CFI-Stream:%20Mining%20Closed%20Frequent%20Itemsets%20in%20Data%20Streams

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CFI-Stream Mining Closed Frequent Itemsets in
DataStreams

• Nan Jiang,Le Gruenwald
• SIGKDD06
• 
  ??????
• 2006/10/04

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Introduction

• mining Closed frequent itemsets
• computes and maintains closed itemsets online and
  incrementally
• perform the closure checking
• output the current closed frequent itemsets in
  real time based on users specified thresholds

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Definition

• Ddata stream
• I , , , a set of n elements,
• called items
• T subsets of all the transactions
• X subsets of all the items appearing
• in a data stream

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Definition

• C(X)the smallest closed set containing X
• Definition 1
• An itemset X is said to be closed if and only
  if C(X) f(g(X)) fg(X) X

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Algorithm

• CFI-Stream algorithm
• DIrect Update (DIU) tree
• perform the closure checking online over a data
  stream sliding window
• Conditions need to check for closed itemsets
• check when performing addition and deletion
  operations on the DIU tree

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DIU tree

• maintain the current closed itemsets
• k levels in the DIU tree, each level i
• stores the closed i-itemsets

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DIU tree

• Each node in the DIU tree stores
• a closed itemset
• its current support information
• links to its parent and children nodes

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Add a Transaction to the DIU Tree

• T1original transaction set
• tnew arrived transaction
• Conditions to Check for Closed Itemsets
• (1)
• t is in the T1, if the largest itemset X
  it
• contains is not currently in the DIU tree
• -gtcheck for all Xs subsets Y, which are in
  
• T1

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• (2)
• when t is not in T1, for each its subset
• Y, if Y is in T1, we need to check

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Closure Checking for Addition
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1. C,D

2 A,B
3 A,B,C
4 A,B,C
1
1
2
AB
2
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Delete a Transaction in DIU Tree

• Conditions to Check for Closed Itemsets
• When the number of the transactions
• with same itemset of X is equal to zero, if Y
  is a subset of X, and Y is a closed itemset in
  the original transaction set

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Closure Checking for Deletion
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1. C,D

2 A,B
3 A,B,C
4 A,B,C
3
C
3
1
CD
AB
2
ABC
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Experiment

• Synthetic datasets
• T10.I6.D100K and T5.I4.D100K

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Experiment
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Experiment