FlExPat: Flexible Extraction of Sequential Patterns

1
FlExPat Flexible Extraction of Sequential
Patterns

• Pierre-Yves ROLLAND
• 2001 IEEE International Conference on Data Mining
  (ICDM.01)

2
Outline

• Introduction
• Formalization
• Two-Phase Algorithm
• Conclusion

3
Introduction

• A sequential pattern is a set of segments from
  the sequential database which share a significant
  degree of resemblance.
• For pairs of segments in the pattern, the
  similarity between the two segments can be
  measured numerically and is above a given
  threshold.

4
Introduction

• MVEM
• multi-description valued edit model
• MVEMs main parameter is the
• allowed pairing type set APTS.

5
Introduction

• The initial M (multi-description) means that
  MVEM has been designed to be able to deal with
  representations of sequences and elements that
  use multiple simultaneous descriptions.

6
Formalization

• A sequence S is an ordered collection of
  individual data structures Si called the
  sequences elements SS1S2 SL.
• A sequence segment is a contiguous part of a
  sequence SiSi1Sim-1 is the segment of S
  with length m and starting at position i.

7
Formalization

• Two sequence segments s1 and s2 are said to be
  equipollent iff their similarity is greater or
  equal to a given threshold.

8
FlExPat Parameters

• The minimum and maximum possible length for
  candidate segments
• Integers mmin?1S and mmax?mmin..S
• The maximum possible length difference between
  segments to be compared
• MaxLenghDiff(m)

9
FlExPat Parameters

• The maximum length of overlap between two
  candidate segments
• The similarity threshold defining equipollence
• A quorum threshold

10
Equipollence Graph Construction

• The segments Si,m that will be compared to
  Si,m verify the following property
• (i,m)lt(i,m),
• which means (lt denotes lexicographic ordering)
  ilti or ii and mltm

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Equipollence Graph Construction

• If Simil(s,s) is greater or equal to ST then
• If no vertex corresponding to s yet exists in the
  equipollence graph then it is created. Same for
  s.
• 2) An edge is created between the vertices
  corresponding to s and s in the equipollence
  graph. It is labeled with the value Simil(s,s).

12
Equipollence Graph Construction
13
Subgraph Extraction
14
Conclusion

• FlExPat allows using a rich and flexible
  similarity model while maintaining reasonable
  time and space complexities
• FlExPat can be used to find approximate repeating
  patterns in a sequence