Applied Semantic Web Technologies

Data-Driven Evaluation of Ontologies  ◾  231

P v c P d c

d

v

p

i

i

v

v c

v

i

i

( | ) (| || )

!

{ }

| |

,

=

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

∏

ii

v| |

∏

9.3.3.2 Conditional Minimum Description

Length of Naive Bayes Classifier

We used a conditional minimum description length (CMDL; Friedman et al.,

1997) score to grade the renement of the naive Bayes classier for the multino-

mial model.

Let v

j

be a set of attribute values of j

th

instance d

j

ÎD, and c

j

ÎC a class label

associated with d

j

. e conditional log likelihood of the hypothesis B given data

D is:

CLL B D D P c v D

P c

D

B

D

B

( | ) | | log{ ( | )} | | log

(

| | | |

= =

∑ ∑

)) ( | )

( ) ( | )

| |

P v c

P c P v c

B

B i B i

c

C

i

∑

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

(9-3)

For a