1. Amer Zaheer PC101005 Mohammad Ali Jinnah University, Islamabad
Progressive Partition Miner: An Efficient Algorithm for Mining General Temporal Association Rules
Amer Zaheer
PC101005
Mohammad Ali Jinnah University, Islamabad

2. Agenda References Basic Definitions Association Rule Generation
Traditional Association Rule Mining Algorithms
General Temporal Association Rules
Progressive Partition Miner
Limitations of PPM

3. References:
C. H. Lee, M. S. Chen, “Progressive Partition Miner: An Efficient Algorithm for Mining General Temporal Association Rules”
C. H. Lee, C. Lin and M. Chen, “On Mining General Temporal Association Rules in a Publication Database”
C. Chang, M. Chen and C. Lee, “Mining General Temporal Association Rules for Items with Different Exhibition Periods”

4. Basic Definitions Exhibition Period Maximal Common Exhibition Period
Temporal Association Rules
Publication Database
Frequent Item set

5. Publication Database, D
Basic Definitions
Publication Database
Publication Database is set of instructions where each transaction T is a set of items of which each item contains and individual exhibition period.
Publication Database, D A B C D
1990
1992
1994
2001

6. Basic Definitions Exhibition Period:
The exhibition period is a starting time of any item or set of items till end of transactions
Example:
In Publication database, D
Item A and B are exhibited from 1990 to 2001
Item C is exhibited from 1992 to 2001
Item D is from 1994 to 2001
So each transaction item has a unique exhibition period

7. Basic Definitions Maximal Common Exhibition Period
Latest exhibition start time of both item set X and Y and common end time.
Temporal Association Rule
An association rule is consider temporal association rule , if and only if its probability is greater then minimum support required and conditional probability is larger than minimum confidence needed.

8. Meaning of Symbols Used
dbi,n
The partial database of D formed by a continuous region from Pi to Pj
|dbi,n|
Number of transactions in dbi,n
Xi,n
A temporal Item set in partial database dbi,n
MCP()
The maximum common exhibition period of an item set
(X⇒Y)MCP()
A general temporal association rule
supp(((X⇒Y)t,n)
The support of X⇒Y in partial database dbi,n
conf((X⇒Y)t,n)
The confidence of X⇒Y in partial database dbi,n
min_supp
Minimum support threshold required
min_conf
Minimum confidence threshold required
min_leng
Minimum length of exhibition period required TI
A maximal temporal itemset SI
A corresponding temporal sub-itemset of TI

9. Association Rules Generation
Let
L= {X1, X2, X3, ……… Xn}
D be a set of transactions, where each transaction T is a set of items such that
A transaction T said to support X if and only if
Conventionally, an association rule is an implication of the form , meaning that the presence of the set X implies the presence of another set Y, where

10. Association Rule Generation
The rule holds in the transaction set D with confidence c if c% of transaction in D that contain X also contain Y.
The rule has support in the transaction set D if s% of transaction in D contain
Problem of mining association rules that have confidence and support greater then corresponding minimum support threshold and minimum confidence threshold.

11. Traditional Association Rule Mining Algorithms
Conventional association rule mining algorithms works in two steps
Generate all frequent item sets that satisfy min_supp
Generate all association rules that satisfy min_conf using the frequent item sets
But
Lack of consideration of Exhibition Period of each individual item
Lack of an fair support counting basis for each item

12. Traditional Association Rule Mining Algorithms Example
Transaction Database
TID
Itemset T1
B D T2
B C D T3
B C T4
A D T5
B C E T6
D E T7
A B C T8
C D E T9
B C E F
T10
B F
T11
T12
B D F

13. Traditional Association Rule Mining Algorithms Example
Assumptions: min_supp=30%
min_conf=75%
Traditional mining technique: Absolute Support Threshold
SA=|12*0.3|=4
Thus
B, C, D, E and BC can be termed as frequent item sets and C⇒B is termed as a frequent association rule with support 41.67% and confidence %
An early publication intrinsically possesses a higher likelihood to be determined as a frequent itemset
Some discovered rules may be expired from user interest

14. General Temporal Association Rules
General Temporal Association Rules, i.e, (X⇒Y)t,n , where t is the latest exhibition-start time of both item set X and Y and n denotes the end time publication database.
An association rule X⇒Y is termed to be frequent if its probability is larger then minimum support required and conditional probability is larger then minimum confidence needed.
Instead of absolute support threshold for each item set, a relative minimum support is used.
SRA = ||DX|*min_supp|, where DX indicates the amount of partial transaction in the exhibition period of itemset X

15. General Temporal Association Rules: Example
Transaction Database
Date
TID
Itemset
Jan-01 T1
B D T2
B C D T3
B C T4
A D
Feb-01 T5
B C E T6
D E T7
A B C T8
C D E
Mar-01 T9
B C E F
T10
B F
T11
A D
T12
B D F
db1,3
db2,3
db2,3

16. General Temporal Association Rules: Example
Assumption: mini_supp = 30%
mini_conf= 75%
General Temporal Association Rules:
(C⇒E)2,3 with relative support 37.5 % and confidence 75%
(E⇒C)2,3 with relative support 37.5 % and confidence 75%
(B⇒F)3,3 with relative support 75 % and confidence 100%
(F⇒B)3,3 with relative support 75 % and confidence 100%

17. Progressive Partition Miner
To deal with the mining of general temporal association rule (X⇒Y)t,n , Progressive Partition Miner (PPM) is devised.
The basic idea of PPM is to first partition the publication database in light of exhibition periods of items and then progressively accumulate the occurrence count of each candidate 2-itemset based on the intrinsic partitioning characteristics.

18. Progressive Partition Miner: Flow Chart
Partition database based
on exhibition periods
Produce
candidate 2-TIs
Use candidate 2-TIs
to produce candidate
k-TIs and k-SIs
Generate frequent
Rule
generation
1st Scan database
2nd Scan Database

19. Progressive Partition Miner: EXAMPLE
Date
TID
Item Set
Jan01 T1
B D T2
B C D T3
B C T4
A D
FEB-01 T5
B C E T6
D E T7
A B C T8
C D E
MARCH-01 T9
B C E F
T10
B F
T11
A D
T12
B D F P1 P2 P3
Transaction database
min_supp = 30%and min_conf = 75%.

20. Progressive Partition Miner: EXAMPLE
P1+P2 C2
START
COUNT BD 1 2 BC 4 CE DE AB AC CD BE
First Scan P1 C2
START
COUNT BD 1 2 BC CD AD
four transactions in P1, the partial
minimal support is (4 ∗ 0.3) = 2.
Support:
α ((4 + 4) ∗ 0.3) = 3
β(4 ∗ 0.3) = 2.
min_supp = 30%and min_conf = 75%.

21. Progressive Partition Miner: EXAMPLE
P1+P2+P3 C2
START
COUNT BC 1 5 CE 2 3 DE DF BE BF CF EF AD BD
CANDIDATE ITEM SET
COUNT BC 5 BF 3 CE

22. Progressive Partition Miner: EXAMPLE
Candidate 2-item set: BC 1,3 CE 2,3 BF 3,3
Candidate 1-item set: B 1,3 C 1,3 C 2,3 E 2,3 B3,3 F 3,3
CANDIDATE ITEM SET
COUNT C1
B1,3 8
B3,3 3
C1,3 6
C2,3 4
F3,3 C2
BC1,3 5
BF3,3
CE2,3

23. Progressive Partition Miner: EXAMPLE
Now count the support according to given rang each item set.
Frequent ITEM SET
COUNT L1
B1,3 8
B3,3 3
C1,3 6
C2,3 4
F3,3 L2
BC1,3 5
BF3,3
CE2,3
After 2nd scan database D, we have frequent itemsets ( relative support = 30% ) as follows:
B 1,3 C 1,3 C 2,3 E 2,3 B3,3 F 3,3
BC1,3 CE 2,3 BF 3,3

24. General Temporal Association :Rule Generation
(B ⇒C)1,3
Total Transaction=12
Support Count= 5
Thus support=41.67%
Confidence (X ⇒ Y) = Support(XUY)/ Support(X)
Confidence(B ⇒Y) =5/8
Confidence(B ⇒Y)=62.5%

25. General Temporal Association :Rule Generation
SUPPORT
CONFIDENCE
(B => C)1,3
41.67%
62.50%
(C => B)1,3
83.33%
(B => F)3,3
75.00%
100.00%
(F => B)3,3
(C => E)2,3
37.50%
(E => C)2,3
min_supp = 30%and min_conf = 75%.

26. General Temporal Association :Rule Generation, Pruning
SUPPORT
CONFIDENCE
(C => B)1,3
41.67%
83.33%
(B => F)3,3
75.00%
100.00%
(F => B)3,3
(C => E)2,3
37.50%
(E => C)2,3

27. Limitation
Partition the database on exhibition period rather than size of database so not uniform partition.
Temporal database is updated continually it not handle the upcoming iteration.

28. Thanks