3. • Gambaran penyilangan Itemset Lattice
– Breadth-first(Menyeluruh) vs Depth-first(Mendalam)
(a) Breadth first (b) Depth first
Metode Pencarian Alternatif
4. ECLAT: Metode Pembentukan Itemset
• ECLAT: untuk setiap item, dinyatakan dalam tabel
transaction ids (tids); tampilan data vertikal
TID Items
1 A,B,E
2 B,C,D
3 C,E
4 A,C,D
5 A,B,C,D
6 A,E
7 A,B
8 A,B,C
9 A,C,D
10 B
Horizontal
Data Layout
A B C D E
1 1 2 2 1
4 2 3 4 3
5 5 4 5 6
6 7 8 9
7 8 9
8 10
9
Vertical Data Layout
TID-list
5. ECLAT: Metode Pembentukan Itemset
• Tentukan support (pendukung) dari setiap k-itemset dengan
menyilangkan tid-lists dari kedua (k-1) subset.
• 3 pendekatan penyilangan:
– Atas-bawah, bawah-atas dan gabungan
• Keuntungan: Proses hitung support lebih cepat dibandingkan
algoritma apriori
• Kerugian: ukuran tid (vertikal) lebih besar dibandingkan
apriori, sehingga memenuhi memori
A
1
4
5
6
7
8
9
B
1
2
5
7
8
10
AB
1
5
7
8
6. First scan – determine frequent 1-
itemsets, then build header
TID Items
1 {A,B}
2 {B,C,D}
3 {A,C,D,E}
4 {A,D,E}
5 {A,B,C}
6 {A,B,C,D}
7 {B,C}
8 {A,B,C}
9 {A,B,D}
10 {B,C,E}
B 8
A 7
C 7
D 5
E 3
7. FP-tree construction
TID Items
1 {A,B}
2 {B,C,D}
3 {A,C,D,E}
4 {A,D,E}
5 {A,B,C}
6 {A,B,C,D}
7 {B,C}
8 {A,B,C}
9 {A,B,D}
10 {B,C,E}
null
B:1
A:1
After reading TID=1:
After reading TID=2:
null
B:2
A:1
C:1
D:1
8. FP-Tree Construction
TID Items
1 {A,B}
2 {B,C,D}
3 {A,C,D,E}
4 {A,D,E}
5 {A,B,C}
6 {A,B,C,D}
7 {B,C}
8 {A,B,C}
9 {A,B,D}
10 {B,C,E}
Transaction
Database
Item Pointer
B 8
A 7
C 7
D 5
E 3
Header table
B:8
A:5
null
C:3
D:1
A:2
C:1
D:1
E:1
D:1
E:1C:3
D:1
D:1 E:1
Chain pointers help in quickly finding all the paths
of the tree containing some given item.
9. FP-Growth (I)
• FP-growth generates frequent itemsets from an FP-tree by
exploring the tree in a bottom-up fashion.
• Given the example tree, the algorithm looks for frequent
itemsets ending in E first, followed by D, C, A, and finally, B.
• Since every transaction is mapped onto a path in the FP-tree, we
can derive the frequent itemsets ending with a particular item,
say, E, by examining only the paths containing node E.
• These paths can be accessed rapidly using the pointers
associated with node E.
11. Conditional FP-Tree for E
• We now need to build a conditional FP-Tree for E, which is the
tree of itemsets include in E.
• It is not the tree obtained in previous slide as result of deleting
nodes from the original tree.
• Why? Because the order of the items change.
– In this example, D has a higher than E count.
12. Conditional FP-Tree for E
Adding up the counts for D we get
2, so {E,D} is frequent itemset.
We continue recursively.
Base of recursion: When the tree
has a single path only.
B:3
null
C:3
A:2
C:1
D:1
E:1
D:1
E:1E:1
The set of paths containing E.
Insert each path (after truncating
E) into a new tree.
Item Pointer
C 4
B 3
A 2
D 2
Header table
The new
header
C:3
null
B:3
C:1
A:1
D:1
A:1
D:1
The
conditional
FP-Tree for E
13. FP-Tree Another Example
A B C E F O
A C G
E I
A C D E G
A C E G L
E J
A B C E F P
A C D
A C E G M
A C E G N
A:8
C:8
E:8
G:5
B:2
D:2
F:2
A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
Freq. 1-Itemsets.
Supp. Count 2
Transactions Transactions with items sorted based
on frequencies, and ignoring the
infrequent items.
14. FP-Tree after reading 1st transaction
A:8
C:8
E:8
G:5
B:2
D:2
F:2
A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
null
A:1
C:1
E:1
B:1
F:1
Header
15. FP-Tree after reading 2nd transaction
A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:2
C:2
E:1
B:1
F:1
Header
16. FP-Tree after reading 3rd transaction
A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:2
C:2
E:1
B:1
F:1
Header
E:1
17. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 4th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:3
C:3
E:2
B:1
F:1
Header
E:1
G:1
D:1
18. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 5th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:4
C:4
E:3
B:1
F:1
Header
E:1
G:2
D:1
19. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 6th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:4
C:4
E:3
B:1
F:1
Header
E:2
G:2
D:1
20. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 7th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:5
C:5
E:4
B:2
F:2
Header
E:2
G:2
D:1
21. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 8th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:6
C:6
E:4
B:2
F:2
Header
E:2
G:2
D:1
D:1
22. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 9th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:7
C:7
E:5
B:2
F:2
Header
E:2
G:3
D:1
D:1
23. A C E B F
A C G
E
A C E G D
A C E G
E
A C E B F
A C D
A C E G
A C E G
FP-Tree after reading 10th transaction
G:1
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:8
C:8
E:6
B:2
F:2
Header
E:2
G:4
D:1
D:1
24. Conditional FP-Tree for F
A:8
C:8
E:8
G:5
B:2
D:2
F:2
null
A:8
C:8
E:6
B:2
F:2
Header
There is only a single path containing F
A:2
C:2
E:2
B:2
null
A:2
C:2
E:2
B:2
New Header
25. Recursion
• We continue recursively on the
conditional FP-Tree for F.
• However, when the tree is just a
single path it is the base case for
the recursion.
• So, we just produce all the subsets
of the items on this path merged
with F.
{F} {A,F} {C,F} {E,F} {B,F}
{A,C,F}, …,
{A,C,E,F}
A:6
C:6
E:5
B:2
null
A:2
C:2
E:2
B:2
New Header
26. Conditional FP-Tree for D
A:2
C:2
null
A:2
C:2
New Headernull
A:8
C:8
E:6
G:4
D:1
D:1
Paths containing D after updating the counts
The other items are
removed as infrequent.
The tree is just a single path; it is
the base case for the recursion.
So, we just produce all the
subsets of the items on this path
merged with D.
{D} {A,D} {C,D} {A,C,D}
