1. A new algorithm for gap constrained sequence mining
Salvatore Orlando, Raffaele Perego,Claudio Silvestri
Proceedings of 2004 ACM Symposium on Applied Computing
Advisor：Jia-Ling Koh
Speaker：Chun-Wei Hsieh
11/19/2004

2. Problem
A sequence occurs in under the minimum gap and maximum gap constraints, denoted as , if there exists integers
such that
, and

3. Min_gap constraint: Let be an input database sequence. If ,
then all its subsequences , , satisfy .
Min_gap constraint is an anti-monotone constraint

4. Max_gap constraint:
Let be an input database sequence.
If ,
then all its subsequences , , satisfy . ?
Max_gap constraint is not an anti-monotone constraint

5. SPADE might loose candidates
A candidate k-sequence is made by a pair of frequent (k-1) –subsequences that share a common (k-2)-preffix. .
SPADE might loose candidates

6. Contiguous sequences
is obtained from by dropping an item from either or ;
is obtained from by dropping an item from , where ;
is a contiguous subsequence of ,
and is a contiguous subsequence of

7. Prefix and Suffix Subsequence
Max_gap constraint becomes anti-monotone, when using contiguous subsequence.
A prefix or suffix of a sequence is a particular contiguous subsequence of

8. cSPADE destroys the prex-class
cSPADE solves the problem by using the contiguous subsequence concept.
It combines the (k-1)-prex and 2-sux of are contiguous subsequences of .
cSPADE destroys the prex-class

9. CCSM 1) Count-based phase: scanning the database and mining the and
2)The horizontal database is transformed into a
vertical one.
3) Intersection-based phase: generating the
candidate k-sequence by merging
with such that

10. Candidate generation
Figure 1: CCSM candidate generation.

11. Idlist intersection
To determine the support of a candidate k-sequence p, we have first to produce the associated idlist L(p).
, , and can be joined to produce .

12. Idlist intersection .

13. Idlist intersection Order.
Left to right :
store the eid of the last item/event
Right to left :
store the eid of the first item/event
(sid,eid) (sid, first_eid,last_eid)

14. Idlist caching Figure 2: Example of cache usage.
Figure 3: CCSM idlist reuse.

15. Experiment 1
Figure 4: Number of intersection operations actually performed using 2-ways,
pure k-ways and cached k-waysintersection methods while mining two synthetic
datasets.

16. Experiment 2
Figure 5: Number of frequent sequences in datasets CS11 (minsup=0:30)
and CS21(minsup=0:40) as afunction of the pattern length for dierent
values of the max gapconstraint.

17. Experiment 3
Figure 6: Execution times of CCSM and cSPADE on datasets CS11 (minsup=0:30)
and CS21 (minsup=0:40)as a function of the max gap value.

18. Experiment 4
Figure 7: Execution times of CCSM and cSPADE on datasets CS11 and CS21 with a xed max gap constraint(max gap=8) as a function of the minimum support threshold.