FP-Tree/FP-Growth Practice

1
FP-Tree/FP-Growth Practice
2
FP-tree construction
After reading TID1
After reading TID2
3
FP-Tree Construction
Transaction Database
Header table
B 8
A 7
C 7
D 5
E 3
Chain pointers help in quickly finding all the
paths of the tree containing some given item.
There is a pointer chain for each item. I have
shown pointer chains only for E and D.
4
Transactions containing E
5
Suffix E
(New) Header table
Conditional FP-Tree for suffix E
A 2
C 2
D 2
null
B doesnt survive because it has support 1, which
is lower than min support of 2.
A2
C1
C1
D1
The set of paths ending in E. Insert each path
(after truncating E) into a new tree.
D1
We continue recursively. Base of recursion When
the tree has a single path only. FI E
6
Suffix DE
(New) Header table
null
The conditional FP-Tree for suffix DE
A 2
A2
C1
D1
null
D1
A2
The set of paths, from the E-conditional FP-Tree,
ending in D. Insert each path (after truncating
D) into a new tree.
We have reached the base of recursion. FI DE,
ADE
7
Suffix CE
(New) Header table
null
The conditional FP-Tree for suffix CE

A1
C1
C1
null
D1
The set of paths, from the E-conditional FP-Tree,
ending in C. Insert each path (after truncating
C) into a new tree.
We have reached the base of recursion. FI CE
8
Suffix AE
(New) Header table
The conditional FP-Tree for suffix AE

null
null
A2
The set of paths, from the E-conditional FP-Tree,
ending in A. Insert each path (after truncating
A) into a new tree.
We have reached the base of recursion. FI AE
9
Suffix D
(New) Header table
Conditional FP-Tree for suffix D
A 4
B 3
C 3
null
A4
B1
B2
C1
C1
C1
The set of paths containing D. Insert each path
(after truncating D) into a new tree.
We continue recursively. Base of recursion When
the tree has a single path only. FI D
10
Suffix CD
(New) Header table
null
Conditional FP-Tree for suffix CD
A 2
B 2
A4
B1
B2
C1
null
C1
C1
A2
B1
B1
The set of paths, from the D-conditional
FP-Tree, ending in C. Insert each path (after
truncating C) into a new tree.
We continue recursively. Base of recursion When
the tree has a single path only. FI CD
11
Suffix BCD
(New) Header table
Conditional FP-Tree for suffix CDB
null

A2
B1
null
B1
The set of paths from the CD-conditional
FP-Tree, ending in B. Insert each path (after
truncating B) into a new tree.
We have reached the base of recursion. FI CDB
12
Suffix ACD
(New) Header table
Conditional FP-Tree for suffix CDA
null

null
The set of paths from the CD-conditional
FP-Tree, ending in A. Insert each path (after
truncating B) into a new tree.
We have reached the base of recursion. FI CDA
13
Suffix C
null
(New) Header table
Conditional FP-Tree for suffix C
B 6
A 4
B6
A1
A3
C3
C1
null
C3
B6
A1
A3
The set of paths ending in C. Insert each path
(after truncating C) into a new tree.
We continue recursively. Base of recursion When
the tree has a single path only. FI C
14
Suffix AC
(New) Header table
null
Conditional FP-Tree for suffix AC
B 3
B6
A1
null
A3
B3
The set of paths from the C-conditional FP-Tree,
ending in A. Insert each path (after truncating
A) into a new tree.
We have reached the base of recursion. FI AC,
BAC
15
Suffix BC
(New) Header table
null
Conditional FP-Tree for suffix BC
B 3
B6
null
The set of paths from the C-conditional FP-Tree,
ending in B. Insert each path (after truncating
B) into a new tree.
We have reached the base of recursion. FI BC
16
Suffix A
null
(New) Header table
Conditional FP-Tree for suffix A
B 5
B5
A2
A5
null
B5
The set of paths ending in A. Insert each path
(after truncating A) into a new tree.
We have reached the base of recursion. FI A, BA

17
Suffix B
(New) Header table
Conditional FP-Tree for suffix B

null
null
B8
The set of paths ending in B. Insert each path
(after truncating B) into a new tree.
We have reached the base of recursion. FI B
18
Array Technique
19
FP-Tree Construction
Transaction Database
Header table
B 8
A 7
C 7
D 5
E 3
First pass on DB Determine the header. Then sort
it. Second pass on DB Build the FP-Tree. Also
build the array.
20
FP-Tree Construction Reading 1
Transaction Database
null
B1
A1
Header table
B 8
A 7
C 7
D 5
E 3
A 1
C
D
E
B A C D
21
FP-Tree Construction Reading 2
Transaction Database
null
B2
A1
C1
D1
Header table
B 8
A 7
C 7
D 5
E 3
A 1
C 1
D 1 1
E
B A C D
22
FP-Tree Construction Reading 3
Transaction Database
null
B2
A1
A1
C1
C1
D1
D1
E1
Header table
B 8
A 7
C 7
D 5
E 3
A 1
C 1 1
D 1 1 2
E 1 1 1
B A C D
23
FP-Tree Construction Reading 4
Transaction Database
null
B2
A2
A1
C1
C1
D1
D1
D1
E1
Header table
E1
B 8
A 7
C 7
D 5
E 3
A 1
C 1 1
D 1 2 2
E 2 1 2
B A C D
24
FP-Tree Construction Reading 5
Transaction Database
null
B3
A2
A2
C1
C1
D1
D1
D1
E1
C1
Header table
E1
B 8
A 7
C 7
D 5
E 3
A 2
C 2 2
D 1 2 2
E 2 1 2
B A C D
25
FP-Tree Construction Reading 6
Transaction Database
null
B4
A2
A3
C1
C1
D1
D1
D1
E1
C2
Header table
E1
D1
B 8
A 7
C 7
D 5
E 3
A 3
C 3 3
D 2 3 3
E 2 1 2
B A C D
26
FP-Tree Construction Reading 7
Transaction Database
null
B5
A2
A3
C2
C1
D1
D1
D1
E1
C2
Header table
E1
D1
B 8
A 7
C 7
D 5
E 3
A 3
C 4 3
D 2 3 3
E 2 1 2
B A C D
27
FP-Tree Construction Reading 8
Transaction Database
null
B6
A2
A4
C2
C1
D1
D1
D1
E1
C3
Header table
E1
D1
B 8
A 7
C 7
D 5
E 3
A 4
C 5 4
D 2 3 3
E 2 1 2
B A C D
28
FP-Tree Construction Reading 9
Transaction Database
null
B7
A2
A5
C2
C1
D1
D1
D1
E1
C3
D1
Header table
E1
D1
B 8
A 7
C 7
D 5
E 3
A 5
C 5 4
D 3 4 3
E 2 1 2
B A C D
29
FP-Tree Construction Reading 10
Transaction Database
null
B8
A2
A5
C3
C1
D1
D1
D1
E1
C3
D1
E1
Header table
E1
D1
B 8
A 7
C 7
D 5
E 3
A 5
C 6 4
D 3 4 3
E 1 2 2 2
B A C D
30
Why have the array?

• Constructing conditional FP-Trees.
• Without array
• Traverse the base FP-Tree to determine the new
  item counts.
• Construct a new header.
• Traverse again the base FP-Tree and construct the
  conditional FP-Tree.
• With array
• Construct a new header helped by the array.
• Traverse the base FP-Tree and construct the
  conditional FP-Tree.
• Saving
• One tree traversal.
• Important because experimentally its shown that
  80 of time is spent on tree traversals.

31
Suffix E
A 5
C 6 4
D 3 4 3
E 1 2 2 2
B A C D
null
(New) Header table
A 2
C 2
D 2
B8
A2
Conditional FP-Tree for suffix E
C3
C1
D1
D1
E1
E1
E1
The set of paths ending in E. Insert each path
(after truncating E) into a new tree.
C
D
A C
32
Suffix E (inserting BCE)
null
(New) Header table
A 2
C 2
D 2
B8
A2
Conditional FP-Tree for suffix E
C3
C1
D1
null
D1
E1
E1
C1
E1
The set of paths ending in E. Insert each path
(after truncating E) into a new tree.
C
D
A C
33
Suffix E (inserting ACDE)
null
(New) Header table
A 2
C 2
D 2
B8
A2
Conditional FP-Tree for suffix E
C3
C1
D1
null
D1
E1
E1
A1
C1
E1
C1
The set of paths ending in E. Insert each path
(after truncating E) into a new tree.
C 1
D 1 1
A C
D1
34
Suffix E (inserting ADE)
null
(New) Header table
A 2
C 2
D 2
B8
A2
Conditional FP-Tree for suffix E
C3
C1
D1
null
D1
E1
E1
A2
C1
E1
C1
D1
The set of paths ending in E. Insert each path
(after truncating E) into a new tree.
C 1
D 2 1
A C
D1