Parallel Mining of Maximal Frequent Itemsets form Databases

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Parallel Mining of Maximal Frequent Itemsets form
Databases

• Soon M.Chunf and Congnan Luo
• Proceedings of the 15th IEEE International
  Conference on Tools with Artificial Intelligence
  (ICTAI03)

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Outline

• Introduction
• Max-Miner Algorithm
• Parallel Max-Miner (PMM) Algorithm
• Performance Evaluation
• Conclusion

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Introduction (1)

• In mining association rules, the most
  time-consuming job is finding all frequent
  itemsets from a large database with respect to a
  given minimum support
• In Apriori, the subset-infrequency based pruning
  step prevents many candidate k-itemsets from
  being counted in each pass k
• In Apriori-like algorithms, if there is a
  frequent itemset with length l, then they will
  generate and count its 2l subsets.

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Introduction (2)

• Our basic idea is that if we find a large
  frequent itemset early, we can avoid counting all
  its subsets because they are all frequent
• We propose a parallel algorithm, named Parallel
  Max-Miner (PMM), for mining maximal frequent
  items
• The PMM requires multiple passes over the
  database, like the Count Distribution algorithm,
  need synchronization between nodes at every pass
  end

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Max-Miner algorithm

• Unlike Apriori, the Max-Miner algorithm extracts
  only the maximal frequent itemset
• Superset-frequency based pruning
• Max-miner always attempts to look ahead in order
  to identify large frequent itemsets early
• So all subsets of these discovered frequent
  itemsets can be pruned form the search space

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Set-enumeration tree of Max-Miner (1)
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Set-enumeration tree of Max-Miner (2)

• Each node in the tree is called a candidate group
• A candidate group g consists of two components
  which are actually two itemsets
• The first itemset is called the head of the group
  and denoted by h(g)
• The second itemset is called the tail of the
  group and denoted by t(g)
• t(g) is an ordered set and contains all the items
  not in h(g) but can potentially appear in any
  subnode derived from node g

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The main procedure of Max-Miner (1)

• From the root of the tree at level 0, count the
  support of 1-itemsets.
• Only the 1-itemsets which are frequent can be
  enumerated at level 1
• 4 nodes are generated at level 1 if 1, 2, 3, and
  4 are all frequent 1-itemsets
• For the node g1, we need to count the support of
  h(g1) t(g1)1,2,3,4
• If the support of h(g1) t(g1) is equal or
  greater than minsup, then we do not need to
  expand the tree from the node g1 anymore

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The main procedure of Max-Miner (2)

• At any node g, if h(g) t(g) is not frequent,
  for each item I in t(g), we check if h(g) i
  is frequent
• If h(g) i is frequent, a corresponding
  subnode is generated
• We notice that for a candidate group node g, if
  an item appears last in the tail of g in
  ordering, it will appear in most offsprings of
  the node g
• To discover the maximal frequent itemsets early,
  we better order the subnodes of each node in
  ascending order of their support

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Parallel Max-Miner (PMM) algorithm

• The database is evenly divided into N partitions
  D0, D1, D2, , DN-1, one for each of the N
  nodes P0, P1, P2, , PN-1
• Each node has the same number of transactions
  allocated
• PMM requires multiple passes over database
• For each pass k, all the nodes have exactly the
  same set of candidate groups, Ck.
• Each node count the support of Ck in local
  database, independently
• At the end of each pass, all nodes exchange the
  count information so that they can generate the
  same set of Ck-1 for the next pass

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Performance Evaluation
Speedup of PMM
Sizeup of PMM
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Conclusion

• We proposed a parallel maximal frequent itemset
  mining algorithm, Parallel Max-Miner, for
  shared-nothing multiprocessor systems
• Drawback quire synchronization between nodes to
  exchange the count information at the end of
  every pass