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Using Attribute Value Lattice to Find Closed Frequent Itemsets – Lin, Hu, Louie. New Apporoach to Data Mining. Find closed frequent itemsets Search only the attribute-value lattice Enables finding only the non-redundant association rule set. Frequent and Closed Itemsets .
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Using Attribute Value Lattice to Find Closed Frequent Itemsets – Lin, Hu, Louie
New Apporoach to Data Mining • Find closed frequent itemsets • Search only the attribute-value lattice • Enables finding only the non-redundant association rule set
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.
Partial order and lattice • Partial Order: A binary relation that is reflexive (a <=a ), antisymmetric (a<=b and b<=a, then a = b) and transitive (a<=b and b<=c, then a<=c) • Lattice: Partially ordered set in which non-empty finite subsets have a least upper bound and a greatest lower bound
Lin’s 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) > threshold • Sort the item in nodes based on bitcount • For each node, Ii , Li ,B(Ii) in nodes • For each sibling Ii • I = Ii Ijand Bcomb = B(Ii) B(Ij) • If Bcomb> 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)
Lin’s Algorithm • Searches attribute value lattice to find closed frequent itemsets