Bottleneck of Frequentpattern Mining

1
Bottleneck of Frequent-pattern Mining

• Multiple database scans are costly
• Mining long patterns (i.e. long frequent
  itemsets)
• needs many passes of scanning
• generates lots of candidates
• To find frequent itemset i1i2i100
• of scans 100
• of Candidates (1001) (1002) (100100)
  2100-1 1.271030 !
• Bottleneck candidate-generation-and-test
• Can we avoid candidate generation?

2
FP-growth Algorithm

• Use a compressed representation of the database
  using a FP-tree
• Once an FP-tree has been constructed, it uses a
  recursive divide-and-conquer approach to mine the
  frequent itemsets
• Database ? 1 scan to get frequent 1-itemsets ?
  Sort transactions based on f-list ? 1 scan to
  create FP-tree
• ? For every frequent item p, create p s
  conditional pattern base (bottom up)
• ? For every frequent item p, create p s
  conditional FP-tree
• ? Generate all frequent itemsets ending in p

3
Construct FP-tree from a Transaction Database
F-listf-c-a-b-m-p
TID Items bought (ordered) 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, w 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
min_support 3

• Scan DB once, find frequent 1-itemsets (single
  item patterns)
• Sort frequent items in frequency descending
  order, f-list
• Scan DB again, construct FP-tree

4
Creating conditional pattern bases

• Starting at the frequent item header table in the
  FP-tree (bottom up)
• Traverse the FP-tree by following the link of
  each frequent item p
• Construct ps conditional pattern base (a
  sub-database which consists of the set of prefix
  paths to p)

Conditional pattern bases item cond. pattern
base p fcam2, cb1 m fca2, fcab1 b fca1, f1,
c1 a fc3 c f3
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From Conditional Pattern-bases to Conditional
FP-trees

• For each pattern-base
• Accumulate the count for each item in the base
• Construct the FP-tree for the frequent items of
  the pattern base

m-conditional pattern base fca2, fcab1
All frequent patterns relate to m m(3), fm(3),
cm(3), am(3), fcm(3), fam(3), cam(3), fcam(3)
?
?
6
Example 2 minsupp 2