Mining Frequent patterns without candidate generation

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Mining Frequent patterns without candidate
generation

• Jiawei Han,
• Jian Pei
• and
• Yiwen Yin

Abdullah Mueen
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Problem Mining Frequent Pattern

• Ia1, a1, , am is a set of items.
• DBT1, T1, , Tn is the database of
  transactions where each transaction is a non
  empty subset of I.
• A pattern is also a subset of I.
• A pattern is frequent if it is contained in
  (supported by) more than a fixed number (?) of
  transactions.

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Previous work Apriori

• It may need to generate a huge number of
  candidate itemsets. To discover a frequent
  pattern of size k it needs to generate more than
  2k candidates in total.
• It may need to scan the database repeatedly and
  check for the frequencies of the candidates.

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FP-growth

• FP-growth mines frequent patterns without
  generating the candidate sets. It grows the
  patterns from fragments.
• It builds an extended prefix tree (FP-tree) for
  the transaction database. This tree is a
  compressed representation of the database. It
  saves repeated scan of the database.

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FP-tree
TID Items Bought Frequent Items
100 f,a,c,d,g,i,m,p f,c,a,m,p
200 a,b,c,f,l,m,o f,c,a,b,m
300 b,f,h,j,o f,b
400 b,c,k,s,p c,b,p
500 a,f,c,e,l,p,m,n f,c,a,m,p
Minimum support (?) 3
sorted in descending order of the freq.
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Conditional FP-tree of p
Minimum support (?) 3
Items Bought Frequent Items
f,c,a,m c
f,c,a,m c
c,b c
Conditional FP-tree of p
Conditional pattern base for p
The set of frequent patterns containing p is
cp , p
p
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Frequent patterns containing m
Items Freq. Items
f,c f,c
f,c f,c
f,c f,c
Items Bought Frequent Items
f,c,a f,c,a
f,c,a f,c,a,
f,c,a,b f,c,a
Conditional pattern base for am
Conditional pattern base for m
Conditional FP-tree of m
Items Freq. Items
f f
f f
f f
Conditional FP-tree of cam
Conditional FP-tree of am
The set of frequent patterns containing m is
pattern base for cam
m, am, cam, fcam, fam
m, am, cam, fcam, fam, cm, fcm
m, am, cam, fcam, fam, cm, fcm, fm
m
m, am
m, am, cam
m, am, cam, fcam
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Complete Frequent Pattern set
Generated by conditional FP tree of m which is a
single Path

• A single path generates each combination of its
  nodes as frequent pattern
• Supports for a pattern is equal to the minimum
  support of a node in it.

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Pseudocode

• Procedure FP-growth(Tree,a)
• if Tree contains a single path P
• for each combination (ß) of the nodes in P
• Generate pattern ßUa with support minimum
  support of a node in ß
• else
• for each ai in the header of Tree do
• Generate pattern ß aUai with support
  ai.support.
• Construct ßs conditional pattern base and
  conditional FP-tree Treeß
• if Treeß ? Ø
• Call FP-growth(Treeß, ß)

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Implementation issues

• For different support thresholds (?) there are
  different FP-trees. We may chose ?20 if 98 of
  the queries have ?20.
• Updating the FP-tree after each new transaction
  may be costly. We may count the occurrence
  frequency of every items and update the tree if
  relative frequency of an item gets a large change.

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New Challenges

• FP-growth may output a large number of frequent
  patterns for small (?) and very small number of
  frequent patterns for large (?). We may not know
  the (?) for our purpose.
• Which frequent patterns are good instances for
  generating interesting association rules?

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Top-K frequent closed patterns

• Closed pattern is a pattern whose support is
  larger than any of its super pattern.

TID Items Bought Frequent Items
100 f,a,c,d,g,i,m,p f,c,a,m,p
200 a,b,c,f,l,m,o f,c,a,b,m
300 b,f,h,j,o f,b
400 b,c,k,s,p f,c,b,p
500 a,f,c,e,l,p,m,n f,c,a,m,p

• We can also specify the minimum length of the
  patterns.
• Top-2 frequent closed patterns with length 2
  is fc and fcam

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Mining Top-K closed FP

• The algorithm starts with an FP-tree having 0
  support threshold.
• While building the tree, it prunes the smaller
  patterns with length lt min_length.
• After the tree is built, it prunes the relatively
  infrequent patterns by raising the support
  threshold.
• Mining is performed on the final pruned FP-tree.

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Compressed Frequent Pattern

• FP-growth may end up with a large set of
  patterns.
• We can compress the set of frequent patterns by
  clustering it minimally and selecting a
  representative pattern from each cluster.

fcam, cam, ap, b
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Clustering Criterion

• For each cluster there must be a representative
  pattern Pr .
• D(P,Pr ) d for all patterns inside the cluster
  of Pr .
• D(P1,P2 ) 1- T(P1)nT(P2) T(P1)UT(P2)
• T(P) is the set of transactions that support P.
• D is a metric for closed patterns.

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Summary

• FP-tree is an extended prefix tree that
  summarizes the database in a compressed form.
• FP-growth is an algorithm for mining frequent
  patterns using FP-tree.
• FP-tree can also be used to mine Top-K frequent
  closed patterns and Compressed frequent patterns.

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References

• Mining Frequent Patterns without Candidate
  Generation
• Jiawei Han, Jian Pei and Yiwen Yin
• Mining Top-K Frequent Closed Patterns without
  Minimum Support
• Jiawei Han, Jianyong Wang, Ying Lu and Petre
  Tzetkov
• Mining Compressed Frequent-Pattern Sets
• Dong Xin, Jiawei Han, Xipheng Yan and Hong Cheng

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Thank You