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ADBIS 20021 Navigation Through Query Result Using Concept Order Tomáš Skopal, Václav Snášel, Daniela Ďuráková Department of Computer Science FEI, VŠB-Technical.

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Presentation on theme: "ADBIS 20021 Navigation Through Query Result Using Concept Order Tomáš Skopal, Václav Snášel, Daniela Ďuráková Department of Computer Science FEI, VŠB-Technical."— Presentation transcript:

1 ADBIS 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

2 ADBIS Contents Motivation Example Application of scaled context Application of  -cut concept order Conclusion

3 ADBIS 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

4 ADBIS Possibility of Web Searching

5 ADBIS Example We are looking for an Alpine ski center that is near to Prague, is situated on the highest elevation 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)

6 ADBIS Numeric Values of Query Result Ski centerAbb.d (km)s (CZK)e (m) MayrhofenMa SöldenSo KitzbühelKi FlattachFl SöllSl Zell am SeeZe RadstadtRa GosauGo RohrmoosRo

7 ADBIS 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

8 ADBIS 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 limbswingsmammal birdXX antX snake dolphinX

9 ADBIS Concept Formal concept of context (O, A, I), is a pair (Q, T) where Q  O, T  A, Q’=T and T’ = Q Ilimbswingsmammal birdXX antX snake dolphinX C1 = {bird - limbs, wings} C2 = {bird, ant - limbs}

10 ADBIS 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}

11 ADBIS Numeric Attributes How to convert many-valued query result table into context table? Attribute scaling – concept lattice of scaled context Our method – concept order

12 ADBIS Scaled Context distance (d)  price (s)  elevation (e) > Maxx xxxx So xxxx Kixxxx Flxxxxxx Slxxxxxxx Zexxx xxx Raxxxx x Goxxxxxxxx Roxxxxxxxx

13 ADBIS of ordinally scaled context containing 36 concepts Concept Lattice objects satisfying all attributes attributes belonging to all objects Objects: Ma,Fl,Ze,Ro Attributes: d1, e3

14 ADBIS 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

15 ADBIS 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

16 ADBIS 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

17 Example of “Fuzzyfication”

18 ADBIS Fuzzy Context Ski Centerdse Mayrhofen Sölden Kitzbühel Flattach Söll Zell am See Radstadt Gosau Rohrmoos

19 ADBIS  -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

20 ADBIS  -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

21 ADBIS dse Maxx Sox Kix Flxx Slxx Zexx Rax Goxx Coxx  -cut  = 0.4 d:1 d:1,s:1 Sl, 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

22 ADBIS dse Maxx Sox Kix Flxx Slxx Zexx Rax Goxx Roxx  -cut  = 0.5 d:1 d:2,s:2 Sl,Go e:1 d:1,e:1 d:1,s:1,e:1 Fl 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

23 ADBIS dse Maxx Sox Kix Flx Slxx Zexx Rax Goxx Rox Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro  -cut  = 0.6 d:1 d:2,s:2 Sl,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:1 Ma,Ze

24 ADBIS dse Max Sox Kix Flx Slxx Zex Rax Goxx Rox  -cut  = 0.7 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro d:1 d:3,s:3 Sl,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:1 Ma,Ze Ki,Sl,Ra,Go,Ro d:1 d:3,s:3,e:3

25 ADBIS dse Max Sox Ki Flx Slx Ze Ra Goxx Rox  -cut  = 0.8 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro d:1 d:3,s:4 Sl,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:1 Ma,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:1 Go Go,Ro d:1

26 ADBIS dse Ma So Ki Fl Slx Ze Ra Gox Ro  -cut  = 0.9 Ma,So,Ki,Fl,Sl,Ze,Ra,Go,Ro d:1 d:3,s:4 Sl,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:1 Ma,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:1 Go Go,Ro d:1 s:1 Sl

27 ADBIS  -Concept Structure Volume reduction - resultant structure contains only fourteen  -concepts Structure suggests to the user the significant concepts Independent on density of  -cuts

28 ADBIS Conclusion Hierarchical order of query result Lower degree of subjective choice (contrary to) context scaling Reduction of number of concepts  -cuts Finding of the significant concepts which are independent on number of  -cuts

29 ADBIS Thank you for your attention.


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