|BN| • Minimum support: • Maximal estimated support error:

4. Problem Definition (2) • True Support of itemset X: Tsup(X) • Estimated Support of X: Esup(X) • X is frequent itemset if • X is sub-frequent itemset if • X is infrequent itemset if

5. Data Structure: IsFI-forest (1) • Item-suffix Frequent Itemset forest. • Extended prefix-tree-based summary data structure. • Definition: • 1. Is-FI forest consist of: • DHT: Dynamic Header Table • a set of CFI-trees (item-suffixes): Candidate Frequent Itemset trees of item-suffixes.

6. Data Structure: IsFI-forest (2) • 2. Entry of DHT: • item-id, support, block-id, head-link. • 3. Entry of CFI-tree(item-suffix): • item-id, support, block-id, node-link. • 4. Each CFI-tree(item-suffix) has a specific DHT(item-sufix)

7. Construction of IsFI-forest • 1. Read a transaction T=(x1x2..xk) from current block BN. • 2. Item-suffix projection IsProjection(T): transaction T is converted into k small transactions (x1x2..xk), (x2..xk),…, (xk-1xk), (xk). • 3. insert IsProjection(T) into IsFI-forest.

8. Algorithm: DSM-FI • DSM-FI is composed of four steps: • step 1 : reading a block of transactions • step 2: constructing IsFI-forest • step 3: pruning the infrequent information from IsFI-forest • Step 4: top-down frequent itemset discovery scheme

9. Example • ms=30%, ε=25% • DS={B1, B2} • B1={(acdef), (abe), (cef), (acdf), (cef), (df)} • B2={(def), (bef), (be), (bde)} • DSM-FI: • Step 1. Read B1 into main memory • Step 2. constructing the IsFI-forest • Step 3. pruning infrequent item • Step 4. mine frequent itemset from IsFI-forest

10. Example – step 2 (1) • (1) T1=acdef • IsProjection(acdef)=acdef, cdef, def, ef, f • [CFT-tree(a), DHT(a)], [CFT-tree(c), DHT(c)], [CFT-tree(d), DHT(d)], [CFT-tree(e), DHT(e)] [CFT-tree(f), DHT(f)] CFT-tree(f) CFT-tree(e) CFT-tree(d) CFT-tree(c) CFT-tree(a)

11. Example – step 2 (2) • (2) T2=abe • IsProjection(abe)=abe, be, e • [CFT-tree(a), DHT(a)], [CFT-tree(b), DHT(b)], [CFT-tree(e), DHT(e)]

12. Example – step 2 (3) • (6) T6=df • IsProjection(abe)=df, f • [CFT-tree(d), DHT(d)], [CFT-tree(f), DHT(f)]

13. Example – step 3 • b is a infrequent item: Esup(b)<0.25*6 • delete CFI-tree(b), DHT(b) and entry b.

14. Example – Step 4 • Start top-down frequent itemset discovery from frequent item a: (frequent: ms*CL=0.3*10=3) Maximal candidate: def Two-candidate: de, df Maximal candidate: cef Maximal candidate: ef Maximal candidate: be Frequent: a be is frequent Tsup(ef)=2 not frequent de, df are frequent TSup(cef)=3, frequent {c, e, f, ce, cf, ef, cef}

15. Upper Bound of Space • i=1, 2, …, k • Nodes of all DHT(i): • (k2-k)/2 • Nodes of the set of CFI-trees:

16. Maximal Estimated Error • (X, X.support, X.block_id) • X.block_id=1: • Tsup(X)=Esup(X) • X.block_id>1: • k: the average size of block

17. Performance (1) • IBM Dataset: T10.I5.D1M, T30.I20.D1M. • 20 blocks with size 50K. • Compare execution time and memory usage of DSM-FI:

18. Performance (2) • Compare of DSM-FI and Lossy Counting: