1. Jian Pei Jiawei Han Behzad Mortazavi-Asl Helen Pinto ICDE’01
PrefixSpan : Mining Sequential Patterns Efficiently by Prefix-Projected Pattern Growth
Jian Pei Jiawei Han Behzad Mortazavi-Asl Helen Pinto
ICDE’01

2. Outlines What is sequential pattern mining? Our previous study
FreeSpan approach
PrefixSpan approach
Conclusion
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3. Sequential Pattern Mining
Finding complete set of frequent subsequences(time-related)
Broad applications : Most data and applications are time-related
Customer shopping sequences:
Natural disasters
Disease and treatment
Stock market fluctuation …
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4. Sequential Pattern Mining
A sequence :
<(ef) (ab)(df)cb >
A sequence database
SID
sequence 10
<a(abc)(ac)d(cf)> 20
<(ad)c(bc)(ae)> 30
<(ef)(ab)(df)cb> 40
<eg(af)cbc>
Elements : items with an element are listed alphabetically
<a(bc)dc> is a subsequence of <a(abc)(ac)d(cf)>
SID
sequence 10
<a(abc)(ac)d(cf)> 20
<(ad)c(bc)(ae)> 30
<(ef)(ab)(df)cb> 40
<eg(af)cbc>
Given support threshold Min_sup = 2, <(ab)c> is a frequent sequential pattern
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5. Previous studies on sequential pattern mining
Concept introduction and an initial Apriori-like algo.
R.Agrawal & R.Srikant. Mining sequential patterns, ICDE’95
GSP : an apriori-based, influential mining method
R.Skrikant & R.Agrawal. Mining sequential patterns: Generalizations and performance improvements, EDBT’96
A projection-based sequential pattern mining method
J. Han, J. Pei, B. Mortazavi. FreeSpan: Frequent pattern-projected sequential pattern mining, KDD’00
2005/4/14
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6. FreeSpan : Frequent Pattern-Projected Sequential Pattern Mining
A divide-and-conquer approach
Recursively project a sequence database into a
set of smaller databases based on the current
set of frequent patterns
Mining each projected database to find its
patterns
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7. FreeSpan approach Def: Step 1: finding f_list -projected database
Ex : b(ce) - projected database = <b(ce)b>
Step 1: finding f_list
Min_sup = 2
f_list = <b:5, c:4, a:3, d:3, e:3, f:3>
SID
sequence 10
<(bd)cb(ac)> 20
<(bf)(ce)b(fg)> 30
<(ah)(bf)abf> 40
<(be)(ce)d> 50
<a(bd)bcb(ade)>
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8. FreeSpan approach
Step 2: using the f_list to construct the following matrix
Table 1: Frequent item matrix after scan of S
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9. FreeSpan approach
Step 3 : using the matrix to generate the ann. of repeating items and projected DBs
Table 2 : Pattern generation from the frequent item matrix
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10. FreeSpan approach Based on the ann. for item-repeating patterns
We get {<bbf>:2, <fbf>:2, <(bf)b>:2, <(bf)f>:2 …}
Based on the ann. for projected DBs
Table 3 : Projected databases and their sequential patterns
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11. PrefixSpan Def : Prefix and Postfix(Projection)
<a>, <aa>, <a(ab)>, and <a(abc)> are prefixes of sequence <a(abc)(ac)d(cf)>
Given sequence <a(abc)(ac)d(cf)>
Prefix
Postfix / Projection
<a>
<(abc)(ac)d(cf)>
<aa>
<(_bc)(ac)d(cf)>
<ab>
<(_c)(ac)d(cf)>
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12. PrefixSpan approach Step 1: find length-1 sequential patterns
<a>, <b>, <c>, <d>, <e>, <f>
Step 2: divide search space.The complete seq. pat. can be partitioned into 6 subsets:
The ones having prefix <a>;
The ones having prefix <b>; …
The ones having prefix <f>;
SID
sequence 10
<a(abc)(ac)d(cf)> 20
<(ad)c(bc)(ae)> 30
<(ef)(ab)(df)cb> 40
<eg(af)cbc>
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13. PrefixSpan approach Step 3 : Finding subsets of sequential patterns
Only need to consider projections w.r.t <a>
<a>-projected database: <(abc)(ac)d(cf)>, <(_d)c(bc)(ae)>, <(_b)(df)cb>, <(_f)cbc>
Find all the length-2 seq. pat. having prefix <a>: <aa>, <ab>, <(ab)>, <ac>, <ad>, <af>
Further partition into 6 subsets
Having prefix <aa>;
Having prefix <ab>; …
Having prefix <af>;
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14. Completeness of PrefixSpan
SDB
SID
sequence 10
<a(abc)(ac)d(cf)> 20
<(ad)c(bc)(ae)> 30
<(ef)(ab)(df)cb> 40
<eg(af)cbc>
Length-1 sequential patterns
<a>, <b>, <c>, <d>, <e>, <f>
Having prefix <c>, …, <f>
Having prefix <a>
Having prefix <b>
<a>-projected database
<(abc)(ac)d(cf)>
<(_d)c(bc)(ae)>
<(_b)(df)cb>
<(_f)cbc>
<b>-projected database …
Length-2 sequential
patterns
<aa>, <ab>, <(ab)>,
<ac>, <ad>, <af>
… …
Having prefix <aa>
Having prefix <af>
<aa>-proj. db …
<af>-proj. db
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15. Conclusion FreeSpan v.s. PrefixSpan PrefixSpan:
Projection-based : No candidate sequence
needs to be generated
Projection can be performed at any point in the
sequence, and the projected sequences do will not
shrink much
PrefixSpan:
Projection-based
Only prefix-based projection : less projections
and quickly shrinking sequences
2005/4/14
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