Mining Compressed FrequentPattern Sets

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Mining Compressed Frequent-Pattern Sets

• Dong Xin, Jiawei Han, Xifeng Yan, Hong Cheng
• Department of Computer Science
• University of Illinois at Urbana-Champaign

VLDB2005
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• Introduction
• Problem statement
• Discovering Representative Patterns
• Performance study
• Conclusion

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Introduction

• Frequent pattern mining
• High minimum support common sense patterns
• Low minimum support explosive number of results
• To solve this problem, its natural to explore
  how to compress the patterns

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Two major approaches

• Lossless compression
• Closed frequent patterns
• Lossy approximation
• Maximal frequent patterns

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A Motivating Example

• A subset of frequent item-sets in accident
  dataset
• High-quality compression needs to consider both
  expression and support

Expression of P1
Support of P1
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A Motivating Example

• Closed frequent pattern
• Report P1,P2,P3,P4,P5
• Emphasize too much on support
• no compression
• Maximal frequent pattern
• Only report P3
• Only care about the expression
• Loss the information of support
• A desirable output P2,P3,P4

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• Our compressing framework
• Clustering frequent patterns by pattern
  similarity
• Pick a representative pattern for each cluster
• Three problems
• How to measure the similarity of the patterns
• How to define quality guaranteed clusters where
  there is a representative pattern best describing
  the whole cluster
• How to efficiently discover these clusters

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Problem statement

• Distance measure Let P1 and P2 be two closed
  patterns. The distance of P1 and P2 is defined
  as
• Ex Let T(P1)t1, t2, t3, t4, t5,
  T(P2)t1, t2, t3, t4, t6, then
  D(P1, P2)1-4/61/3

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Clustering criterion

• A pattern P is d-covered by another pattern P if
  P can be expressed by P and D(P, P)?d.
• A set of patterns form a d-cluster if there
  exists a representative pattern Pr such that for
  each pattern P in the set, P is d-covered by Pr.

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Pattern Compressing Problem

• Given a transaction database, a min_sup M and the
  cluster quality measure d
• The pattern compression problem is to find a set
  of representative patterns R
• For each frequent pattern P, there is a
  representative pattern Pr?R which covers P
• The value of R is minimized.

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Discovering Representative Patterns

• RPglobal
• RPlocal

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To collect the complete coverage information

• Input FP, M, d
• Output representative patterns
• Begin
• for each P?FP s.t. support(P)?M
• insert P into the set E
• for each Q?FP, s.t. Q covers P
• insert P into set(Q)
• while E!F
• find a RP that maximizes set(RP)
• for each Q?set(RP)
• remove Q from E and the remaining sets
• output RP
• End

To find the set of representative patterns
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• RPglobal is expensive
• Assume all frequent patterns are mined
• Need to compute the pair-wise distance between
  all frequent patterns
• Need to find the globally best representative
  pattern
• RPlocal
• Find a locally good representative pattern
• Directly mine from raw data
• Do not compute the distance pair-wisely

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RPlocal

• Algorithm
• Follow the depth-first search in pattern space
• Remember all previously discovered representative
  patterns
• For each pattern P
• Not covered yet
• Being Visited in the second time which traversal
  back from its sons
• Select a representative pattern using local
  method (with P as new probe pattern)

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Pattern P
Ps son
Visited patterns covering P
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Efficient Implementation

• Non Closed Pattern
• Exist a super pattern with same support
• Closed_Index (N bits)
• Each bit remembers the consistency of an item
• Aggregate the closed_index with pattern
• Not closed if at least one out-pattern bit is set

(c,a) 111010
f does not belong to (c,a). Support of (c,a) is
same as support of (f,c,a). (c,a) is not closed
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Performance study

• Comparing algorithms
• FPclose an efficient algorithm to generate all
  closed itemsets, winner of FIMI workshop 2003
• RPglobal first use FPclose to generate closed
  itemsets, then use global greedy method to find
  representative patterns
• RPlocal directly used local method to find
  representative patterns from raw data

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Performance Study

• Number of Representative Patterns

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Performance Study

• Running Time

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Performance Study

• Quality of Representative Patterns

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Conclusion

• To approximate a collection of frequent patterns
• RPglobal
• works well on small collection of patterns
• RPlocal
• much more efficient
• Still quite good compression quality