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

Martin RaubalSemantic similarity measurement in a wayfinding service 2 At large yellow building turn left. Walk straight until light green historical building. Turn right …

Martin RaubalSemantic similarity measurement in a wayfinding service 3 Problem Assumption: LANDMARK System = LANDMARK User Needed: System must adapt semantics of its concepts to user‘s semantics.  Formal conceptual spaces  Measuring semantic similarity between geospatial concepts.

Martin RaubalSemantic similarity measurement in a wayfinding service 4 Outline Cognitive semantics Geometrical models Conceptual spaces Formalization of conceptual spaces Application to case study Conclusions and future work

Martin RaubalSemantic similarity measurement in a wayfinding service 5 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

Martin RaubalSemantic similarity measurement in a wayfinding service 6 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.

Martin RaubalSemantic similarity measurement in a wayfinding service 7 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).

Martin RaubalSemantic similarity measurement in a wayfinding service 8 Color domain brightness saturation hue

Martin RaubalSemantic similarity measurement in a wayfinding service 9 Geometric structures of dimensions [Schwering forthcoming]

Martin RaubalSemantic similarity measurement in a wayfinding service 10 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) C n = {(c 1, c 2, …, c n ) | c i  C} c j = D n = {(d 1, d 2, …, d n ) | d k  D}

Martin RaubalSemantic similarity measurement in a wayfinding service 11 c1c1 c2c2 c3c3

Martin RaubalSemantic similarity measurement in a wayfinding service 12 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: |d uv | 2 = (z 1 v - z 1 u ) 2 + (z 2 v - z 2 u ) 2 + … + (z n v - z n u ) 2 Weights: C n = {(w 1 c 1, w 2 c 2, …, w n c n ) | c i  C, w j  W}

Martin RaubalSemantic similarity measurement in a wayfinding service 13 Z-transformation z i is the i-th value of the new variable Z x i is the i-th value of the old variable X is the mean of X s x is the standard deviation of X

Martin RaubalSemantic similarity measurement in a wayfinding service 14 z1z1 z2z2 z3z3 u v d(u,v)

Martin RaubalSemantic similarity measurement in a wayfinding service 15 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‘.

Martin RaubalSemantic similarity measurement in a wayfinding service 16

Martin RaubalSemantic similarity measurement in a wayfinding service 17 Global measure of landmark saliency

Martin RaubalSemantic similarity measurement in a wayfinding service 18 Intersection Haas building

Martin RaubalSemantic similarity measurement in a wayfinding service 19 Wayfinding instruction [ AT landmark ] [ TURN LEFT | RIGHT | MOVE STRAIGHT ] { ONTO streetname } { PASSING | CROSSING landmark } [ UNTIL landmark ] XY LEFT ] Stephansplatz } Haas building, a big building of architectural significance ] Stephansdom, a visually salient world cultural heritage building }

Martin RaubalSemantic similarity measurement in a wayfinding service 20 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.

Martin RaubalSemantic similarity measurement in a wayfinding service 21 Conceptual space for facade System view: area, shape factor, shape deviation, color (RGB), visibility, cultural importance, identifiability by signs. C 7 system = {(c 1, c 2, …, c 7 ) | c i  C} c 4 = D 3 = {(d 1, d 2, d 3 ) | d i  D} User view: color (HSB), cultural importance C 6 user = {(c 1, c 2, …, c 6 ) | c i  C} c 4 = E 3 = {(e 1, e 2, e 3 ) | e i  E}

Martin RaubalSemantic similarity measurement in a wayfinding service 22 Intersection Graben / Dorotheergasse iddistrank iddistrank System User

Martin RaubalSemantic similarity measurement in a wayfinding service 23 Representing different contexts People select different landmarks by day and night. Weights from subjects‘ scoring of facades. AreaShapeColorVisibilityIdentif. Day Night

Martin RaubalSemantic similarity measurement in a wayfinding service 24

Martin RaubalSemantic similarity measurement in a wayfinding service 25 Day versus night iddist day rank day dist night rank night

Martin RaubalSemantic similarity measurement in a wayfinding service 26 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: C 7 system → C 6 user ) (c 1 s, c 1 u ), (c 2 s, c 2 u ), (c 3 s, c 3 u ), {(d 1 s, d 1 u ), (d 2 s, d 2 u ), (d 3 s, d 3 u )}, (c 5 s, c 5 u ), (c 7 s, c 6 u )

Martin RaubalSemantic similarity measurement in a wayfinding service 27 cultural color RGB shape area color HSB shape transformation projection

Martin RaubalSemantic similarity measurement in a wayfinding service 28 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.

Martin RaubalSemantic similarity measurement in a wayfinding service 29 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.