27th April 2006Semantics & Ontologies in GI Services Semantic similarity measurement in a wayfinding service Martin Raubal [email protected]

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27th April 2006 Semantics & Ontologies in GI Services

Semantic similarity measurement in a wayfinding service

Martin Raubal

[email protected]

Martin Raubal Semantic similarity measurement in a wayfinding service 2

At large yellow building turn left.

Walk straight until light green historical building.

Turn right …


Problem

Assumption:

LANDMARKSystem = LANDMARKUser

Needed:

System must adapt semantics of its concepts to user‘s semantics.

Formal conceptual spaces

Measuring semantic similarity between geospatial concepts.


Outline

• Cognitive semantics

• Geometrical models

• Conceptual spaces

• Formalization of conceptual spaces

• Application to case study

• Conclusions and future work


Cognitive semantics

• Efforts to solve semantic interoperability problems => realist semantics

• Problems: learning, mentally constructed objects, change of meaning of concepts

• Cognitive semantics: meanings are mental entities

After Gärdenfors 2000, p.153/154


Geometrical models

• Similarity between entities as geometric models consisting of points in dimensional metric space.

• Similarity inversely related to distance (dissimilarity) between two entities => linear decaying function of the semantic distance d.

rn

k

r

jkikij xxd/1

1


Conceptual spaces (Gärdenfors)

• Conceptual space = set of quality dimensions with a geometrical / topological structure for 1 or more domains

• Domain = set of integral dimensions, e.g., color domain (hue, saturation, brightness)

• Learning: extension of conceptual space through new quality dimensions

Let no one ignorant of geometry enter here (Plato).


Color domain

a

brightnesssaturation

hue


Geometric structures of dimensions

[Schwering forthcoming]


Formalization

• Conceptual vector space = set of vectors representing quality dimensions

• Ideally a basis, but hard to achieve.

• Multi-domain concepts => dimensions can represent whole domain (i.e., subspaces)

Cn = {(c1, c2, …, cn) | ci C}

cj = Dn = {(d1, d2, …, dn) | dk D}


c1

c2

c3


Semantic distances and weights

Euclidean distances between points (i.e., instances of concepts as vectors).

• Calculation of z scores for components => same relative unit of measurement

• Calculation of semantic distance:|duv|2 = (z1

v - z1u)2 + (z2

v - z2u)2 + … + (zn

v - znu)2

Weights:Cn = {(w1c1, w2c2, …, wncn) | ci C, wj W}


Z-transformation

• zi is the i-th value of the new variable Z

• xi is the i-th value of the old variable X

• is the mean of X

• sx is the standard deviation of X

x

ii s

xxz

x


z1

z2

z3

u

v

d(u,v)


Case study: wayfinding service

• Facades of buildings as landmarks.

• Concept of facade represented by different variables.

• Utilize conceptual vector spaces => capture difference between system‘s and user‘s view of ‚facade‘.



Global measure of landmark saliency

Mea

sure

Pro

pert

y

Val

ue

Sig

nifi

canc

e (P

rope

rty)

Sig

nifi

canc

e (M

easu

re)

Wei

ght

Wei

ghte

d S

igni

fica

nce

Tot

al

… s

1 … s1

2 … s2 … s

Visual attraction

… s

svis = (s+ s1+s2+ s+s) / 5

wvis

svis*wvis

… s Semantic attraction … s

ssem = (s+s) / 2

wsem ssem*wsem

… s Structural attraction … s

sstr =

(s+s) / 2 wstr sstr*wstr

svis*wvis +

ssem*wsem +

sstr*wstr


Intersection Haas building


Wayfinding instruction

[ AT landmark ]

[ TURN LEFT | RIGHT | MOVE STRAIGHT ]

{ ONTO streetname }

{ PASSING | CROSSING landmark }

[ UNTIL landmark ]

XY

LEFT ]

Stephansplatz }

Haas building, a big building ofarchitectural significance ]

Stephansdom, a visually salientworld cultural heritage building }


Problem

• User and service provider have different concepts of facade / building!

=> System needs to adapt the semantics of its concepts to the user’s semantics, leading to improved human-computer interaction.


Conceptual space for facade

• System view: area, shape factor, shape deviation, color (RGB), visibility, cultural importance, identifiability by signs.

C7system = {(c1, c2, …, c7) | ci C}

c4 = D3 = {(d1, d2, d3) | di D}

• User view: color (HSB), cultural importance

C6user = {(c1, c2, …, c6) | ci C}

c4 = E3 = {(e1, e2, e3) | ei E}


Intersection Graben / Dorotheergasse

id dist rank

1 5.97 1

2 5.40 2

3 4.25 6

4 4.62 5

5 5.28 4

6 4.15 7

7 5.33 3

0 0.00 -

id dist rank

1 6.72 2

2 7.12 1

3 5.84 7

4 6.62 5

5 6.66 3

6 6.61 6

7 6.65 4

0 0.00 -

System User


Representing different contexts

• People select different landmarks by day and night.

• Weights from subjects‘ scoring of facades.

Area Shape Color Visibility Identif.

Day 0.11 0.15 0.36 0.26 0.12

Night 0.26 0.0 0.21 0.23 0.30



Day versus night

id distday rankday distnight ranknight

1 0.70 6 0.97 2

2 0.84 1 1.06 1

3 0.69 7 0.75 6

4 0.83 2 0.88 4

5 0.74 4 0.71 7

6 0.73 5 0.78 5

7 0.76 3 0.89 3


Mapping from system to user space

• Final goal: bridging semantic gap between system‘s and user‘s concepts.=> mappings (transformations, projections)

• Example:

partial mapping (R: C7system → C6

user)

(c1s, c1

u), (c2s, c2

u), (c3s, c3

u), {(d1s, d1

u), (d2

s, d2u), (d3

s, d3u)}, (c5

s, c5u), (c7

s, c6u)


cultural

colorRGB

shapeareaarea

colorHSB

shape

tran

sfor

mat

ion

projection


Conclusions

• Contribution to formal representations of cognitive semantics.

• Formalizing conceptual spaces based on vector spaces and z transformation => semantic similarity measurement

• Measuring semantic distances between concept instances and prototypes.

• Formal conceptual spaces can be utilized for knowledge and context representation.


Future work

• Covariances between dimensions and their representation (human subject tests).

• Comparison of different metrics.

• Identification and representation of prototypical regions (fuzzy boundaries).

• Mappings between conceptual vector spaces and loss of information thereby.

Documents

27th April 2006Semantics & Ontologies in GI Services Semantic similarity measurement in a wayfinding service Martin Raubal [email protected]