1 weighted partonomy-taxonomy trees with local similarity measures for semantic buyer-seller...

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Weighted Partonomy-Taxonomy Trees with Local Similarity Measures for Semantic Buyer-Seller Matchmaking

By: Lu Yang

March 16, 2005

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Outline

Motivation Similarity Measures Partonomy Similarity Algorithm

– Tree representation– Tree simplicity– Partonomy similarity

Experimental Results Node Label Similarity

– Inner-node similarity– Leaf-node similarity

Conclusion

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Motivation

– Keywords/keyphrases– Trees

e-business, e-learning … Buyer-Seller matching Metadata for buyers and sellers

Tree similarity

4

Similarity measures

Similarity measures apply to many research areas

– CBR (Case Based Reasoning), information retrieval, pattern recognition, image analysis and processing, NLP (Natural Language Processing), bioinformatics, search engine, e-Commerce and so on

In e-Commerce– Product P satisfies demand D ?

Is it an “All or Nothing” question? Additional knowledge needed Bridge the gap between demand and product descriptions

Now, a “How similar?” question!

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Numerical modeling of similarity– A similarity measure on a set M is a real function

sim: M2 [0,1] – Similarity measures have following properties

Reflexivity x M: sim(x,x) = 1

Symmetry iff x,yM: sim(x,y) = sim(y,x)

Similarity measures (Cont’d)

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An opposite notion of similarity measures A distance measure on a set M is a real valued

function d: M2 IR+

Distance measures have following properties

– Reflexivity xM d(x,x) = 0

– Symmetry iff x, yM d(x,y) = d(y,x)

– Triangle Inequality

iff x, yM d(x,y) = 0 x = y

x, y, zM d(x,y) + d(y,z) d(x,z)

Similarity measures – distance measures

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Transformation of similarity measures and distance measures– If a bijective, order inverting mapping f: [0,1] [0,1]

exists with

f(d(x,y)) = sim(x,y)

then sim and d are compatible

Similarity measures – distance measures

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Global measures are defined on the whole object– reflect the task and have a pragmatic character

Local measures are defined on details (e.g. the domains of some attribute)– reflect technical and domain character– task independent

Similarity measures – global and local

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Local to global– each object A is constructed from so-called

“components” Ai by some construction process

C(Ai |i n) = A

given two objects A and B, simi(Ai, Bi) denotes

the similarity of their ith components– amalgamation function f

sim(A, B) is the global similarity measure of A and B

sim(A, B) = f(simi(Ai , Bi) |i n )

Similarity measures – global and local

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Tree representation

Characterises of our trees – Node-labled, arc-labled and arc-weighted– Arcs are labled in lexicographical order– Weights sum to 1

0.3

0.2

0.5Make

Model

Year

2002

Car

Ford Explorer

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Tree representation – serialization of trees

– XML attributes for arc weights and subelements for

arc labels

– Weighted Object-Oriented RuleML

<Cterm>

<Ctor>Car</Ctor>

<slot weight="0.3"><Ind>Make</Ind><Ind>Ford</Ind></slot>

<slot weight="0.2"><Ind>Model</Ind><Ind>Explorer</Ind></slot>

<slot weight="0.5"><Ind>Year</Ind><Ind>2002</Ind></slot>

</Cterm>

Tree serialization in WOO RuleML

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Tree representation – Relfun version of tree

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[2002]]

]

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Tree simplicity

A

0.1

a

ed0.90.80.2

E

b0.70.3

B C

f

D

c

F G

– Treeplicity(i,t) Depth degradation index “i” = 0.9

– Reciprocal of tree breadth– Depth degradation factor = 0.5

(0.9)

(0.45)

(0.225)

tree simplicity: 0.0563

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Partonomy similarity – simple trees

Escape

Car

Make Model

Ford

0.3 0.7

Mustang

Car

Make Model

Ford

0.3 0.7

tree t tree t´ (House)

01Inner nodes

01Leaf nodes

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Partonomy similarity – complex trees

(si (wi + w'i)/2)

(A(si)(wi + w'i)/2)

A(si) ≥ si

lom

educational

0.5

general

format platform0.50.50.5

Introduction to Oracle

t t´

technical0.3334 0.33330.3333

edu-set gen-set tec-set

language

en

title

HTML WinXP

lom

0.1

general

format platform0.90.80.2

Basic Oracle

technical0.70.3

gen-set tec-setlanguage

en

title

* WinXP

* : Don’t Care

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Partonomy similarity – main recursive functions

– Treesim(t,t'): Recursively compares any (unordered) pair of trees

Paremeters N and i

Three main recursive functions (Relfun)

– Treemap(l,l'): Recursively maps two lists, l and l', of labeled

and weighted arcs: descends into identical–labeled subtrees

– Treeplicity(i,t): Decreases the similarity with decreasing simplicity

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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

0.55

1.0

t1 t2

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Experimental results – simple trees (cont’d)


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


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

20

b2

Experimental results – complex trees

0.33340.333

3

b1

1.00.25 0.25 0.25

0.33340.3333

1.00.3333 0.333

3

0.3334

c2

0.3333

0.25 c3c1

c2

c

b3

A

B C D

b d

b1b4

c1 c3 d1

B1 B4 C1 C3 D1 B2 B3

c4

c

A

B C D

b d

d1

B1

C1 C4C3 D1

0.3334

0.3333

0.50.5

0.3333

0.3333

E F

t t´

0.8160 0.9316 0.8996 0.9230 0.9647 0.9793

21

b2


0.33340.333

3

b1

1.00.25 0.25 0.25

0.33340.3333

1.00.3333 0.333

3

0.3334

c2

0.3333

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c2

c

b3

A

B C D

b d

b1b4

c1 c3 d1

B1 B4 C1 C3 D1 B2 B3

c4

c

A

B C D

b d

d1

B1

C1 C4C3 D1

0.3334

0.3333

0.50.5

0.3333

0.3333

E E F

t t´

0.8555 0.9626 0.9314 0.9499 0.9824 0.9902

22

b2


0.33340.333

3

b1

1.00.25 0.25 0.25

0.33340.3333

1.00.3333 0.333

3

0.3334

c2

0.3333

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c2

c

b3

A

B C D

b d

b1b4

c1 c3 d1

B1 B4 C1 C3 D1 B2 B3

c4

c

A

B * D

b d

d1

B1

C1 C4C3 D1

0.3334

0.3333

0.50.5

0.3333

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E F

t t´

0.9134 0.9697 0.9530 0.9641 0.9844 0.9910

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Node label similarity

For both inner nodes and leaf nodes– Exact string matching binary result 0.0 or 1.0– Permutation of strings

“Java Programming” vs “Programming in Java”

Number of identical words

Maximum length of the two strings

Example 1:

For two node labels “a b c” and “a b d e”, their similarity is:2

4= 0.5

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Example 2:

Node labels “electric chair” and “committee chair”

Node label similarity (cont’d)

1

2= 0.5 meaningful?

• Semantic similarity

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Node label similarity – inner nodes vs. leaf nodes

Inner nodes — class-oriented– Inner node labels can be classes– classes are located in a taxonomy tree– taxonomic class similarity measures

Leaf nodes — type-oriented– address, currency, date, price and so on– type similarity measures (local similarity measures)

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Node label similarity

String Permutation (both inner

and leaf nodes)

Exact String Matching (both inner

and leaf nodes)

Non-Semantic Matching

Taxonomic Class Similarity

(inner

nodes)

Type Similarity (leaf nodes)

Semantic Matching

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Inner node similarity – partonomy trees

Distributed Programming

Credit

“Introduction to Distributed Programming”

Textbook

TuitionDuration

$8002months3

0.20.1 0.3

0.4

t1 t2

Object-Oriented Programming

Credit

“Objected-Oriented Programming Essentials”

Textbook

TuitionDuration

$10003months3

0.10.5 0.2

0.2

partonomy trees

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Inner node similarity – taxonomy tree

Programming Techniques

Applicative Programming

0.50.2General

Automatic Programming

Concurrent Programming

Sequential Programming



Parallel Programming

0.7 0.40.5

0.3

0.3 0.9

• arc weights

• at the same level of a subtree do not need to add up to 1

• assigned by machine learning algorithms or human experts

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Applicative Programming

0.50.2General

Automatic Programming

Concurrent Programming

Sequential Programming



Parallel Programming

0.7 0.4 0.50.3

0.3 0.9

• red arrows stop at their nearest common ancestor

• the product of subsumption factors on the two paths (0.018)

Inner node similarity – taxonomic class similarity

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Inner node similarity – separate to encoded taxonomy tree

Separate taxonomy tree– extra taxonomic class similarity measures

How to compute semantic similarity without – changing our partonomy similarity algorithm– losing taxonomic semantic similarity

Encode the (subsections) of taxonomy tree into partonomy trees

Disjoint subsections of taxonomy lead to zero semantic similarity

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Inner node similarity – encoding taxonomy tree into partonomy tree


Applicative Prgrm

0.1

0.1

GeneralAutomatic Prgrm

Concurrent Prgrm

Sequential Prgrm

Object-Oriented Prgrm

Distributed Prgrm

Parallel Prgrm

0.3

0.15

0.40.6

0.20.15

* **

*

* * *

*encoded taxonomy tree

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Credit TitleTuition

Duration

$8002months30.05 0.1 0.15

0.05

t1

Classification0.65

taxonomy


$10003months3

0.2 0.05 0.050.05

t2

Classification0.65

taxonomy

Distributed Prgrm

course

Concurrent Prgrm

Parallel Prgrm

0.6 0.4


0.7 0.3

0.8 0.2

course

1.0


1.0*

Distributed Prgrm

Credit TitleTuition

Duration


Sequential Prgrm

**

**

**

*Sequential Prgrm

Inner node similarity – encoding taxonomy tree into partonomy tree (cont’d)

encoded partonomy trees

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Leaf node similarity (local similarity)

0.5

end_date

Nov 3, 2004

0.5

t1 t 2

start_date

May 3, 2004

Project

0.5

end_date

Feb 18, 2005

0.5

start_date

Jan 20, 2004

Project

Example: “date” type leaf nodes

DS(d1, d2) = {

0.0

otherwise

if | d1 – d2 | ≥ 365

1 –| d1 – d2 |

365

0.74

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Implementation

Relfun version– exact string matching– don’t care

Java version– exact string matching– don’t care– string permutation– encoded taxonomy tree in partonomy tree (Teclantic)– “date” type similarity measure

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Conclusion

Arc-labeled and arc-weighted trees Partonomy similarity algorithm

– Traverses trees top-down– Computes similarity bottom-up

Node label similarity– Exact string matching (both inner and leaf nodes)– String permutation (both inner and leaf nodes)– Taxonomic class similarity (only inner nodes)

Taxonomy tree Encoding taxonomy tree into partonomy tree

– Type similarity (only leaf nodes) “date” type similarity measures

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Questions?

1 weighted partonomy-taxonomy trees with local similarity measures for semantic buyer-seller...

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