Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data - Advanced Techniques in Knowledge Discovery and Data Mining - page 52

d NNjk

Distance to
Rank of
Number of
NN of same/
different class

Fig. 2.14. Class overlap assessment.

Proposals for e cient application of these simple measures will be given in
the following sections on feature selection strategies.
A nonparametric overlap measure q o , which was inspired by the edited-
nearest-neighbor (ENN) algorithm [2.8], in contrast to q s , provides a very
fine-grained value range and thus is better suited for optimization schemes.
However, the price tag is an increased complexity of O( N 2 )withregardto
q s . The basic idea of q o is illustrated in Fig. 2.14. The overlap measure q o is
computed by:

k k

q NN ji + n i

N

1
N

i =1 i =1

q o = (2.19)

k

j =1

2 n i

i =1

with

d NN ji
d NN jk

n i =1 − (2.20)

and

q NN ji = n i

: ω j = ω i

(2.21)

−n i : ω j = ω i .

Here, n i denotes the weighting factor for the position of the i th nearest neigh-
bor NN ji , d NN ji denotes the distance between x j and NN ji , d NN jk denotes