1. Using Attribute Value Lattice to Find Closed Frequent Itemsets – Lin, Hu, Louie

2. New Apporoach to Data Mining
Find closed frequent itemsets
Search only the attribute-value lattice
Enables finding only the non-redundant association rule set

3. 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

4. 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

5. 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  Ij and 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)

6. Lin’s Algorithm
Searches attribute value lattice to find closed frequent itemsets