Mining Asynchronous Periodic Patterns in Time Series Data

1
Mining Asynchronous Periodic Patterns in Time
Series Data
Appearing in IEEE Transactions on Knowledge and
Data Engineering 2001

• Jiong Yang, Wei Wang, Philip S. Yu

Presented by Chih-chieh Hung 2004.12.1
2
Outline

• Introduction
• General Model
• Algorithm
• Experimental Results
• Conclusion

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Introduction

• Synchronous v.s Asynchronous

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Introduction

• Two parameters are used to qualify valid patterns
  and the symbol sequence containing it.
• min_rep make sure the periodicity
• max_dis make sure the system behavior

min_rep 3, max_dis 3
Valid segment
Valid segment
Valid segment
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Main Difficulties

• Longest valid subsequence Composing

• All periodic patterns discovery
• The period is not always available a priori.

6
Outline

• Introduction
• General Model
• Algorithm
• Experimental Results
• Conclusion

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General Model (1 of 2)

• Set of features L
• Dont care character
• Pattern over
• Period l
• i-pattern
• La,b,c,d,e , s a,,c, d, e
• s is a 4-pattern of period 5.
• Generalization Specialization

Generalization
Specialization
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General Model (2 of 2)

• Match
• Valid segment
• min_rep 2
• Valid subsequence

( , , , ) is a match.
valid_seg1
valid_seg2
valid_seg3
?max_dis
?max_dis
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Outline

• Introduction
• General Model
• Algorithm
• Experimental Results
• Conclusion

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Algorithm

• Algorithm Overview
• Distance-based Pruning
• Single Pattern Verification
• Complex Pattern Verification

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Distance-Based Pruning

• If DCd,l lt min_rep-1, then d doesnt participate
  in some valid pattern of period l.

min_rep 3 max_dis 3
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Single Pattern Verification

• If a symbol d and period l pair has passed the
  distance-based pruning, then Algorithm SB is
  employed to discover the subsequence with the
  most repetitions of (d,,,,) with period l.

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Extendibility Dominance

• At position i X is longer than Y

But Y should be kept, because

• At position j

Y-V is longer than X
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Algorithm SB

• Phase A Segment validation
• at least 1 instance of (d,,,) found
• of rep. lt min_rep
• Phase B Valid segment growth
• the segment becomes valid ( of rep.
  min_rep )
• Phase C Extension
• valid segment may end or extend

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Ambiguity in Phase Transition
Phase B to Phase C
Phase C to Phase A
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Pruning Issue Dominance

• After recognizing D7, X overtakes Y

• K is a good point to check the dominance.

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Extendible Principles

• Mark the subsequence that end priori i-1 as in
  Phase C.
• If repetition of subsequence in Phase A
  min_rep, mark it as in Phase B.
• The most repetitions in Phase B and C is
  identified and used to update the longest valid
  subsequence for (d,,,,).
• The dominating subsequence in Phase C is extended.

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Three Data Structure

• longest_seq
• longest valid subsequence that is known (at
  position i) to be not extendible.
• ongoing_seq
• a set of subsequences that are currently being
  extended (whether valid or not)
• valid_seq
• a set of subsequences that may be extendible

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Example (1 of 3)

• 8th occurrence of d1 at position 14

Before
After
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Example (2 of 3)

• 9th occurrence of d1 at position 16

Before
After
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Example (3 of 3)

• 10th occurrence of d1 at position 17

Before
After
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Complex Pattern Verification

• Symbol Property
• If a pattern P is valid, then all of its
  generalizations are also valid.
• Segment Property
• If D is a valid segment for pattern P, then D
  is also a valid segment of all generalizations of
  P.

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Outline

• Introduction
• General Model
• Algorithm
• Experimental Results
• Conclusion

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Experimental Results

• Apply this model to a real trace of a web access
  log of http//www.scour.net.
• Collect all hits on 100 days.
• Total number of accesses is over 170 million.
• Time division and labeling
• 0-4999 A
• 5000-9999 B
• .
• The summarized sequence 14400 occurrences of 71
  symbols.

000
010
020
030
050
040
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Experimental Results

• Parameter min_rep 4 , max_dis 200.
• Discover 212 patterns.
• Example
• (b, b, b) in weekdays between 3am and 830am.
• (c, c, c) in weekdays between 11am and 5pm.

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Outline

• Introduction
• General Model
• Algorithm
• Experimental Results
• Conclusion

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Conclusion

• This paper proposed a flexible model of
  asynchronous periodic patterns to mine patterns.
• Two parameters used to ensure the correctness of
  pattern periodicity (min_rep) and system
  behaviors (max_dis).
• Proposed algorithm first generates potential
  periods and then validate candidate patterns and
  locate the longest valid subsequence. At last,
  complex patterns are composed.