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 (ICTAI’03)
Outline
Introduction
Max-Miner Algorithm
Parallel Max-Miner (PMM) Algorithm
Performance Evaluation
Conclusion
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.
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 MaxMiner (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
Max-Miner algorithm
Unlike Apriori, the Max-Miner algorithm extracts only
the maximal frequent itemset
Superset-frequency based pruning
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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
Set-enumeration tree of Max-Miner (1)
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
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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
The main procedure of Max-Miner (1)
From the root of the tree at level 0, count the
support of 1-itemsets.
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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
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
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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
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}
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Each node has the same number of transactions allocated
PMM requires multiple passes over database
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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
Performance Evaluation
Speedup of PMM
Sizeup of PMM
Conclusion
We proposed a parallel maximal frequent itemset
mining algorithm, Parallel Max-Miner, for sharednothing multiprocessor systems
Drawback: quire synchronization between nodes to
exchange the count information at the end of every
pass