Using Attribute Value Lattice to Find Closed Frequent Itemsets

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Using Attribute Value Lattice to Find Closed
Frequent Itemsets Lin, Hu, Louie
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New Apporoach to Data Mining

• Find closed frequent itemsets
• Search only the attribute-value lattice
• Enables finding only the non-redundant
  association rule set

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Frequent and Closed Itemsets

• Frequent Itemset Itemset that occurs in a
  user-specified percentage of the database
• Closed Itemset An itemset (A) that is identical
  to its closure Cl(A)
• Closure of an Itemset Cl(A) all items that
  appear in all tuples that contain A.
• Eg. Cl(A) 1,3,4,5
• Cl(C) 1,2,3,4,5
• Cl(W) 1,2,3,4,5
• Cl(A)Cl??(C ) ?? Cl(W) I,3,4,5
• ACW is a closed frequent itemset.

1 ACTW
2 CDW
3 ACTWHG
4 ACDWHF
5 ACDTWH
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Partial order and lattice

• Partial Order A binary relation that is
  reflexive (a lta ), antisymmetric (altb and blta,
  then a b) and transitive (altb and bltc, then
  altc)
• Lattice Partially ordered set in which non-empty
  finite subsets have a least upper bound and a
  greatest lower bound

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Lins Algorithm

• Attribute value lattice constructed from database
• Construct bitmap of each frequent itemset B(Ii)
• Set level number Li of Ii to 1
• Nodes contain Ii , Li , and B(Ii) where B(Ii) gt
  threshold
• Sort the item in nodes based on bitcount
• For each node, Ii , Li ,B(Ii) in nodes
• For each sibling Ii
• I Ii ? Ij and Bcomb B(Ii)? B(Ij)
• If Bcombgt threshold
• If B(Ii) B(Ij)
• remove Ij from nodes
• replace Ii with I
• 2. If If B(Ii) ? B(Ij)
• create an edge from Ii to Ij
• Lj max(Lj , Lj 1)
• 3. If B(Ij) ? B(Ii)
• create an edge from Ij to Ii
• Li max(L, Lj 1)

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Lins Algorithm

• Searches attribute value lattice to find closed
  frequent itemsets