频繁模式树

A B C D E C D E D E
e.g., { A B C D E } for f_is = D i = A, p_base = (ABCD), (ACD), (AD) i = B, p_base = (ABCD) i = C, p_base = (ABCD), (ACD) i = E, p_base = null
Frequent Itemsets
Apriori generates candidate sets FP-Growth uses specialized data structures (no candidate sets)
Find

Association Rules
Outside the scope of both FP-Growth & Apriori
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 f:4 c:3 a:3 b:1 {} c:1 b:1 p:1
m:2
p:2
b:1
m:1
FP-Growth Algorithm
FP-Growth Recursive Input: FP-Tree, f_is (frequent algorithm itemset) creates FP-Tree Output: All freq_patterns structures and calls FP-Growth if FP-Tree contains single Path P then for each combination of nodes in P Claims no generate pattern f_is combination candidate else for each item i in header generation
Item Conditional pattern-base Conditional FP-tree
p m b a c f {(fcam:2), (cb:1)} {(fca:2), (fcab:1)} {(fca:1), (f:1), (c:1)} {(fc:3)} {(f:3)} Empty {(c:3)}|p {(f:3, c:3, a:3)}|m Empty {(f:3, c:3)}|a {(f:3)}|c Empty
generate pattern f_is i construct pattern’s conditional cFP-Tree if (FP-Tree 0) then call FP-Growth (cFP-Tree, pattern)
Two-Part Algorithm
A if FP-Tree contains single Path P then for each combination of nodes in P generate pattern f_is combination B C D
Null
Header: A B F G H I M
A:50 B:1 G:1 M:1 B:45 G:1 I:1 M:1 F:40 G:1 I:1 M:1 G:35 H:1 I:1 M:1
i=F pattern = { F M } support = 1 pattern base cFP-Tree = null
e.g., { A B C D }
p
= |pattern| = 4 AD, BD, CD, ABD, ACD, BCD, ABCD
(n=1 to p-1) (p-1Cn)
Two-Part Algorithm
else for each item i in header generate pattern f_is i construct pattern’s conditional cFP-Tree if (cFP-Tree null) then call FP-Growth (cFP-Tree, pattern)
TID 100 200 300 400 500 Items bought (ordered) frequent items {f, a, c, d, g, i, m, p} {f, c, a, m, p} {a, b, c, f, l, m, o} {f, c, a, b, m} {b, f, h, j, o} {f, b} {b, c, k, s, p} {c, b, p} {a, f, c, e, l, p, m, n} {f, c, a, m, p}
FP-Growth Algorithm
FP-CreateTree Two passes Input: DB, min_support through DB Output: FP-Tree Tree creation is 1. Scan DB & count all frequent based on items. number of items 2. Create null root & set as current node. in DB. 3. For each Transaction T Complexity of
Items bought (ordered) frequent items {f, a, c, d, g, i, m, p} {f, c, a, m, p} {a, b,c, f, l, m, o} {f, c, a, b, m} {b, f, h, j, o} {f, b} {b, c, k, s, p} {c, b, p} {a, f, c, e, l, p, m, n} {f, c, a, m, p}
FP-Growth Mining Example
Null
Header: A B F G H I M
A:50 B:1 G:1 M:1 B:45 G:1 I:1 M:1 F:40 G:1 I:1 M:1 G:35 H:30 I:20 H:1 I:1 M:1
Transactions: A (49) B (44) F (39) G (34) H (30) I (20) ABGM BGIM FGIM GHIM
Pattern bases are generated by following f_is
path from header to each node in tree having it, up to tree root, for each header item.
FP-Growth Complexity
{} c:1 b:1 p:1 Conditional pattern bases item cond. pattern base
c
a b m p
f:3
fc:3 fca:1, f:1, c:1 fca:2, fcab:1 fcam:2, cb:1
m:2
p:2
b:1
m:1
FP-Growth Example
FP-Growth Mining Example
Null
Header: A B F G H I M
A:50 B:1 G:1 M:1 B:45 G:1 I:1 M:1 F:40 G:1 I:1 M:1 G:35 H:1 I:1 M:1
i=A pattern = { A M } support = 1 pattern base cFP-Tree = null

You MUST take into account all paths that contain an item set with a test item. You CANNOT determine before a conditional FP-Tree is created if new frequent item sets will occur. Trivial examples hide these assertions, leading to a belief that FP-Tree operates more efficiently.
Sample Data FP-Tree
null A B C … D C E D … … … K L M … M L M M
J
K L M
K
L M
L
M
M
L
M
M
M
M
Algorithm Results (in English)
Candidate Generation sets exchanged
for FP-Trees.
Therefore, FP-Growth is a competitor to
Apriori
FP-Growth Example
TID 100 200 300 400 500
Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 f:4 c:3 a:3 b:1
The FP-Growth/Apriori Debate
Presentation Overview
FP-Growth Algorithm
Refresher Motivation
& Example
FP-Growth Complexity
Vs.
Apriori Complexity Saving calculation or hiding work?
freq_itemset = { M }
FP-Growth Mining Example
Null
Header: A B F G H I M
A:50 B:1 G:1 M:1 B:45 G:1 I:1 M:1 F:40 G:1 I:1 M:1 G:35 H:1 I:1 M:1
Real World Application