Imprecise Data and Knowledge Based OLAP

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Imprecise Data and Knowledge Based OLAP
Ermir Rogova, Panagiotis Chountas, Krassimir
Atanassov

• Harrow School of Computer Science
• Data Knowledge Management Group
• University of WestminsterWatford Road,
  Northwick Park, HA1 3TPLondon, UK

CLBME Bulgarian Academy of Sciences Sofia,
Bulgaria
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Overview

• Imprecision and OLAP
• IF-Cube
• IF-OLAP Operators
• Knowledge Based OLAP
• Summary

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Imprecision and OLAP

• Current models are mainly concerned with the
  querying of imprecision at the fact table.
• Use of inflexible hierarchies makes it difficult
  to reconcile data coming from different sources.
• Knowledge has to be incorporated as part of the
  OLAP operators in order to enhance the results.

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The need for the IF Cube

• To accommodate imprecise data using IFS measures
• To accommodate precise information expressed in
  the form of concepts i.e. Whole milk, whole
  pasteurised milk, etc.
• In the latter case, the information stored in the
  cube is precise, but the concept is not, i.e.
  Whole pasteurised milk satisfies requests for
  whole milk as well (to some extent)

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The IF Cube

• A cube is an abstract structure that serves as
  the foundation for the multidimensional data cube
  model. A cube C is defined as a five-tuple (D, l,
  F, O, H) where
• D is a set of dimensions
• l is a set of levels l1,, ln,
• F is a set of facts instances
• O is a partial order between the elements of l.
• H is an object type history which allows to trace
  the evolution of the cubic structure

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The need for IF OLAP operators

• Standard OLAP operators cannot cope with
  imprecise facts
• Standard OLAP operators cannot cope with
  concept-based information i.e. How do you detect
  and SUM up reconcilable concepts? i.e. whole
  semi-skimmed and skimmed milk?

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IF OLAP operators

• Selection (S)
• The selection operator selects a set of
  fact-instances from a cubic structure that
  satisfy a predicate ( ? ).
• Input Ci (D, l, F, O, H) and the predicate ?
  
• Output Co (D, l, Fo , O, H) where
• Fo? F and Fof (f ?F)(f satisfies ?)
• S(amountgt1000 ? (µgt0.4 ? ?lt0.3) ?
  year2004)(Sales)CResult

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IF OLAP operators

• Cubic Product (?)
• This is a binary operator Ci1 ? Ci2 . It is used
  to relate two cubes Ci1 and Ci2
• Input Ci1 (D1, 11, F1, O1, H1) and
• Ci2 (D2,l2, F2, O2, H2)
• Output Co (Do, lo, Fo, Oo, Ho) where
• Do D1 ? D2 , lo l1 ? l2, Oo O1 ? O2 Ho
  H1 ? H2,
• Fo F1 X F2, ltltx, ygt, min(µf1(x), µf2(y)),
  max(?f1(x), ?f2(y),)gtltx, ygt? X?Y

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IF OLAP operators

• Union (?)
• The union operator is a binary operator that
  finds the union of two cubes. Ci1 and Ci2 have to
  be union compatible.
• Input Ci1 (D1, l1, F1, O1, H1) and Ci2
  (D2,l2, F2, O2, H2)
• OutputCo (Do, lo, Fo, Oo, Ho) where DoD1D2,
  lol1l2, OoO1O2, HoH1H2,
• Fo F1 ? F2 lt x, max(?F1 (x), ?F2(x)),
  min(?F1(x),?F2(x)) gt x ? X

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History

• Why do we need to keep track of the history?
• The structured history of the datacube allows us
  to keep all the information when applying Roll up
  and get it all back when Roll Down is performed.
  To be able to apply the operation of Roll Up we
  need to make use of the IFSSUM aggregation
  operator
• H is an object type history that corresponds to
  a cubic structure ( l, D, A, H ) which allows us
  to trace back the evolution of a cubic structure
  after performing a set of operators i.e.
  aggregation.

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Roll up ( ? )

• The result of applying Roll up over dimension di
  at level dlr using the aggregation operator over
  a datacube Ci is another datacube (Co )
• Input Ci (Di ,li ,Fi , O , Hi )
• Output Co (Do ,lo ,Fo , O , Ho )
• An object of type history ? is the
  initial state of the cube
• is a recursive structure H ( l, D, A, H )
  is the state of the cube after performing
  an operation on the cube

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Group Operators

• Will the result over which the aggregate is
  performed be either crisp or Intuitionistic
  Fuzzy?
• What is the meaning of the result after the IF
  aggregation is performed?
• Using the standard definitions for the group
  operators (SUM, AVG, MIN and MAX), we provide
  their IFS extensions and meaning.

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Group Operators
IFSSUM
Example IFSUM((Amount)(ProdID)) lt.8,.1gt/10
(lt.4,.2gt/11),(lt.3,.2gt/12)(lt.5,.3gt/13),(lt.5,.1gt
/12) (lt.3, .3gt/34), (lt.4, .2gt/33), (lt.3,
.3gt/35)
IFAVG The IFAVG aggregate makes use of the
IFSUM that was discussed previously and the
standard COUNT.
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IFSMAX
Group Operators
Example IFMAX((Amount)(ProdID)) lt.8,.1gt/10,
(lt.4,.2gt/11),(lt.3,.2gt/12),(lt.5,.3gt/13),(lt.5,
0.1gt/120) (lt.3,.3gt/13),(lt.3,.2gt/12)
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Knowledge Based OLAPKNOLAP

• Concepts are used to describe how the data is
  organized in the data sources.
• These definitions are used to rewrite queries
  conditions and to combine OLAP features in this
  process.
• This supports the analysis according to the
  context of users explorations in order to guide
  the decision making, feature inexistent in
  current analytical tools.

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The KNOLAP environment
Milk lt0.8, 0.1gt
Skim milk
lt0.8, 0.1gt
Whole milk lt1.0, 0.0gt
Half skim milk
lt0.8, 0.1gt
Sweetened milk
lt0.8, 0.1gt
Pasteurized milk
lt0.8, 0.1gt
Condensed milk lt0.4, 0.3gt
Condensed whole milk
lt1.0, 0.0gt
lt0.4, 0.3gt
Sweetened condensed milk
lt1.0, 0.0gt
Whole pasteurized milk
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KNOLAP (cont.)

• If the hierarchical IFS structure expresses
  preferences in a query, the choice of the maximum
  allows us not to exclude any possible answer. In
  real cases, the lack of answers to a query
  generally makes this choice preferable, because
  it consists of widening the query answer rather
  than restricting it.
• If the hierarchical IFS set represents an
  ill-known concept, the choice of the maximum
  allows us to preserve all the possible values,
  but it also makes the answer less specific.

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Conclusions-Future Work

• Flexible hierarchies and data
• Extend querying language
• Extend the OLAP modelling construct (definition
  of facts cube)
• Intuitionistic Fuzzy OLAP
• Extending the OLAP operators
• KNOLAP
• Imprecise hierarchical Intuitionistic fuzzy
  concepts
• Involvement of the domain knowledge in answering
  OLAP queries
• Automatic navigation/summarisation paths
• Implementation

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Thank you for your attention

• Harrow School of Computer Science
• Data Knowledge Management Group
• University of WestminsterWatford Road,
  Northwick Park, HA1 3TPLondon, UK

CLBME Bulgarian Academy of Sciences Sofia,
Bulgaria