Concept%20lattices%20constrained%20by%20attribute%20dependencies

1
Concept lattices constrained by attribute
dependencies

• Radim Belohlávek, Vladimír Sklenár, Jirí Zacpal
• radim.belohlavek_at_upol.cz
• vladimir.sklenar_at_upol.cz
• jiri.zacpal_at_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 ÎB then y1 ÎB or or yn ÎB

9
Example

• Objects
• cars
• Attributes
• car properties (sedan, diesel engine, ABS, )

10
(No Transcript)
11
Engine is most important
12
(No Transcript)
13
Type of car is most important
14
(No Transcript)
15
Safety is most important
16
(No Transcript)
17
Another approach

• Concept lattice constrained by equivalence
  relations