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Concept lattices constrained by Concept lattices constrained by attribute dependenciesattribute dependencies
Radim Bělohlávek, Vladimír Sklenář, Jiří Zacpal
[email protected]@upol.cz
Formal concept anaysisFormal concept anaysis
Finding interesting patterns in data – formal concepts
Formal CFormal Contextontext
Triplet (X, Y, I)
X – set of Objects
Y – set of Attributes
I X Y
Object x has attribute y
FormFormal Conceptal Concept
Pair (A,B)A X – set of all objects sharing all
attributes from B
B Y - set of all attributes shared by all objects from B
Concept LatticeConcept Lattice
Set of all concepts
Partial order
(A1,B1) (A2,B2) iff A1 A2
(equivalently B2 B1)
Additional informationAdditional information
Attribute x is more important than attribute y
AD - AD - FormFormulaula
yyyn
...1
Constrained Concept LatticeConstrained Concept Lattice
Concept (A,B) satisfies an AD-formula
if y then y1 or … or yn
ExampleExample
Objects cars
Attributescar properties (sedan, diesel engine, ABS, …)
Engine is most importantEngine is most important
sedanhatchbackairbag
dieselgasolinesedan
sedanhatchbackABS
sedanhatchbackingpowerstear sedanhatchbackngconditioniair
dieselgasolinehatchback
Type of car is most importantType of car is most important
dieselgasolineairbag
sedanhatchbackdiesel
dieselgasolineABS
dieselgasolineingpowerstear dieselgasolinengconditioniair
sedanhatchbackgasoline
Safety is most importantSafety is most important
ABSairbag
dieselgasolineingpowerstear dieselgasolinengconditioniair
sedanhatchbackdiesel sedanhatchbackgasoline
airbagABS
ABSsedanABShatchback
Another approachAnother approach
Concept lattice constrained by equivalence relations