Practical Applications of Data Mining

56 Chapter 2 assoCiation rules

A = {a

1

, a

2

, …, a

m

}, is a set of attributes.

P is a set of positive integers.

A

V

denotes the set {<x, v> ∈ A × P}.

A

R

denotes the set {<x, l, u> ∈ A × P × P | l ≤ u if x is quantitative;

l = u if x is categorical}.

For any X ⊆ A

R

attributes( X ) is the set {x|<x, l, u> ∈ X}.

From the above definitions, it should be noted that either a pair <x, v>

∈ A

V

or a triple <x, l, u> ∈ A

R

represents an item.

ˆ

X

is a generalization of X

(i.e., X is a specialization of

ˆ

X

) if attributes(X ) = attributes(

ˆ

X

) and

∀x

∈ attributes(X ){<x, l

1

, u

1

> ∈ X ∧ <x, l

2

, u

2

> ∈

ˆ

X

⇒ l

2

≤ l

1

≤ u

1

≤ u

2

}. For the

uniform treatment of categorical and quantitative attributes, the categorical

attribute values are mapped into a set of consecutiv