1. An Efficient Algorithm for Incremental Mining of Association Rules
Chin-Chen Chang, Yu-Chiang Li, Jung-San Lee
RIDE-SDMA’05
Speaker：董原賓 Advisor：柯佳伶

2. Introduction Previous incremental mining algorithms Problem Solution
FUP (Fast Update Algorithm)
FUP2
negative border
※They all have to rescan the originally database
Problem
Publication-like database
EX：Publication database, web log records, etc.
The original database is normally much larger
than the incremental database
Solution
NFUP (New Fast Update Algorithm)

3. Definition DB：original database db：the set of newly added transactions
DB+：DB + db
n, Pn：db is divided into n partitions,
db = P1UP2U,…,UPn-1UPn
dbm,n = PmUPm+1U,…,UPn-1UPn

4. Definition α set: frequent itemsets in DB+
β set: frequent in dbm,n , (m ≤ n), but infrequent in dbm-1,n
γ set: frequent in dbm,m, but infrequent in dbm+1,n
X.count：occurrence count
X.start：partition number when X becomes frequent
X.type：denotes one of the three types α,β, and γ

5. FUP (Fast Update Algorithm)
In case2, itemset is easily calculated
In case3, FUP needs to rescan the original database

6. NFUP (New Fast Update Algo.)
A backward method that only requires scanning incremental database
A frequent itemset in the incremental database is also important even if it is infrequent in the updated database
Partition the incremental database (db) by the time interval

7. NFUP The frequent set of itemsets of DB is known in advance
NFUP scans each partition backward, the last partition is scanned first
In each partition, the process is performed like that of Apriori.

8. NFUP

9. Scan from Pn to P1 and find the
α,β,γ itemsets in db
After P1 is scanned, the occurrence count
is accumulated with itemsets of DB

10. The latest partition is scanned first,
initialize variables and accumulate
the occurrence
Still frequent in Pm then
accumulate count
Still frequent in dbm,n then
accumulate count
Only frequent in dbm+1,n then
Remove from α set and add
Into β set
Not belong to any set and frequent in
Pm then check if Pm is the latest partition
Yes  α set
No  γ set

11. Example Min sup = 50% {A: 2} {B: 2} {C: 3} {D: 1} {E: 1} {F: 2}
{AB: 2} {AC: 2} {AF: 1}
{BC: 2} {BF: 1} {CF: 2}
Else check itemset doesn’t belongs to any set
Check if itemset belongs to α set
Check if itemset’s count >= 1.5
Run Apriori-gen
Else check itemset doesn’t belong to any set
Check if itemset belongs to α set
Check if P2 is the latest partition yes α
no  γ
Check if P2 is the latest partition yes α
no  γ
Scan p2 : 1-itemset
Scan P2 : 3-itemset
scan P2 : 2-itemset
Check if itemset’s count >= 1.5
3 x 0.5 = 1.5
α set
start
count
β set
start
count
γ set
start
count
{A} 2 2
{B} 2 2
{C} 2 3
{F} 2 2
{AB} 2 2
{AC} 2 2
{BC} 2 2
{CF} 2 2
{ABC} 2 2

12. Example Min sup = 50% 3 x 0.5 = 1.5 {A: 1} {B: 3} {C: 2}
{D: 1} {E: 3} {F: 0}
{AB: 1} {AC: 0} {BC: 2}
{BE: 3} {CE: 2}
Yesaccumulate count
Count < s*|dbm,n| = 0.5x6 = 3  β set
Else check if itemset’s count >= 1.5
Run Apriori-gen
Else check if itemset’s count >= 1.5
Check if P1 is the latest partition yes α
no  γ
Check if itemset belongs to α set
scan P1 : 2-itemset
Check itemset doesn’t belongs to any set
Yesaccumulate count
Count < s*|dbm,n| = 0.5x6 = 3  β set
Check itemset doesn’t belong to any set
Check if itemset belongs to α set
Check if P1 is the latest partition yes α
no  γ
Scan p1 : 1-itemset
α set
start
count
β set
start
count
γ set
start
count
{A} 1 2 2 3
{F} 2 2
{E} 1 3
{B} 2 1 2 5
{AC} 2 2
{BE} 1 3
{C} 1 2 5 3
{CF} 2 2
{CE} 1 2
{F} 2 2
{ABC} 2 2
{AB} 2 1 3 2
{AC} 2 2
{BC} 2 1 2 4
{CF} 2 2
{ABC} 2 2

13. Example α set start count β set start count γ set start count {A} 1 33 7
{F} 2 2
{E} 1 3
{B} 1 5 8
{AC} 2 2
{BE} 1 3
{C} 1 9 5
{CF} 2 2
{CE} 1 2
{AB} 1 3
{AB}
{ABC} 2 1 2 3
{AE} 3
{BC} 1 4
{BC} 1 4
{ABC} 2 2

14. Experiment Intel Pentium IV 1.5GHz CPU, 640 MB main memory
Microsoft Windows 2000 Professional
Synthetic datasets:

15. Experiment

16. Experiment

17. Experiment