1 Mining Sequential Patterns with Constraints in Large Database Jian Pei, Jiawei Han,Wei Wang Proc. of the 2002 IEEE International Conference on Data Mining (ICDM’02) Adviser: Jia-Ling Koh Speaker: Yu-ting Kung

2 Introduction In past studies, two problems remain: 1. Many practical constraints are not covered 2. There lack a systematic method to push various constraints into the mining process In this paper: Develop a framework—Prefix-growth, is built based on a prefix-monotone property The constraints can be effectively and efficiently pushed deep into sequential pattern mining under this new framework

3 Categories of constraints 1. Item constraints For example: 2. Length constraint The number of transactions or occurrences of items… For example:

4 Categories of constraints (Cont.) 3. Super-pattern constraint where P is a given set of patterns For example: 4. Aggregate constraint Aggregate function: sum, avg, max, min,etc For example: We like sequential patterns where average price of all the items in each pattern is over $100

5 Categories of constraints (Cont.) 5. Regular expression constraints Constraints specified as a regular expression For example: 6. Duration constraints 7. Gap constraints For example: Find purchasing patterns such that “the gap between each consecutive purchases is less than 1 month”

6 Characterization of constraints Anti-monotonic If a sequence  satisfies C implies that every non- empty subsequence of  also satisfies C For example: dur(  ) < 3 Monotonic If a sequence  satisfies C M implies that every super- sequence of  also satisfies C M For example: len(  ) >= 10, super-pattern constraints Succinct constraint For example: item-constraint

7 Characterization of constraints (Cont.)

8 Prefix-Monotone Property Prefix anti-monotonic for each sequence  satisfying the constraint, so does every prefix of  Prefix monotonic for each sequence  satisfying the constraint, so does every sequence having  as a prefix. A constraint is called Prefix-monotone if it is prefix-monotonic or prefix monotonic.

9 Theorem All the commonly used constraint discussed above, except for g_sum and average, have prefix-monotone property

10 Push Prefix-Monotone Constraints into Sequential Pattern Mining Regular expression Min_sup = 2

11 Push Prefix-Monotone Constraints into Sequential Pattern Mining (Cont.) Mining step: 1. find length-1 sequential and remove irrelevant sequence Patterns,,,, are identified as length-1 patterns, infrequent item is removed S_id = 10 is removed  fail this constraint 2. divide the set of sequential patterns into subsets without overlap prefix, prefix, prefix, prefix, prefix are pruned!!

12 Push Prefix-Monotone Constraints into Sequential Pattern Mining (Cont.) 3. construct -projected database and mine it SDB| ={,, } Locally frequent items and satisfy the constraint:  prefix, prefix, prefix 4. recursive mining To mining patterns with prefix 、 、, and form the projected database 5. Final pattern outputted {, }

13 Handling Touch aggregate constraint Constraint: Min_sup = 2 Item i called a small item if its value i.value <= 25, otherwise, it is called a big item

14 Experimental results Compare the efficiency of mining sequential patterns without constraint

15 Experimental results (Cont.) Compare the efficiency of mining sequential patterns with constraint Capability of GSP and prefix-growth on pushing anti- monotone constraint (dur(  ) <= t)

16 Experimental results (Cont.) Experimental results on mining with regular expression constraint

17 Experimental results (Cont.)  Scalability of prefix-growth with Constraint avg(  ) ≤ v Number of projected databases in prefix-growth with Constraint avg(  ) ≤ v 

18 Experimental results (Cont.) Scalability of prefix-growth w.r.t. support threshold

19 Experimental results (Cont.) Scalability of prefix-growth w.r.t. database size

20 Conclusion Prefix-monotone property covers many commonly used constraints Experiment results and performance study show that prefix-growth is efficient and scalable in mining large databases