Incremental Mining of Web Sequential Patterns Using PLWAP Tree on Tolerance MinSupport

1. Incremental Mining of Web Sequential Patterns Using PLWAP Tree on Tolerance MinSupport C.I. Ezeife Min Chen IDEAS’04

2. Introduction • This paper proposes an algorithm, PL4UP, which uses the PLWAP tree structure to incrementally update web sequential patterns. • The process of generating new patterns in the updated database (old + new data) using only the updated part (new data) and previously generated patterns is called incremental mining of sequential patterns.

3. The Proposed Incremental PL4UP Algorithm • F :frequent items S: small items • F’: updated large (frequent) items S’: updated small items in the updated database U (old + new data) six categories of items : (1) large in old database, DB and still large in updated database U (F→F’) (2) large in old DB but small in U (F→S’) (3) small in old DB but large in U(S→F’) (4) small in old DB and still small in U(S→S’) (5) new items that are large in U (∅ →F’) (6) new items that are small in U (∅ →S’). The main idea of PL4UP is to avoid scanning the whole updated database, U (DB+db) but to scan only the changes to the database (db).

4. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP • 1. Construct initial PLWAP tree using tolerance minimum support, t • t = factor * s 0≤factor≤1. • frequent 1-items (meeting support s), F1 • frequent 1-items (meeting support t), Ft • Small 1-items (not meeting support s), S1. • potentially frequent 1-items (in S1 list but meeting support t), PF1. • potentially still small 1-items, SS1 (in S1 list but not meeting the support t) • we obtain two subsequences, the frequent subsequence meeting s requirements (seq s) and the frequent subsequence meeting the t requirements (seq t).

5. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP >3 >2 C1 ={a:5, b:5, c:3, d:1, e:2, f:2:, g:1, h:1}. F1 ={a, b, c} >=3 Ft ={a, b, c, e, f} >=2 S1 ={e, f, d, g, h}, <3 PF ={e, f} 2=<X<3 SS ={d, g, h} <2

6. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP

7. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP After checking all patterns, the list of TFP mined is:{a:5, aa:4, aac: 3, ab:5, aba:4, abac:3,abc:3, abcc:2, abe:2, abf:2, ac:3, acc:2, ae:2, af:2, b:5.ba:4, bac:3, bab:1, bc:3, bcc:2, be:2, bf:2, c:3, cc:2,e:2, f:2}. SFP ={a:5, aa:4, aac: 3, ab:5, ac:3, aba:4,abac:3, abc:3, b:5. ba:4, bac:3, bc:3, c:3}.

9. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP C’1 = C’1∪Cdb1 . C1 ={a:5, b:5, c:3, d:1, e:2, f:2:, g:1, h:1}. Cdb1={a:2, b:1, e:2, f:2, g:2, h:2}, C’1 ={a :7,b : 6,c : 3,d : 1,e : 4,f : 4,g : 3,h : 3}. F’1 ={a : 7,b : 6,e : 4,f :4} >=4 F’t ={a : 7,b : 6,c : 3,e : 4,f : 4,g : 3,h : 3}.>=3 Fdb1 = Cdb1∩F’1={a:2, b:1, e:2, f:2}. Fdbt = Cdb1∩F’t={a : 2,b : 1,e : 2,f : 2,g : 2,h : 2}. Sdb1 = Cdb1∩S’1={g:2}. PF’={c:3, g:3, h:3 }. PFdb= Cdb1∩PF’={g:2, h:2}. SS’={d:1}. SSdb= Cdb1∩SS’=∅

10. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP Fdbt = Cdb1∩F’t ={a : 2,b : 1,e : 2,f : 2,g : 2,h : 2}.

11. 2.1 Steps in Mining Frequent PatternsIncrementally with PL4UP The mined TFPdb={a:2, ae:2, aef:2, af:2, b:1, ba:1, bae:1, baef:1, be:1, bf:1, ..., e:2, ef:2, f:2} =SFPdb • SFP’=TFP∪ SFPdb ={a:7, aa:4, aac:3, ab:5,aba:4, abac:3, abc:3, ac:3, ae:4, af:4, b:6, ba:5, bac:3,bc:3, be:3, bf:3, c:3, e:4, f:4} SFP’={a:7,aa:4, ab:5, aba:4, ae:4, af:4, b:6, ba:5, e:4, f:4} >4 • TFP’=TFP∪ TFPdb ={a:7, aa:4, aac:3, ab:4, aba:4, abac:3, abc:3,ac:3, ae:4, af:4, b:6, ba:5, bac:3, bc:3, be:3, bf:3, c:3,e:4, f:4}.

12. SSM : A Frequent Sequential Data Stream Patterns Miner C.I. Ezeife, Mostafa Monwar CIDM 2007

13. Introduction Existing work on mining frequent patterns on data streams are mostly for non-sequential patterns. This paper proposes SSM-Algorithm (Sequential Stream Mining-algorithm), that uses three types of data structures 1.D-List, 2.PLWAP tree 3.FSP-tree to handle the complexities of mining frequent sequential patterns in data streams.

14. Example Assume a continuous stream with rst stream batch B1 consisting of stream sequences as: [(abdac, abcac , babfae, afbacfcg)]. minimum support, s is 0.75 tolerance error e, is 0.25 C1B1 = {a:4, b:4, c:3, d:1, e:1, f:2, g:1} L1B1 = {a:4, b:4, c:3, f:2}. >=2 For the items (a, b, c, d, e, f, g) given as (2, 100, 0, 202, 10, 110, 99) are used in the hash function (mod 100)

15. Example

16. Example • Step 3: Construct FSP-tree and insert all FPB1 into FSPtree without pruning any items for the rst batch B1 to obtain Figure 5. • FPB1 = {a:4, aa:4, aac:3, ab:4,aba:4, abac: 3, abc: 3, ac: 3, acc:2, af: 2, afa: 2, b: 4, ba:4, bac: 3, bc: 3, c: 3, cc: 2, f: 2, fa: 2}.

17. Example • When the next batch, B2 of stream sequences, (abacg, abag, babag, abagh) arrives, • 1.The SSM updating the D-List using the stream sequences. • 2.deletes all elements not meeting the minimum tolerance support of |D| * e (or 8 * 0.25 = 2) from the D-List, and keeps all items with|D| ∗ (s − e) = 8 ∗ 0.5 = 4 frequency counts in the L1B2 • 3. construct PLW APB2 • 4.mined to generate the FSPB2 . This FSPB2 is used for obtaining frequent sequential patterns on demand.

18. Incremental Mining of Sequential Patterns over a Stream Sliding Window Chin-Chuan Ho, Hua-Fu Li *, Fang-Fei Kuo and Suh-Yin Lee

19. introduction • For mining of sequential patterns over data streams, there are three models adopted by many researchers in ways of time spanning: landmark model sliding window model, and damped window model • IncSPAM= sliding window model+ SPAM

20. 3. The IncSPAM Algorithm

21. 3.1 A Brand-New Concept of Sliding Windowfor Sequences

22. 3.2 Customer Bit-Vector Array with SlidingWindow (CBASW)

23. 3.2 Customer Bit-Vector Array with SlidingWindow (CBASW)

24. 3.2 Customer Bit-Vector Array with SlidingWindow (CBASW)

25. 3.2 Customer Bit-Vector Array with SlidingWindow (CBASW)

26. 3.6 Incremental Mining of Sequential Patternsusing SPAM (IncSPAM)

27. 3.6 Incremental Mining of Sequential Patternsusing SPAM (IncSPAM)

28. 3.7 Weight of Customer-Sequence

29. COMPARE