1. Incremental Discovery of Sequential Patterns (ACM-SIGMOD's 96 Data Mining Workshop)

2. Abstract produces the update patterns by scanning only the affected part of the database and data structure handles the dynamism of the minimum support and confidence without recomputat- ion

3. Suffix Trees sequence S : –a list of records ordered by position number starting with 1 –delimited by the special symbol $ that occurs only at the right end of the list –ex. S = 123523423$ suffix tree T for S –whose paths are the suffix of S –whose terminal nodes correspond uniquely to positions within S

4. Suffix Trees properties of suffix tree T for S –T1: An arc of T may represent any nonempty subsequence of S –T2: Each nonterminal node of T, except the root, must have at least two offspring arcs –T3: The subsequences represented by sibling arcs of T must begin with different records

5. Example 2.1 S = 123523423$

6. Suffix Trees Straightforward way  O(n 2 ) Linear Time Construction –is to start the search at the lowest possible level, by maintaining suffix links between nonterminal nodes of the tree –a suffix link from u to v is created if the paths from the root to u and v have the form x  and , respectively u, v : nonterminal node x : a single record,  : a subsequence

7. Sequential Patterns support of a subsequence  w.r.t S –the number of positions in S at which  occurs locus(  ) –the first node in T encounted after  is spelled out v.support –the number of terminal nodes in the subtree rooted at a nonterminal node v

8. Sequential Patterns  is a pattern if –locus(  ).support  min_sup and –locus(  ).support/locus(  ).support  min_conf pattern tree(w.r.t min_sup) –the portion of T above all nonterminal nodes v such that v.support  min_sup

9. A Single Sequence How to update T when S =    Update Strategy –  * : the longest suffix of  which occurs in at least two different places in  –  -splitters : those sequences of the form , where  is a nonempty suffix of  *  –delete all  -splitters from T, and insert into T all  -splitters of the form , where  is a nonempty suffix of  * 

10. Update Strategy Example S = 123523423$,  = 52   = 678 –  : 123,  = 3423$,  * : 23 –delete all  -splitters from T  *  : 2352  -splitters : 2 , 52 , 352 , 2352  –insert all  -splitters into T  *  : 23678  -splitters : 8 , 78 , 678 , 3678 , 23678 

12. Support by Occurrences The database consists of multiple sequences support of a sequence  –the sum of the support of  in all sequences D = {S 1, …, S k } replace D with S = {S 1 $ 1, …,S k $ k } to locate all paths of a sequences, a B+tree on pairs (id, head) is maintained with id being the search key

13. Figure. Locating all suffixes of a sequence

14. Support by Sequences Support of a subsequence  –the number of sequences in which  occurs