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Transcript of 1 A Weighted-Tree Similarity Algorithm for Multi-Agent Systems in e-Business Environments Virendra...
1
A Weighted-Tree Similarity Algorithm for Multi-Agent Systems in e-Business Environments
Virendra C.Bhavsar*Harold Boley**Lu Yang**Faculty of Computer Science, Univ. of New Brunswick, Fredericton
**Institute for Information Technology – e-Business, NRC, Fredericton
2
Outline
Introduction Multi-agent system architecture Tree representation Similarity of trees Experimental results Conclusion
3
Introduction
e-business, e-learning.
– Buyer-seller message exchange.
Semantic Web and Web Services. – Virtual marketplace.
Semantic match-making in multiagent systems.– Keywords/keyphrases.
4
Multi-agent system architecture
Agent-based Community Oriented Routing Network (ACORN)
Cafe-n
Main Server
User Info
User Profiles
User Agents
…
…
Agents
…
…
Cafe-1
To other sites (network)
Web BrowserUser
Cafe-n
5
Tree representation
Why tree representation? – Flexibly represent complex structures.– Why arc-labelled, arc-weighted tree?
0.3
0.2
0.5
2002
Car
Ford Explorer
Make
Model
Year
2002
Car
Ford Explorer
6
Matchmaking of agents
Match-making in the Cafe.
.
.
.
.Cafe
Leaner 1
..
Course 1
Leaner 2
Leaner n
Course 2
Course m
Programming in Java
Credit
Thinking in Java
Textbook
TuitionDuration
$12002 months3
0.2 0.10.3
0.4
carri
ed b
y
carried by
Programming in Java
Credit
Introduction to Java
Textbook
TuitionDuration
$15002 months3
0.2 0.10.3
0.4
7
Tree representation - lexicographic order
The arcs are labelled in lexicographic
(alphabetical) order.
2002
Car
Make
Model
Year
Ford Explorer
0.3
0.2
0.5
A tree describing “Car”.
Hotel
Location
Beds FrederictonDowntown
0.5
0.8
0.5
UptownSingle0.2
0.90.1
100 Sheraton Hotel
150 LincolnHotel
Capacity
Queen
A tree describing “Hotel”.
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Tree representation - depth and breadth
The depth and breadth of any subtree are not
limited. Jobbank
IT Education
Oldpost
Preliminary
0.9
0.5
0.1
Advanced0.4 0.6
Newpost
DBAProgrammer
College High School
University
School
SoftwareHardware
0.50.1
0.4
0.5
0.2 0.8
… …Position
JavaOracleCertificate
Seneca College
LiverpoolHigh School
UNB
A tree that describes “Jobbank”.
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Serialization of trees
– XML attributes for arc labels and weights.
– Weighted Object-Oriented RuleML.
cterm[ -opc[ctor[car]], -r[n[make],w[0.3]][ind[ford]], -r[n[model],w[0.2]][ind[explorer], -r[n[year],w[0.5]][ind[1999]] ]
<cterm> <_opc><ctor>Car</ctor></_opc> <_r n=“Make” w=“0.3”><ind>Ford</ind></_r> <_r n=“Model” w=“0.2”><ind>Explorer</ind></_r> <_r n=“Year” w=“0.5”><ind>1999</ind></_r></cterm>
Tree serialization in OO RuleML. Tree representation in Relfun.
10
Similarity of trees – simple trees
1 0
1999
Car
Make Year
Ford
0.3 0.7
2002
Car
Make Year
Ford
0.3 0.7
tree t tree t´ (House)
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Similarity of trees – complex trees
A(si)(wi + w'i)/2
A(si) = si
A(si) = . is
vehicle
autumn
autoautomake
0.5 0.5
modelyear
0.3334
ford
mini1999
summer
make
model
year0.3334 0.3333
0.3333
0.3333
0.3333
van2000
freestar
e-serieswagon
monteryfreestar
0.50.5 0.50.5
vehicle
autumn
autoautomake
0.5 0.5
modelyear 0.3334
fordvan1999
summer
make
model
year0.3334 0.3333
0.3333
0.33330.3333
ford2001
0.50.5big
ford
big mini
van
big mini
e-serieswagon
freestar
truck
tree t tree t´
si(wi + w'i)/2
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Algorithm for tree similarity
– Treesim(t,t'): Recursively compares any (unordered) pair of trees.
Three main recursive functions of the algorithm.
– Treemap(l,l'): Co-recursively maps two lists, l and l', of labelled
and weighted arcs: descends into identical–labelled subtrees.
– Treeplicity(i,t): Decreases the similarity with decreasing simplicity.
13
Experimental results –simple trees
auto
0.5make
2002ford
year0.5
auto
0.5make
1998chrysler
year0.5
auto
0.0make
2002ford
year1.0
auto
1.0make
1998ford
year0.0
t1 t2
auto
0.0make
2002ford
year1.0
auto
1.0make
2002ford
year0.0
t3 t4
Experiments Tree Tree Results
1
2
0.1
0.5
1.0
t1 t2
14
Experimental results – simple trees (cont’d)
Experiments Tree Tree Results
3
0.1
make
auto
mustang
auto
0.45model
2000ford
year
t1 t2
1.0model 0.45
explorer
0.9
make
auto
mustang
auto
0.05model
2000ford
year
t3 t4
1.0model 0.05
explorer
0.2823
0.1203
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Experimental results – identical tree structures
Experiments Tree Tree Results
4
0.2make
auto
0.3
1999ford
year
t2
model0.5
explorer
make
auto
1999ford
year
t4
model
explorer
0.33330.33330.3334
0.2
make
auto
0.3
2002ford
year
t1
model 0.5
explorer
make
2002ford
year
t3
model
explorer
0.33330.33330.3334
auto
0.55
0.7000
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Experimental results – progressively complex trees
Experiments Tree Tree Results
5
auto
t1
t2auto
make1.0
fordauto
model
ford explorer
make0.5 0.5
t3
auto
modelyear
ford explorer 2002
make0.3
0.20.5
t4
0.3025
0.3025
0.3025
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Experimental results – complex trees
vehicle
autumn
autoautomake
0.5 0.5
modelyear
0.3334
ford
mini1999
summer
make
modelyear
0.3334 0.3333
0.3333
0.3333
0.3333
ford2000
freestar
freestar
e-serieswagon
e-serieswagon
0.50.5 0.50.5
vehicle
autumn
autoautomake
0.5 0.5
modelyear
0.3334
ford van1999
summer
make
modelyear
0.3334 0.3333
0.33330.3333
0.3333ford
2001
freestar
e-serieswagon
0.50.5
tree t1 tree t2
bigbig mini mini
SiisExperiments Tree Tree
6
0.5950
0.7611big
van van van
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Experimental results – complex trees (cont’d)
SiisExperiments Tree Tree
7
vehicle
auto
1.0
0.3334
summer
makemodel
year0.3333
0.3333
ford 2000
tree t1
vehicle
autumn
autoauto
make
0.5 0.5
model
year 0.3334
ford 1994
summer
make
modelyear
0.3334 0.3333
0.3333
0.3333
0.3333
ford 2001
tree t2
0.5894
0.6816van
van van
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Conclusion
Tree representations – useful for e-Business, e-
Learning. Matchmaking in multiagent systems – a versatile
tree similarity algorithm is proposed.
Executable specification available in functional-logic
language: Relfun.
Future work - Clustering of agents.
- A Java implementation is in progress.
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