Semantic Metrics

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Semantic Metrics

• Bo Hu Y. Kalfoglou, H. Alani,
• D. Dupplaw, P. Lewis, N. Shadbolt
• School of Electronics and Computer Science
• University of Southampton, UK

2
Gist

• Yet another metrics?
• Current approaches
• Why we need yet another one?
• Background
• Distance measures
• Description logics
• Distances between concepts
• signaturing concepts
• How far apart are they?
• Beyond concept distances
• Discussion and Conclusions

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Why we need it?

• Ontology authoring and publishing is far easier
  than we once could imagine
• Gxxgle person ontology 574 returns
• Swxxgle person 3967 results
• person is defined in FoaF, Akt-portal,
  umbc-publication, etc. in different ways.
• Semantic distance is the root for many semantic
  web tasks
• Ontology mapping/alignment/articulation/merging
• Ontology search, ranking and reuse
• Ontology segmentation
• Ontology evaluation

4
Current approaches

• Name-based and lexical approaches
• Consider only names and URIs with help from
  lexicons, e.g. WordNet, UMLS
• Ignore concept definitions
• Graph-based approaches
• Convert ontologies into graphs
• Ignore the difference among links
• Feature-based approaches
• Discompose concepts as features
• Process of featuring concepts is not formally
  studied
• Should interim concepts along inheritance paths
  or role chains be considered equally important?
• Logic-based approaches
• Rewrite as SAT problem
• Only gives abstract relations

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Background
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Distance functions

• A distance function satisfies non-negative,
  symmetry and triangle inequality
• Some distance measures
• Minkowski distance
• Vector space model
• Kullback-Leibler divergence

7
Description logics

• Subset of FOPL describing knowledge with concepts
  and roles
• father is a man whose child is a human
• Morden DL systems are built on Tableau-based
  algorithms
• Underlying logic for OWL-Lite, OWL-DL
• OWL-DL is based on SHOIN
• SHOIN constructs

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Semantic distance measure

• Take full advantage of DLs
• Unfold concepts into signatures
• Weight semantics-bearing signatures
• Compute distance

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Signaturing concepts1/3

• In DLs, concepts are restricted with roles
  through role value (range) and role cardinality
  restrictions
• E.g.
• Unfold all the relevant restrictions
• Beth definability implicit restriction can be
  made explicit
• Acyclic definitions

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Signaturing concepts2/3

• Unfolding rules
• Tableau construction rules of DL (Baader, et.al.
  2003)
• Disjoint is explicated as complement

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Signaturing concepts3/3

• Examples
• Signature of book, elements are tuples headtail,
  A-Box assertions
• Signature of author
• Implicit restrictions on authors have been
  expanded as part of the Book signature

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Weighting signatures

• tf-idf
• Why tf-idf vector space model?
• Provide a foundation for computing numeric
  similarity
• Computationally cheap and easy to implement
• Emphasise on differences
• Pure syntactic approach
• Add semantic flavour
• Assign -1 to complement
• Reduce the weight value based on its contexts
• Weight of hasPublication property referred to
  in author concept is

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Computing distances

• Distance between concepts is reduced to distance
  between signature vectors
• Compute similarity of signature
• vectors
• Compute distance of signatures
• Find the minimum distance of concepts

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The distances

• Symmetric, non-negative
• Only a relative value
• Bigger distance value suggests two concepts are
  further apart
• 0 suggests identical concepts
• Disadvantages
• Only a distance value, not able to represent
  abstract relations, e.g. more general than, more
  specific than
• A mix of semantic and syntactic methods,
  difficult to formalise
• Cannot handle negative similarity values.
• Advantages
• Anonymous concepts, e.g. ltowlRestrictiongt, are
  made explicit.
• Non-primitive concepts are recursively unfolded
• Interim concepts are replaced with their
  signatures.
• Weights are computed systematically.

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Extending semantic metric of concepts
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Distance between concept from different ontologies

• Effectively, ontology mapping
• Inputs from other systems and human experts are
  necessary
• ?(C, C) need to be initiated with mappings among
  primitive concepts and properties from different
  ontology
• Initial mappings can be defined based on concept
  names
• String distance based algorithms
• WordNet, UMLS, etc.
• Compute distance
• Compute similarity of signatures
• vectors

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Distance between concept and a set of concepts

• Distance between C and group of concepts O
• Accumulate individual similarities
• ?(O,C) is accumulated as the information gain of
  each concept in O with regard to C.
• Emulate probability with similarity
• Yet, probability ? similarity
• p(DC) sim(D,C) / ?D?O sim(D, C)

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Distance between groups of concepts

• Compute as an aggregation of pair-wise concept
  distances
• Aggregation method
• Mindowski ?1,2,
• Kullback-Leibler
• A perfect concept C0 is defined as the
  reference point
• p(Ck) computed as the relative tightness with
  regard to C0

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Discussion and conclusions

• Possible applications
• Ontology mapping
• Ontology segmentation
• Compute distance between concepts
• Cut off concept below the threshold
• Ontology ranking
• Compute the aggregated distance between two
  ontologies
• Or compute the aggregated distance between an
  ontology and a group of concepts.
• Future work
• Neat solution for un-unfolded universal
  quantification
• Find a proper p(DC) replacement
• Problem with tf-idf
• How to treat negative concept similarity
• Syntactic based, a semantic-oriented weight
  schema
• More evaluation is forthcoming

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Questions?
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