ADBIS 2002 1
Navigation Through Query Result Using Concept Order
Tomáš Skopal, Václav Snášel, Daniela Ďuráková
Department of Computer Science
FEI, VŠB-Technical University of Ostrava
Czech Republic
www.cs.vsb.cz/arg
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Contents Motivation Example Application of scaled context Application of -cut concept order Conclusion
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Motivation
SQL like specified query Query result – a (possibly large) set of objects
having acceptable parameters, not structured Unsatisfactory for human decision Navigation in the query result offers:
• How to find the best object• How to compare objects
Realized using hierarchical structures –ordered sets
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Possibility of Web Searching
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Example
We are looking for an Alpine ski center that is near to Prague, is situated on the highestelevation and offers inexpensive ski-pass.
Our requirements can be expressed by a query as follows:
distance from Prague < 600 km (d) price of ski-pass < 5200 CZK (s) elevation of pistas > 1500 m a. s. (e)
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Numeric Values of Query Result Ski center Abb. d (km) s (CZK) e (m)
Mayrhofen Ma 483 5196 3250
Sölden So 506 4866 3260
Kitzbühel Ki 465 4741 2000
Flattach Fl 490 4411 3125
Söll Sl 460 3664 1835
Zell am See Ze 482 4632 3029
Radstadt Ra 450 4625 2130
Gosau Go 390 3774 1600
Rohrmoos Ro 426 4565 2700
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Characteristics of Query Result
Set of objects with parameters Quality of an object can is given by a
relevance of values of the object’s parameters to the query specification.
Types of object’s parameter
- boolean values (without problem)
- numeric values Formal Concept Analysis
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Context Context is a triple (O, A, I), where O is a
set of objects and A is a set of attributes and a relation I O A
I O A
limbs wings mammal
bird X X
ant X
snake
dolphin X
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Concept Formal concept of context (O, A, I), is a pair (Q, T) where Q O, T A, Q’=T and T’ = Q
I limbs wings mammal
bird X X
ant X
snake
dolphin X
C1 = {bird - limbs, wings}
C2 = {bird, ant - limbs}
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Concept Lattice Concept lattice is a set of concepts ordered by inclusion on attributes (or by inverted inclusion on objects)
C0 = {bird, ant, snake, dolphin - no attribute}
Cn = {no object - limbs, wings, mammal }
C2 = {bird, ant - limbs}
C1 = {bird - limbs, wings}C3 = {dolphin - mammal}
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Numeric Attributes
How to convert many-valued query result table into context table?• Attribute scaling
– concept lattice of scaled context• Our method
– concept order
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Scaled Context distance (d) price (s) elevation (e) >550 490 470 440 4.8 4.5 4.4 4.0 2.0 2.5 3.0 3.2
Ma
x x x x x x
So
x x x x
Ki
x x x x
Fl x x x x x x
Sl x x x x x
x x
Ze
x x x x x x
Ra
x x x x x
Go
x x x x x x x x
Ro
x x x x x x x x
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of ordinally scaled contextcontaining 36 concepts
Concept Lattice objects satisfying all attributes
attributes belonging to all objects
Objects: Ma,Fl,Ze,RoAttributes: d1, e3
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Drawbacks of Context Scaling
Volume of scaled lattice is very large
exponential dependence on number of attributes
Choice of scale user dependent
Our goal was to reduce the number of concepts and to design a scale independent structure
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Our Solution Creation of new context with fuzzy values The “fuzzy context” is transformed back
to several crisp -cut contexts Concept lattice for every -cut context,
called -cut concept lattice, is produced Some concepts occur repeatedly in
-cut concept lattices – we denote this concepts as significant ones
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How Can We Get the “Fuzzy Context”? Fuzzyfication is a transformation of
numerical values into interval 0,1. Membership function is linear Upper and lower bounds of the
membership function are the maximum/minimum values of the particular query parameter
Example of “Fuzzyfication”
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Fuzzy Context
Ski Center d s e
Mayrhofen 0.58 0.00 0.85
Sölden 0.12 0.09 0.86
Kitzbühel 0.67 0.17 0.12
Flattach 0.55 0.39 0.78
Söll 0.70 0.89 0.02
Zell am See 0.59 0.24 0.72
Radstadt 0.75 0.25 0.19
Gosau 1.00 0.82 0.00
Rohrmoos 0.87 0.29 0.53
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-cut Context
Let K is a fuzzy context then K = {x X, K(x) }
is an -cut context for 0,1 We obtain a set of -concepts for this
context
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-Concept Order We produce a new structure as a union
of all -concepts The -concepts are unified to multiset U
on equality of the object set of the -concept
Repetition of an attribute in -concept denotes a more significant concept
The multiset U can be ordered according to inclusion on objects
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d s e
Ma x x
So x
Ki x
Fl x x
Sl x x
Ze x x
Ra x
Go x x
Co x x
--cutcut = 0. = 0.44 d:1
d:1,s:1Sl, Go
e:1
d:1,e:1
d:1,s:1,e:1
Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
Ma,So,Fl,Ze,Ro
Ma,Fl,Ze,Ro
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d s e
Ma x x
So x
Ki x
Fl x x
Sl x x
Ze x x
Ra x
Go x x
Ro x x
--cutcut = 0. = 0.55 d:1
d:2,s:2Sl,Go
e:1
d:1,e:1
d:1,s:1,e:1Fl
Ma,Fl,Ze,Ro
d:1,s:1,e:1
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
Ma,So,Fl,Ze,Ro
Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro
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d s e
Ma x x
So x
Ki x
Fl x
Sl x x
Ze x x
Ra x
Go x x
Ro x
Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro--cutcut = 0. = 0.66
d:1
d:2,s:2Sl,Go
e:1
d:1,e:1
Ma,Fl,Ze,Ro
d:2,s:2,e:2
Ma,So,Fl,Ze,Ro
Ma,So,Fl,Ze
e:1
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
Ma,Ki,Sl,Ze,Ra,Go,Ro
d:1
d:1,e:1Ma,Ze
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d s e
Ma x
So x
Ki x
Fl x
Sl x x
Ze x
Ra x
Go x x
Ro x
--cutcut = 0. = 0.77 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro
d:1
d:3,s:3Sl,Go
e:1
d:1,e:1
Ma,Fl,Ze,Ro
Ma,So,Fl,Ze,Ro
Ma,So,Fl,Ze
e:2
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
Ma,Ki,Sl,Ze,Ra,Go,Ro
d:1
d:1,e:1Ma,ZeKi,Sl,Ra,Go,Ro
d:1
d:3,s:3,e:3
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d s e
Ma x
So x
Ki
Fl x
Sl x
Ze
Ra
Go x x
Ro x
--cutcut = 0. = 0.88 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro
d:1
d:3,s:4Sl,Go
e:1
d:1,e:1
Ma,Fl,Ze,Ro
Ma,So,Fl,Ze,Ro
Ma,So,Fl,Ze
e:1
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
d:1
d:1,e:1Ma,Ze
d:1
d:4,s:4,e:4
Ma,So,Fl
Ma,Ki,Sl,Ze,Ra,Go,Ro
Ki,Sl,Ra,Go,Ro
e:2
d:1,s:1Go
Go,Ro
d:1
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d s e
Ma
So
Ki
Fl
Sl x
Ze
Ra
Go x
Ro
--cutcut = 0. = 0.99 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro
d:1
d:3,s:4Sl,Go
e:1
d:1,e:1
Ma,Fl,Ze,Ro
Ma,So,Fl,Ze,Ro
Ma,So,Fl,Ze
e:1
Ma,Ki,Fl,Sl,Ze,Ra,Go,Ro
d:1
d:1,e:1Ma,Ze
d:1
d:4,s:4,e:4
Ma,So,Fl
Ma,Ki,Sl,Ze,Ra,Go,Ro
Ki,Sl,Ra,Go,Ro
e:2
d:2,s:1Go
Go,Ro
d:1
s:1Sl
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-Concept Structure
Volume reduction - resultant structure contains only fourteen -concepts
Structure suggests to the user the significant concepts
Independent on density of -cuts
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Conclusion
Hierarchical order of query result Lower degree of subjective choice
(contrary to) context scaling Reduction of number of concepts Finding of the significant concepts
which are independent on number of -cuts-cuts
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Thank you for your attention.
www.cs.vsb.cz/arg