GenMax

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GenMax

• From
• Efficiently Mining Frequent Itemsets
• By
• Karam Gouda Mohammed J. Zaki

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The Problem

• Given a large database of items transactions,
  find all frequent itemsets
• A frequent itemset is a set of items that occurs
  in at-least a user-specified percentage of the
  data-base
• We call this percentage min_sup (for minimum
  support).

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• A Maximal Frequent Itemset is a frequent
  itemset, that doesnt have a frequent superset
• FI frequent itemsets
• MFI maximal frequent itemsets
• Fact
• MFI ltlt FI
• GenMax is an algorithm to find the exact MFI

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Example
Item/Tid A B C D
1 x x x
2 x x
3 x x x
4 x x x x
5 x
6 x x
7 x
Min_sup 3
ABCD ABC ABD
ACD BCD AB AC AD BC BD
CD A B C D
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Some Useful Definitions

• The Combine-Set of an itemset I , is the set of
  items that can be added to I to create a frequent
  itemset.
• For example , in the previous example, The
  combine-set of the itemset A is B, C.
• The combine-set of the empty itemset is called F1
  and is actually the set of frequent itemsets
  ofsize 1.

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Improvement

• At each level, sort the combine-set (C) in
  increasing order of support
• An itemset with low support has a smaller chance
  of producing a large combine-set in the next
  level
• The sooner we prune the tree, the more work we
  save
• This heuristic was first used in MaxMiner

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Bottlenecks

• Superset checking
• The best algorithms for superset checking give
  an amortized bound of per
  operation.
• thats bad if we have many itemsets in the MFI.
• 2. Frequency testing
• How can we make frequency testing faster ?

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Optimizing Superset Checking

• A technique called Progressive Focusing is
  used to narrow down the group of potential
  supersets, as the recursive calls are made
• LMFI Local MFI
• Before each recursive call, we construct the LMFI
  for the next call, based on the current LMFI and
  the new item added.

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LMFI Example
FGHI FGHJ
FGH FGI
FG
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Frequency Testing Optimization

• GenMax uses a vertical database format
• For each item , we have a set of all the
  transactions containing this item.
• This set is called a tidset. (Transaction ID
  Set).
• This method makes support computations easier,
  because we dont have to go over the entire
  database.

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Vertical Database
Item/Tid A B C D
1 x x x
2 x x
3 x x x
4 x x x x
5 x
6 x x
7 x
A 1, 3, 4, 5 B 1, 3, 4, 6 C
1 ,2 ,3 ,4 ,7 D 2, 4, 6 t(A) 1, 3, 4,
5 t(AC) 1, 3, 4 supp(I) t(I)
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ABC ABD ABE AB
C , E
t(ABC) t(ABE)
Each item y in the combine-set ,
actually represents the itemset ,
and stores the tidset associated with it.
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Additional Optimization

• Diffsets dont store the entire tidsets, only
  the differences between tidsets (described in
  Fast Vertical Mining Using Diffsets)

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Experimental Results

• GenMax is compared with
• MaxMiner , MAFIA, MAFIA-PP
• MaxMiner MAFIA-PP give the exact MFI, while
  MAFIA gives a superset of the MFI
• The Databases used in the experiments are grouped
  according to the MFI length distribution

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Type I Datasets
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Type II Datasets
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Type III Datasets
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Type IV Datasets
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The End