1. 25th April 2006 Semantics & Ontologies in GI Services Semantic Similarity Measurement Martin Raubal raubal@uni-muenster.de

2. Martin RaubalSemantic Similarity Measurement 2 Outline Motivation Semantic interoperability, concepts Semantic similarity measurement Geometric model Feature-based model Alignment-based model Transformational model Conclusions

3. Martin RaubalSemantic Similarity Measurement 3 Motivating example (1) Customer of OS wants to set up flood warning system. Need for existing flooding areas to analyze current flood defense situation in U.K. OS Master Map: geographic & topographic; information on areas used for flooding but not designated as such. ‘Watermeadow', 'carse‘, 'haugh' identified as flooding areas by their semantic description only (properties in ontology).

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5. Martin RaubalSemantic Similarity Measurement 5 User conceptualization of roads & residential areas System model of roads & residential areas Roads overlap residential areas? Intersect to find roads going through residential areas Motivating example (2)

6. Martin RaubalSemantic Similarity Measurement 6 Semantic interoperability “Capacity of (geographic) information systems and services to work together without the need for human intervention” (Harvey, Kuhn et al. 1999) Achieving sufficient degree of semantic interoperability => necessary to determine semantic similarity between concepts.

7. Martin RaubalSemantic Similarity Measurement 7 Similarity (psychology) “Similarity is fundamental for learning, knowledge and thought, for only our sense of similarity allows us to order things into kinds so that these can function as stimulus meanings. Reasonable expectation depends on the similarity of circumstances and on our tendency to expect that similar causes will have similar effects" [Quine 1969, p. 114].

8. Martin RaubalSemantic Similarity Measurement 8 Computer science Similarity plays major role to enable machine-based solutions: decision support systems, data mining, pattern recognition. Semantic information retrieval: similarity indicates relevance of results with regard to being similar to the query.

9. Martin RaubalSemantic Similarity Measurement 9 Concept A concept is "a mental representation of a class or individual and deals with what is being represented and how that information is typically used during the categorization" [Smith 1989, p. 502]. Concept vs. Category?

10. Martin RaubalSemantic Similarity Measurement 10 Concepts in knowledge representation Conceptual knowledge can be represented in ontologies that consist of specifications of concepts, relations and axioms. Relations link concepts together and enable reasoning and measurement within an ontology. Taxonomical (hierarchical) relations are the most important for reasoning and structuring knowledge.

11. Martin RaubalSemantic Similarity Measurement 11 dist (Bus, Ferry) < dist (Bus, Bike)

12. Martin RaubalSemantic Similarity Measurement 12 Similarity measurements Approaches from different research areas (psychology, computer science, artificial intelligence) => apply to ontology-based semantic similarity measurement. Application areas: Information retrieval & integration Data mining & maintenance Categorization Natural-language processing Pattern recognition

13. Martin RaubalSemantic Similarity Measurement 13 Measure and representation Representational model used to describe concepts determines semantic similarity measure (based on one notion of similarity). Representation => similarity measure

14. Martin RaubalSemantic Similarity Measurement 14 Semantic similarity measurement How close are two entities to each other conceptually? Value between 0 and 1: ‘0’ => no similarity ‘1’ => both entities are equal Different measurement theories.

15. Martin RaubalSemantic Similarity Measurement 15 [Schwering forthcoming]

16. Martin RaubalSemantic Similarity Measurement 16 Approaches Geometric Model / MDS Gärdenfors: Conceptual Spaces Feature-based Model Tversky: Contrast Model Rodriguez: MDSM Alignment-based Model Goldstone: SIAM Transformational Model Hahn, Example.: ABBA  AABB

17. Martin RaubalSemantic Similarity Measurement 17 Geometric models and MDS Multidimensional scaling (MDS) => 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.

18. Martin RaubalSemantic Similarity Measurement 18 Geometric models and MDS cont. n … number of dimensions x ik and x jk … values for dimension k of the entities i and j Minkowski metric: r = 1 => city-block metric, r = 2 => Euclidean metric, etc.

19. Martin RaubalSemantic Similarity Measurement 19 MDS in cognitive science Applied to discover mental representations of stimuli and explanations of similarity judgments. MDS as mathematical model of categorization, identification, recognition, memory, generalization (Nosofsky 92, Shepard 87). Degree of relation between stimuli ~ spatial distance

20. Martin RaubalSemantic Similarity Measurement 20 Representational model

21. Martin RaubalSemantic Similarity Measurement 21 Geometric models and MDS cont. Choice for metric to best fit human similarity assessments => depends on entities (stimuli) and subjects’ strategies. Euclidean metric provides better fit to empirical data when stimuli are composed of integral, perceptually fused dimensions (e.g., brightness and saturation of color). City-block metric appropriate for psychologically separated dimensions (e.g., color and shape).

22. Martin RaubalSemantic Similarity Measurement 22 Euclidean metric City-block metric

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24. Martin RaubalSemantic Similarity Measurement 24 shape color

25. Martin RaubalSemantic Similarity Measurement 25 MDS vs. Geometric models MDS determines number of dimensions from subjects‘ pairwise judgments. Goal: maximum correlation between judgments and distances in n-dim. space with minimum number of dimensions. Geometric models start with defining dimensions.

26. Martin RaubalSemantic Similarity Measurement 26 Axioms of geometric model Minimality: Symmetry: Triangle Inequality: These axioms may not hold for human similarity assessments!

27. Martin RaubalSemantic Similarity Measurement 27 Problems with geometrical model Distance between compared entities is not symmetric but asymmetric (Tversky 1977). Example: North Korea is judged to be more similar to Red China than vice versa. Category members are judged more similar to category prototypes than prototype to several category members.

28. Martin RaubalSemantic Similarity Measurement 28 Problems with geometrical model A lamp is similar to the moon (light); moon similar to soccer ball (shape); lamp NOT similar to soccer ball (?); (James 1892) Adding common features to entities does not increase their similarity (distance grows).

29. Martin RaubalSemantic Similarity Measurement 29 Requirements and assumptions Independence of properties. Property set must reflect human conceptualization to provide good similarity results – how to achieve this? Comparability of different dimensions – same relative unit.

30. Martin RaubalSemantic Similarity Measurement 30 Feature-based models Common elements approach Two entities (stimuli) are similar if they have common features (elements). The more elements they share, the more similar the stimuli are. Problem: always possible to find endless amount of common elements depending on the view.

31. Martin RaubalSemantic Similarity Measurement 31 Representational model Set-theoretic: concepts represented as unstructured sets of features. Characterization through properties common in analysis of cognitive processes. Application areas: speech perception, pattern recognition, perceptual learning.

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33. Martin RaubalSemantic Similarity Measurement 33 [Schwering forthcoming]

34. Martin RaubalSemantic Similarity Measurement 34 Feature-matching model Proposed by Amos Tversky. A. Tversky (1977) Features of Similarity. Psychological Review 84(4): 327-352. Supports asymmetric similarity measurement. Elementary set operations can be applied to estimate similarities and differences.

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36. Martin RaubalSemantic Similarity Measurement 36 Requirements and assumptions Independence of features. Feature set must be sufficiently rich to account for human categorization. Invariance of representational elements (no transformations as in geometric models).

37. Martin RaubalSemantic Similarity Measurement 37 Feature-based models cont. Contrast model Similarity is defined not only by the entities’ common features, but also by their distinctive features (Tversky 1977). In contrast to the common elements approach a flexible weighting is used.

38. Martin RaubalSemantic Similarity Measurement 38 Contrast model q, a, b … weights for common / distinctive features (A  B) … number of features that A and B have in common (A-B) … features possessed by A but not B (B-A) … features possessed by B but not A Asymmetric because a is not constrained to be equal to b nor f(A-B) to f(B-A).

39. Martin RaubalSemantic Similarity Measurement 39 Ratio model Similarity is normalized => S between 0 and 1.

40. Martin RaubalSemantic Similarity Measurement 40 Assertions Similarity measurement is directional and asymmetric. Model used to test Rosch‘s (1978) hypothesis that perceived distance from prototype to variant is larger than perceived distance from variant to prototype.

41. Martin RaubalSemantic Similarity Measurement 41 Matching-Distance Similarity Measure Matching-Distance Similarity Measure (MDSM): context sensitive, asymmetric semantic similarity measurement approach for geographic entity classes (Rodríguez and Egenhofer 2004). Based on Tversky‘s contrast model. Different kinds of features: Features are classified by types (parts, functions, attributes).

42. Martin RaubalSemantic Similarity Measurement 42 MDSM cont. Different feature classes in analogy to WordNet‘s description of nouns. Parts: structural elements of a class. Functions: what is done to or with instances of concept. Attributes: additional characteristics not considered by former two.

43. Martin RaubalSemantic Similarity Measurement 43 MDSM t … type of feature (part, attribute, function) c1, c2 … compared entity classes C1, C2 … respective sets of features of type t for c1, c2 Measure applied to each feature type.

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45. Martin RaubalSemantic Similarity Measurement 45 Degree of asymmetry Calculate degree of asymmetry depending on degree of generalization of concepts. Based on following idea: people perceive similarity from subconcept to superconcept greater than vice versa. Depth = shortest path of each concept to immediate common superconcept that subsumes both concepts.

46. Martin RaubalSemantic Similarity Measurement 46 Exemplar calculation

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48. Martin RaubalSemantic Similarity Measurement 48 Calculation: theatre - building depth (theatre) [1] > depth (building) [0] =>  = 1 – 1 / (1+0) = 0 S p = 3 / (3 + 0 + 0) = 1 S f = 0 (no functions for building) S a = 1 (same attributes)

49. Martin RaubalSemantic Similarity Measurement 49 Calculation: building - theatre depth (building) [0]  = 0 / (1+0) = 0 S p = 3 / (3 + 0 + 6) = 1/3 S f = 0 (no functions for building) S a = 1 (same attributes)

50. Martin RaubalSemantic Similarity Measurement 50 Similarity values Entity classes  SpSp SfSf SaSa S(a,b) theatre, building 0.01.00.01.00.67 building, theatre 0.00.330.01.00.44 theatre, sport arena 0.50.530.331.00.62

51. Martin RaubalSemantic Similarity Measurement 51 Discussion Information retrieval: Descriptions of query and data source concepts may differ greatly in their granularity - query concepts often focus on the very characteristic properties, data source concepts are described broadly to be context- independent. Query ‘flooding area’ (shape, relation to waterbodies) vs. data source ‘floodplain’ (additional hydrologic & ecologic properties) => distinct properties reduce similarity!

52. Martin RaubalSemantic Similarity Measurement 52 Problems with feature-based models Features, dimensions are unrelated, but in reality entities are not simply unstructured bags of features. Also true for relations between entities!

53. Martin RaubalSemantic Similarity Measurement 53 Alignment-based models Use commonalities and differences as notion of similarity, but include also relational structure of properties. Motivation: Similarity is like Analogy. Similarity involves structural alignment and mapping.

54. Martin RaubalSemantic Similarity Measurement 54 Two spatial scenes are described by a set of features. The similarity between these scenes depends on the correct alignment of these features [Gentner et al. 1995, p. 114]

55. Martin RaubalSemantic Similarity Measurement 55 Transformational model Transformations required to make one concept equal to another are defined. Similarity depends on number of transformations needed to make concepts transformationally equal. Example: Operations modifying the geometric arrangement are rotation, reflection, translation and dilation.

56. Martin RaubalSemantic Similarity Measurement 56 Transformational model Similarity assumed to decrease monotonically when number of transformations increases. Transformational model is asymmetric, but the metric axioms minimality and triangle inequality hold.

57. Martin RaubalSemantic Similarity Measurement 57 Comparison of models (Schwering)

58. Martin RaubalSemantic Similarity Measurement 58 Conclusions Semantic similarity measurement is basis for semantic interoperability. Different measurement theories => advantages & disadvantages Most common: geometric & feature-based approaches.

59. Martin RaubalSemantic Similarity Measurement 59 References Gärdenfors, P. (2000). Conceptual Spaces - The Geometry of Thought. Cambridge, MA, Bradford Books, MIT Press. Goldstone, R. L. and A. Kersten (2003). Concepts and Categorization. Comprehensive handbook of psychology. A. F. Healy and R. W. Proctor. 4: 599-621. Rodríguez, A. and M. J. Egenhofer (2004). "Comparing Geospatial Entity Classes: An Asymmetric and Context- Dependent Similarity Measure." International Journal of Geographical Information Science 18(3): 229-256.