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Concept lattices constrained by attribute dependencies

Concept lattices constrained by attribute dependencies. Radim B ě lohl á vek, Vladimír Sklenář, Jiří Zacpal radim . belohlavek @ upol.cz vladimir.sklenar @ upol .cz jiri.zacpal@upol.cz. Formal concept anaysis. F inding interesting patterns in data – formal concepts. Formal C ontext.

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Concept lattices constrained by attribute dependencies

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  1. Concept lattices constrained by attribute dependencies Radim Bělohlávek, Vladimír Sklenář, Jiří Zacpal radim.belohlavek@upol.cz vladimir.sklenar@upol.cz jiri.zacpal@upol.cz

  2. Formal concept anaysis • Finding interesting patterns in data – formal concepts

  3. Formal Context Triplet(X, Y, I) X – set of Objects Y – set of Attributes I  X Y Object x has attribute y

  4. Formal 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

  5. Concept Lattice Set of all concepts Partial order (A1,B1) £ (A2,B2) iff A1 A2 (equivalently B2  B1)

  6. Additional information • Attribute x is more important than attribute y

  7. AD - Formula

  8. Constrained Concept Lattice Concept (A,B) satisfies an AD-formula if y ÎBthen y1ÎB or … or ynÎB

  9. Example Objects cars Attributes car properties (sedan, diesel engine, ABS, …)

  10. Engine is most important

  11. Type of car is most important

  12. Safety is most important

  13. Another approach • Concept lattice constrained by equivalence relations

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