Constraintbased sequential pattern mining: the patterngrowth method

1
Constraint-based sequential pattern mining the
pattern-growth method
AuthorsJian Pei, Jiawei Han, and Wei
Wang SourceJournal of Intelligent Information
Systems, Volume 28, Number 2, pp.133-160,
2007/4 ReporterChin-Chih Chan Date2007/12/17 E-m
ail m9622967
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Outline

• Introduction
• Definition
• Constraint Sequential pattern mining
• Categories of constraints
• Algorithm PG
• Computing projection
• Mining sequential patterns with prefix-monotone
  constraints
• Experimental results and performance

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Introduction

• Sequential pattern mining is an important data
  mining task with broad applications
• Sequential pattern mining finding the often
  occur sequence in a large database
• Often occur the support of the sequence the
  user defined minimum support
• Support of sequence s how many sequence in DB
  contain s
• Applications network traffic analysis, bio
  information

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Example sequential pattern mining

• If the support threshold min_sup 2
• (ab)d is a subsequence of both the second
  sequence, lt e(ab)(bc)dd gt, and the third one,
  lt c(aef )(abc)ddgt
• (ab)d is one of the sequential pattern

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Introduction

• Mining the complete set of sequential patterns is
  still tough in both effectiveness and efficiency
• We want to only mine the sequential patterns that
  are highly interesting to users
• Improve the effectiveness by focusing only on
  interesting patterns
• We want to mine sequential patterns with all
  kinds of constraints

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Pattern-growth (PG) method

• We present a algorithm pattern-growth (PG)
• Constraints can be effectively and efficiently
  pushed deep into the sequential data mining method

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Sequential pattern mining concepts

• I x1, , xn be a set of items
• An itemset is a non-empty subset of items
• A sequence a ltX1, , Xlgt is an ordered list of
  itemsets
• An itemset Xi (1 ? i ? l ) in a sequence is
  called a transaction
• The number of transactions in a sequence is
  called the length of the sequence
• For an l-sequence a, we have len(a) l

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Subsequence and super-sequence

• A transaction Xi have a special attribute,
  times-stamp, denoted by Xi.time
• For a sequence a lt X1, , Xl gt, we assume
  Xi.time lt Xj.time for 1? I lt j ? l
• lt X1, X2gt ? lt X2, X1gt
• A sequence a lt X1, , Xn gt is called a
  subsequence of sequence ß lt Y1, , Ym gt (n?m),
  denoted by a?ß, if there exist integers 1?
  i1ltltin ? m such that Xi ? Yi1, , Xn ? Yin
• And ß is a super-sequence of a

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Example subsequence

• Sequence lt(ab)dgt is a subsequence of both
  lte(ab)bcddgt and ltc(aef)(abc)ddgt

e
(ab)
d
b
c
d
c
(aef)
d
(abc)
d
(ab)
d
(ab)
d
Contain and in time order
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Categories of constraints

• Constraint 1 (Item constraint)
• Example Cbookstore (a) (?i 1 i len(a),
  a i ? B)
• Constraint 2 (Length constraint )
• Example Clen(a) (len(a) 50)
• Constraint 3 (Super-pattern constraint)
• Example Cpat(a) lt (PC)(digital_camera) gt?a
• Constraint 4 (Aggregate constraint)
• Example Cavg(a) avg(a) 30
• Constraint 5 (Regular expression constraint)
• Example Travel ( New York New York City )
  ( Hotels Motels )

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Algorithm PG

• Difference with traditional sequential pattern
• Definition
• Prefix
• Projection
• Projected DB
• Algorithm PG

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The classical sequential pattern mining

• The claaical Apriori property base algorithm
• Property any super-pattern of an infrequent
  pattern cannot be frequent
• A breadth-first, level-by-level search
• Just squeeze constraints into the
  Apriori-framework
• However, some important constraints can not be
  solved with Apriori property base
• EX regular expression

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Prefix growth(PG) algorithm

• A prefix-monotone property
• Can solve most of the constraints discussed so
  far
• PG push such constraints into sequential pattern
  mining
• Make it more efficiency and effectiveness
• Efficiency take less computational time and
  space
• Effectiveness some pattern that user didnt
  interesting is pruned

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Definition order

• All items in a transaction are written with
  respect to the order R
• written in the form of (ade)(bc) instead of
  (dae)(cb)
• item x precedes item y is denoted by x ? y
• The alphabetical order is often used

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Definition the prefix

• Given a sequence a lt X1 , , Xn gt, sequence
  ß lt X1 , , XkY gt is called a prefix ofa
  if
• (1) k lt n
• (2) Y ? Xk1
• (3) ?y ? Y, ?z ? (Xk1 - Y), y ? z
• Example sequence a lt(abc)(acd)(bef ) gt
• sequence ß lt(abc)(ac)gt is a prefix of sequence
  a
• sequence ? lt (abc)(ad) gt is not a prefix of a

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The concept of projected database

• For sequence a ? ß, sequence ? is said the
  projection of ß with respect to a if
• (1) ? ? ß
• (2) a is a prefix of ?
• (3) there exists no proper super-sequence ? of ?
  such that ? ? ß and ? also has a as a prefix
• Projection is also denoted by ? ß / a

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Example for projection

• For example, if a bc, ß (abc)d(ace) f , then
  ? ß/a b(ce) f

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Algorithm for computing projection
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Example for computing projection

• For example, if a bc, ß (abc)d(ace) f , then
  ? ß/a b(ce) f

J1
J2
J3
J4
d
(abc)
(ace)
f
x c
Z e
c
b
Output lt b (c ? e) f ) gt
i2
i1
A2
A1
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Algorithm for PG
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Flow for PG
Sequence DB S
Scan S for 1-item support
ltagt
ltbgt
ltcgt
If frequent then do
ltagt-projected DB
ltbgt-projected DB
ltcgt-projected DB
Scan ltagt-projected DB for 2-sequence support
ltaagt
ltabgt
ltacgt
lt(ab)gt
lt(ac)gt
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Example for mining sequential patterns with
prefix-monotone constraints

• The task be mining sequential patterns with a
  regular expression constraint
  C a bb(bc)ddd and min_sup 2

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Prefix_growth(ltgt, SDB)
SDBltgt

• Let l be the length of ltgt, Scan SDB ltgt,
  find length-(l 1) frequent prefix in SDBltgt

ltagt 4, ltbgt 4, ltcgt 4, ltdgt 3, ltegt 3
ltf gt 1, is Infrequent item
SDBltgt
lta(bc)egt contains no subsequence satisfying the
constraint
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SDBltagt
lt a gt fails C
lt (ae) gt 1, is Infrequent item lt aa gt 1, is
Infrequent item
lt (ab) gt 2, ltabgt 3, ltacgt 3, ltadgt 3
SDBltabgt
lt (abc) gt 1, lt (abb) gt 1, is Infrequent item
lt a(bc) gt 2, ltabdgt 3
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SDBlta(bc)gt
Sequential pattern a(bc)d satisfies the
constraint
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SDBltacgt
Every sequence in the projected database contains
no subsequence satisfying the constrain
SDBltadgt
lt add gt is a sequential pattern satisfying the
constraint
It results in two final patterns a(bc)d, add
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Experimental results and performance study

• Experiment hardware
• Compare response time without constraint
• GSP, SPADE, Prefix growth
• Regular expression constraints into sequential
  pattern mining
• Scalability of PG
• With support threshold
• With database

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Experiment hardware
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Compare response time without constraint

• Experiment On dataset C10T5S4I1.25D200k
• Contains 100, 000 sequences with 10, 000 items.
• The expected average number of items within a
  transaction is 5
• Denoted as T5
• The expected average number of transaction in
  maximal sequential pattern is 4
• Denoted as S4

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Pushing regular expression constraints into
sequential pattern mining

• We randomly generate 1,000 constraints
• The support threshold is set to 0.2
• PG can prune both patterns and projected
  databases, but SPIRIT(V) has to scan the whole
  sequence database repeatedly

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Scalability of PG with respect to support
threshold
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Scalability of PG with respect to database size

• The support threshold is set to 0.2

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Conclusions

• We characterize constraints for sequential
  pattern mining
• An efficient algorithm, PG, is developed to push
  prefix-monotone constraints deep into the mining
  process