Association Rule Mining - MaxMiner

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Association Rule Mining- MaxMiner
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Mining Association Rules in Large Databases

• Association rule mining
• Algorithms Apriori and FP-Growth
• Max and closed patterns
• Mining various kinds of association/correlation
  rules

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Max-patterns Close-patterns

• If there are frequent patterns with many items,
  enumerating all of them is costly.
• We may be interested in finding the boundary
  frequent patterns.
• Two types

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Max-patterns

• Frequent pattern a1, , a100 ? (1001) (1002)
  (110000) 2100-1 1.271030 frequent
  sub-patterns!
• Max-pattern frequent patterns without proper
  frequent super pattern
• BCDE, ACD are max-patterns
• BCD is not a max-pattern

Tid Items
10 A,B,C,D,E
20 B,C,D,E,
30 A,C,D,F
Min_sup2
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Maximal Frequent Itemset
An itemset is maximal frequent if none of its
immediate supersets is frequent
Maximal Itemsets
Infrequent Itemsets
Border
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Closed Itemset

• An itemset is closed if none of its immediate
  supersets has the same support as the itemset

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Maximal vs Closed Itemsets
Transaction Ids
Not supported by any transactions
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Maximal vs Closed Frequent Itemsets
Closed but not maximal
Minimum support 2
Closed and maximal
Closed 9 Maximal 4
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Maximal vs Closed Itemsets
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MaxMiner Mining Max-patterns

• Idea generate the complete set-enumeration tree
  one level at a time, while prune if applicable.

? (ABCD)
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Local Pruning Techniques (e.g. at node A)

• Check the frequency of ABCD and AB, AC, AD.
• If ABCD is frequent, prune the whole sub-tree.
• If AC is NOT frequent, remove C from the
  parenthesis before expanding.

? (ABCD)
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Algorithm MaxMiner

• Initially, generate one node N ,
  where h(N)? and t(N)A,B,C,D.
• Consider expanding N,
• If h(N)?t(N) is frequent, do not expand N.
• If for some i?t(N), h(N)?i is NOT frequent,
  remove i from t(N) before expanding N.
• Apply global pruning techniques

? (ABCD)
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Global Pruning Technique (across sub-trees)

• When a max pattern is identified (e.g. ABCD),
  prune all nodes (e.g. B, C and D) where h(N)?t(N)
  is a sub-set of it (e.g. ABCD).

? (ABCD)
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Example
Tid Items
10 A,B,C,D,E
20 B,C,D,E,
30 A,C,D,F
? (ABCDEF)
Items Frequency
ABCDEF 0
A 2
B 2
C 3
D 3
E 2
F 1
Min_sup2
Max patterns


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Example
Tid Items
10 A,B,C,D,E
20 B,C,D,E,
30 A,C,D,F
? (ABCDEF)
B (CDE)
C (DE)
E ()
D (E)
A (BCDE)
Min_sup2
Node A
Items Frequency
ABCDE 1
AB 1
AC 2
AD 2
AE 1
Max patterns


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Example
Tid Items
10 A,B,C,D,E
20 B,C,D,E,
30 A,C,D,F
? (ABCDEF)
B (CDE)
C (DE)
E ()
D (E)
A (BCDE)
Min_sup2
Node B
Items Frequency
BCDE 2
BC
BD
BE
Max patterns


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Example
Tid Items
10 A,B,C,D,E
20 B,C,D,E,
30 A,C,D,F
? (ABCDEF)
B (CDE)
C (DE)
E ()
D (E)
A (BCDE)
AC (D)
AD ()
Min_sup2
Node AC
Items Frequency
ACD 2
Max patterns
BCDE