1. A distributed method for mining association rules
Pham Nguyen Anh Huy*
Department of Information Technology
Vietnam National University of HoChiMinh city
presented by Ho Tu Bao
School of Knowledge Science
Japan Advanced Institute of Science and Technology
(*work done during 3 months of the author JSPS’s fellowship in JAIST)

2. Outline Introduction Background
A distributed Apriori algorithm using mobile agents
Experimental evaluation
Conclusion

3. Introduction
Association analysis is a new and attractive research area in data mining
Apriori algorithm (R. Agrawal, IBM 1993) is a key technique for association analysis
Though the apriori principle allows us to considerably reduce the search space, the technique still requires a huge computation, particularly for large database
This research proposes a distributed version of Apriori algorithm using mobile agents. The experiments show that we can reduce computation time when using computers in a distributed computing environment.

4. Outline Introduction Background
Association rules and Apriori algorithm
Mobile agents and Aglets
A distributed Apriori algorithm using mobile agents
Experimental evaluation
Conclusion

5. Association rules: Market basket analysis
Analyzes customer buying habits by finding associations between the different items that customers place in their “shopping baskets” (in the form X  Y, where X and Y are sets of items)
I = {I1=beer, I2=cake, I3=onigiri}
Transactional database
An association rule {I1}  {I3}
How often people buy onigiri and beer together?
TID1: {I1, I2, I3}
TID2: {I1, I2}
TID3: {I2, I3}
TID4: {I2}
TID5: {I1, I2}

6. Rule measures: Support and Confidence
Association rule X Y
support s = probability that a transaction contains X and Y
confidence c = conditional probability that a transaction having X also contains Y
A  C (s=50%, c=66.6%)
C  A (s=50%, c=100%)
Customer buys both
Customer
buys beer
Customer buys onigiri

7. Association mining: Apriori algorithm
It is composed of two steps:
Find all frequent itemsets: By definition, each of these itemsets will occur at least as frequently as a pre-determined minimum support count
Generate strong association rules from the frequent itemsets: By definition, these rules must satisfy minimum support and minimum confidence
(Agrawal, R., 1993)

8. Association mining: Apriori principle
Min. support 50%
Min. confidence 50%
For rule A  C
support = support({A and C}) = 50%
confidence = support({A and C})/support({A}) = 66.6%
The Apriori principle:
Any subset of a frequent itemset must be frequent
(if an itemset is not frequent, its supersets are not)

9. C1  …  Li-1  Ci  Li  Ci+1  …  Lk
The Apriori algorithm: Finding frequent itemsets using candidate generation
Find the frequent itemsets: the sets of items that have support higher than the minimum support
A subset of a frequent itemset must also be a frequent itemset
i.e., if {AB} is a frequent itemset, both {A} and {B} should be a frequent itemset
Iteratively find frequent itemsets Lk with cardinality from 1 to k (k-itemset) by from candidate itemsets Ck (Lk  Ck)
Use the frequent itemsets to generate association rules.
C1  …  Li-1  Ci  Li  Ci+1  …  Lk

10. Example (min_sup_count = 2)
Scan D for count of each candidate
Compare candidate support count with minimum support count
Transactional data
TID List of items_IDs
T100 I1, I2, I5
T200 I2, I4
T300 I2, I3
T400 I1, I2, I4
T500 I1, I3
T600 I2, I3
T700 I1, I3
T800 I1, I2, I3, I5
T900 I1, I2, I3 C1 L1
Itemset Sup.Count
{I1}
{I2}
{I3}
{I4}
{I5}
Itemset Sup.Count
{I1}
{I2}
{I3}
{I4}
{I5}

11. Example (min_sup_count = 2)
Itemset
{I1, I2}
{I1, I3}
{I1, I4}
{I1, I5}
{I2, I3}
{I2, I4}
{I2, I5}
{I3, I4}
{I3, I5}
{I4, I5}
Itemset S.count
{I1, I2} 4
{I1, I3} 4
{I1, I4} 1
{I1, I5} 2
{I2, I3} 4
{I2, I4} 2
{I2, I5} 2
{I3, I4} 0
{I3, I5} 1
{I4, I5} 0
Compare candidate support count with minimum support count
Generate candidates C2 from L1
using Apriori principle
Scan D for count of each candidate L2
Itemset S.count
{I1, I2} 4
{I1, I3} 4
{I1, I5} 2
{I2, I3} 4
{I2, I4} 2
{I2, I5} 2
Compare candidate support count with minimum support count
Generate candidates C3 from L2
using Apriori principle C3 L3
Scan D for count of each candidate
Itemset
{I1, I2, I3}
{I1, I2, I5}
Itemset Sc
{I1, I2, I3} 2
{I1, I2, I5} 2
Itemset Sc
{I1, I2, I3} 2
{I1, I2, I5} 2

12. Agents and Mobile agents
Mobile network agents are programs that:
can migrate from system to system within a network environment
Performs some processing at each host
Agent decides when and where to move next
How does it move?
Save state
Transport saved state to next system
Resume execution of saved state
An agent is a computation entity that:
Acts on behalf of other entities in autonomous fashion.
Performs its actions with some level of pro-activity and re-activeness.
Exhibits some level of the key attributes of co-operation.

13. Distributed Computing using Mobile Programs

14. Mobile agent tools 

15. What are Aglets ?
Aglets (Agile Applets) are Java objects that can move from one host on the Internet to another, and perform arbitrary operations within the security limits.
When an Aglet moves it takes along its program code as well as its data.
The Aglets framework is implemented by the Aglets Software Development Kit (ASDK) from IBM. It is an environment for programming mobile Internet Agent in Java.

16. Aglets at Runtime
Currently aglets use the Agent Transfer Protocol (ATP) as a default implementation of the communication layer (ATP is modeled after HTTP)
Used on the Tahiti aglet server
Use the Aglets Server Interface to write application capable of hosting, receiving and dispatching aglets

17. Outline Introduction Background
A distributed Apriori algorithm using the mobile agents
Experimental evaluation
Conclusion

18. A distributed Apriori algorithm1
(1) spawn n slave processes; (2) divide database into partitions
(3) distribute partitions to each slave process 2
Master process
send global candidate (k-1)-itemsets Ck-1 to each slave process
wait and receive local supports, count global supports for global candidate (k-1)-itemsets Ck-1
compute frequent (k-1)-itemsets Lk-1, and send clusters of frequent (k-1)-itemsets Lk-1 to slave processes
8. wait and receive local candidate k-itemsets from slave processes
9. unionize local candidate k-itemsets and prune to form global candidate k-itemsets.
Slave processes
receive the global candidate (k-1)-itemsets Ck-1
count local supports for global candidate (k-1)-itemsets Ck-1, and send local supports to the master process.
receive frequent (k-1)-itemsets Lk-1 from the master process
generate local candidate k-itemsets and send these local candidate k-itemsets to the master process

19. A distributed Apriori algorithm
SEND global candidate
(k-1) itemsets Ck-1
COUNT and SEND local supports for global candidate (k-1)-itemsets
(counting support Aglets)
COUNT global supports for global candidate (k-1)-itemsets Ck-1
JOIN and SEND local candidate k-itemsets
(Aprio_gen Aglet)
UNIONIZE local candidate k-itemsets and PRUNE to form global candidate k-itemsets Ck
e.g.,{AB} 2 3 1 …
DB1
DB1 … DB DB
DB2
DB2 DB 8 . .
FIND and SEND frequent (k-1)-itemsets Lk-1
DBn
DBn
master slaves master slaves master

20. Global support count & Global candidate itemsets
X is a candidate itemset, global support count of X is
The set of global candidate k-itemsets GCk formed by local candidate k-itemsets
GLk formed by Apriori-gen with ID segment (p, q) of GLk-1
GLk = {GCk ׀ GCk.G-Supp  G-Min-Supp}

21. Outline Introduction Background
A distributed Apriori algorithm using the mobile agents
Experimental evaluation
Conclusion

22. Experiments: Synthetic datasets
Using synthetic datasets of varying sizes:
Name
|D|
|T|
Size (MB)
D100k.T30
100K 30 3M
D100k.T100
100
10M
D320k.T150
320K
150
48M
|D| Number of transactions
|T| Average amount of items on transactions

23. Experiment environment
Software
Database : Oracle server
Language: Java – JDK1.3-Sun
Mobile agents: Aglet- IBM
Protocol traffic: ATP – Aglet Transfer Protocol
Platform: Windows
Hardware
PC Petium3-300 Mhz, RAM 128MB
15 machines (at Knowledge Science Center, JAIST)

24. Execution time (sec.) with different minimum support thresholds
35%
40%
50%

25. Execution time with min_sup 35%

26. Execution time with min_sup 40%

27. Execution time with min_sup 50%

28. Rate of execution time
The rate between execution time and number of slaves is nearly linear

29. Conclusion
Proposed a distributed apriori algorithm for mining association rule
Experimental evaluation show that when the number of slaves increases the execution time decreases nearly linear
Future work:
Segment both the master and GLk for support counts
Develop incremental algorithms for association analysis using the MA technology