1. Sequential PAttern Mining using A Bitmap Representation
2014/11/20
Sequential PAttern Mining using A Bitmap Representation
Jay Ayres, Johannes Gehrke, Tomi Yiu, and Jason Flannick
Dept. of Computer Science Cornell University (SIGKDD 2002)
Presenter
李佩書 P
楊璨瑜 P
陳奕廷 P
李昕純 Q

2. Outline Introduction The SPAM algorithm Data representation
2014/11/20
Outline
Introduction
The SPAM algorithm
Data representation
Experimental
Conclusion & Discussion

3. 2014/11/20
Introduction

4. Sequential Patterns R. Agrawal and R. Srikant.(In ICDE 1995)
2014/11/20
Sequential Patterns
R. Agrawal and R. Srikant.(In ICDE 1995)
Algorithm：AprioriALL, AprioriSOME, PrefixSpan…

5. Problem Mining sequential patterns Given a minimum support minSup
2014/11/20
Problem
Mining sequential patterns
Given a minimum support minSup
Find all frequent sequential patterns Sa
supD(Sa) ≥ minSup

6. SPAM Algorithm Sequential PAttern Mining Algorithm
2014/11/20
SPAM Algorithm
Sequential PAttern Mining Algorithm
The first DFS(depth-first search) strategy for mining sequential patterns
Vertical bitmap representation for simple, efficient counting.

7. 2014/11/20
The SPAM Algorithm

8. Lexicographic Tree Sequence-extended Sequence (S-step)
2014/11/20
Lexicographic Tree
Sequence-extended Sequence (S-step)
Generate by adding a new transaction consisting of a single item to the end of sequence
Ex: ({a, b, c}, {a, b})→({a, b, c}, {a, b}, {a})
Itemset-extended sequence (I-step)
Generate by adding an item to the last itemset in the sequence
Ex 1: ({a, b, c}, {a, b}) →({a, b, c}, {a, b, d})
Ex 2: ({a, b, c}, {a, b, d}) →({a, b, c}, {a, b, d, c})
Identifies two sets of each node n
Sn: the set of candidate items for S-step extensions
In: the set of candidate items for I-step extensions

9. 2014/11/20
I={a,b}

10. Pruning Apriori-Based Minimizing the size of Sn and In
2014/11/20
Pruning
Apriori-Based
Minimizing the size of Sn and In
Pruning candidate by DFS.
S-step Pruning
I-step Pruning

11. S-step Pruning S({a}) = {a, b, c, d} I({a}) = {b, c, d}
2014/11/20
S-step Pruning
S({a}) = {a, b, c, d}
I({a}) = {b, c, d}
S({a}, {a}) = S({a}, {b}) = {a, b, c, d}
I({a}, {a}) = {b, c, d}
I({a}, {b}) = {c, d}

12. I-step Pruning S({a, b}) = S({a, d}) = {a, b} I({a}, {b}) = {c, d}
2014/11/20
I-step Pruning
S({a, b}) = S({a, d}) = {a, b}
I({a}, {b}) = {c, d}
I({a}, {d}) = {}

13. 2014/11/20

14. 2014/11/20
Data Representation

15. We store each candidate sequence as a vertical bitmap
2014/11/20
We store each candidate sequence as a vertical bitmap
Each customer is assigned a fixed slice of each bitmap for all of its transactions
If the size of a sequence between 2k+1 and 2k+1
2k+1-bit sequence

16. 2014/11/20
Bitmap of itemset
{a}
{b}
{a,b} 1 1 1
&

17. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c})

18. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c})

19. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c})

20. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c})

21. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c})

22. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c}) 1

23. Bitmap of sequence Define B(s) as the bitmap for sequence s. Example1:
2014/11/20
Bitmap of sequence
Define B(s) as the bitmap for sequence s.
In sequence s
If the last itemset is in transaction j and the other itemsets is in transaction before j
Then set 1，otherwise set 0
Example1:
Customer ID
Transaction ID
Itemset 1
{b} 2
{d} 3
{e} 4
{c}
({b},{c}) 1

24. Example2 ({a},{b,d}) Customer ID Transaction ID Itemset 1 {a,b,d} 3
2014/11/20
Example2
Customer ID
Transaction ID
Itemset 1
{a,b,d} 3
{b,c,d} 6 --
({a},{b,d}) 1

25. 2014/11/20
S-step Process
Step 1 : S-Step Process to construct the transformed bitmap ({a})s
Step 2 : ANDing B({a})s and B({b})s
Support=2

26. 2014/11/20
S-step Process
Step 1:S-Step Process to construct the transformed bitmap ({a})s
Step 2:ANDing B({a}) s and B({b})s

27. 2014/11/20
I-step Process
Support=2

28. 2014/11/20
I-step Process

29. 2014/11/20
Experimental

30. Comparison With SPADE and PrefixSpan
2014/11/20
Comparison With SPADE and PrefixSpan
Method-1
Compare for various minimum support values on
Small datasets
Medium datasets
Large datasets
Methods-2 Compare several parameters in the dataset
Number of customers
Number of transactions per customer
Number of items per transaction
Average length of the maximal sequences

31. 2014/11/20

32. Conclusion & Discussion
2014/11/20
Conclusion & Discussion

33. CONCLUSION ALGORITHM DATA REPRESENTATION
2014/11/20
CONCLUSION
ALGORITHM
Outperforms SPADE and PrefixSpan on large datasets
Faster then SPADE and PrefixSpan
DATA REPRESENTATION
Bitmap representation
S-step/I-step traversal
S-step/I-step pruning
Especially efficient when the sequential patterns are very long

34. Implement SPAM algorithm
2014/11/20
Implement SPAM algorithm
SPMF is an mining mining framework
Written in Java/Open-source data
Philippe-Fournier-Viger, Antonio Gomariz, Ted Gueniche, Azadeh Soltani, Cheng-Wei Wu and Vincent S. Tseng, "SPMF: a Java Open-Source Pattern Mining Library," accepted and to appear in Journal of Machine Learning Research.  

35. 2014/11/20
DISCUSSION
SPAM assumes that the entire database completely fit into main memory, what is the solution ?
Why they set the size of a sequence between 2k+1 and 2k+1 ?