Mining Cardinalities from Knowledge Bases

Paper presented at DEXA 2017, Lyon, France

Transcript

1. Mining Cardinalities from
   Knowledge Bases
   Emir Muñoz and Matthias Nickles
   Fujitsu Ireland Ltd.
   Insight Centre for Data Analytics, NUI Galway
   DEXA 2017, August 28-31, Lyon, France
   

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2. Structured data Dynamic data Schema-less data
   Resource Description Framework (RDF) is …
   Good for the Web (data integration, transfer, etc.)
   Bad for users (reusability, trust, understanding, etc.)
   Challenges arise due to the Open World Assumption (OWA) and
   non-Unique Name Assumption (nUNA) in OWL/RDF
   Motivation (1/4)
   

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3. Motivation (2/4)
   ▷ Open World Assumption:
   The truth value of an assertion is not necessarily known
   If an assertion is not in the knowledge base we cannot say
   it is negative
   ▷ No Unique Name Assumption:
   Individuals may have more than one name
   

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4. Motivation (3/4)
   ▷ Domains, ranges, and cardinalities are usually not defined
   :Ireland
   6,378,000
   idemo:population
   dbpedia-
   owl:Population
   6,378,000
   igeo:capitale
   :Dublin
   dbpedia-
   owl:Capital
   :Dublin
   No central schema!
   • Hard to write queries [1]
   • How am I suppose to reuse these data?
   Cardinalities!
   :Irlande
   igeo:capitale
   :Dublin
   Many different ontologies
   [1] Schmidt, M., Meier, M., Lausen, G.: Foundations of SPARQL query optimization. In: ICDT, ACM (2010) 4-33
   Same
   entity
   

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5. Motivation (4/4)
   ▷ Cardinalities indicate us the structure of things (concepts)
   height
   width
   weight
   legs
   (2)
   arms
   (2)
   head
   (1) name
   address
   age
   …
   capital
   (1)
   counties
   (many)
   height
   weight
   rivers
   (0 to many)
   mountains
   population languages
   (1 to many)
   time
   zone
   

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6. Related work (1/2)
   ▷ Cardinality constraints/bounds
   Constraint Languages for RDF: ShEx[2], RDD[3], SHACL[4], SPIN[5], OSLC[6]
   ▷ Consistency in RDF KBs
   No work has focused on the extraction of cardinalities to detect
   inconsistencies in KBs.
   Previous work focused on property values missing, not cardinalities
   ▷ RDF schema discovery
   Use of rule mining to infer an ontology
   Use of SPARQL queries to mine simple cardinalities (issues)
   [2] https://www.w3.org/2013/ShEx/Primer
   [3] P. M. Fischer, G. Lausen, A. Schatzle, and M. Schmidt. RDF Constraint Checking. EDBT/ICDT Workshops 2015.
   [4] https://www.w3.org/TR/shacl/
   [5] http://spinrdf.org/
   [6] https://www.w3.org/Submission/2014/SUBM-shapes-20140211/
   

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7. Related work (2/2)
   ▷ The cardinality query problem: how many cities?
   :Ireland dbpedia-owl:city
   :Dublin
   :Irlande
   dbpedia-owl:city
   :Galway
   owl:sameAs
   SELECT COUNT(?city)
   WHERE {
   :Ireland dbpedia-owl:city ?city .
   }
   SELECT COUNT(?city)
   WHERE {
   :Irlande dbpedia-owl:city ?city .
   }
   1
   1
   2
   

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8. Preliminaries (1/2)
   ▷ Knowledge bases can be represented using RDF model
   ▷ RDF does not assume unique names  we need UNA 2.0
   RDF model
    Set of resource: ℛ e.g.: ex:JonSnow
    Set of blank nodes: ℬ e.g.: _:bnode
    Set of predicates: e.g.: rdf:type
    Set of literals: ℒ e.g.: “Francia@es”
    ≡ { , , ∈ ∪ × × ( ∪ ∪ )}
   

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9. Preliminaries (2/2)
   ▷ Knowledge bases can be represented using RDF model
   ▷ RDF does not assume unique names  we need UNA 2.0
   

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10. Cardinality bounds in RDF
    ▷ A cardinality bound in RDF data restricts the number of
    properties P related with a resource in a given context
    ▷ Formally, ≡ , = (, )
    ▷ Lower bound ∈ ℕ, and upper bound ∈ ℕ ∪ ∞
    

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11. Mining cardinality patterns (1/6)
    ▷ In practice, a cardinality bound could be validated using
    SPARQL 1.1
    ▷ (1) But a normalization on equality is required
    Two implementations: SPARQL rewrite, and Programmatic rewrite
    

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12. Mining cardinality patterns (2/6)
    ▷ owl:sameAs is reflexive, symmetric and transitive
    owl:sameAs-cliques and data rewriting
    :Ireland
    :Irlande
    owl:sameAs
    :Irlanda
    owl:sameAs
    :Irlandia
    owl:sameAs
    :Ireland
    :Irlande
    owl:sameAs
    :Irlanda
    owl:sameAs
    :Irlandia
    owl:sameAs
    owl:sameAs owl:sameAs
    

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13. Mining cardinality patterns (3/6)
    ▷ (2) After, cardinality can be extracted
    ▷ (3) However, data are not always clean
    Outliers detection and filtering is required
    max
    min
    median
    box
    Q1
    Q3
    arms (4)?!?
    

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14. Mining cardinality patterns (4/6)
    

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15. Mining cardinality patterns (5/6)
    Representative
    element equivalence
    type induced by
    owl:sameAs-cliques
    Very
    expensive
    query!
    

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16. Mining cardinality patterns (6/6)
    Parallelism 
    

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17. Evaluation (1/6)
    ▷ We took different syntactic and real-world knowledge
    bases
    Good number of
    owl:sameAs
    axioms
    

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18. Evaluation (2/6)
    ▷ Qualitative evaluation: runtime
    ▷ UOBM with owl:sameAs axioms
    ▷ Mondial without owl:sameAs axioms
    SPARQL 253.908 sec
    Spark 15.634 sec
    SPARQL 117.739 sec
    Spark 2.948 sec
    16x faster
    40x faster
    

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19. Evaluation (3/6)
    ▷ Quantitative evaluation: consistency and completeness
    ▷ Randomly selected 1 class per dataset and 5 predicates
    ▷ A property in the context of a type is complete given a
    cardinality constraint if every entity of type has the ‘right
    number’ of triples (, , ); and incomplete otherwise
    ▷ A predicate in the context of a type is consistent if the
    triples with predicate and subject of type comply with
    the cardinality bounds; and inconsistent otherwise
    

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20. Evaluation (4/6)
    ▷ For example:
    ▷ Completeness:
    All books should have a property author, but not all
    should have a review property
    ▷ Consistency
    A single book should have between x and y authors
    

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21. Evaluation (5/6)
    ▷ Synthetic datasets are more consistent than real-world
    

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22. Evaluation (6/6)
    ▷ Subset of cardinality bounds from the Mondial dataset
    ▷ card({mondial:hasCity}, mondial:Country) = (1, 31)
    Not satisfied by China (306), India (99), USA (250), Brazil (210)
    and Russia (171)
    

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23. Thanks!
    Any questions?
    Emir Muñoz
    emir@emunoz.org
    Key points:
    - KBs lack the description of cardinalities
    - A data normalization is required to
    extract accurate cardinalities
    - An outlier filtering is required to extract
    robust cardinalities
    - Cardinality bounds can help us to assess
    consistency and completeness
    

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