Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data - Advanced Techniques in Knowledge Discovery and Data Mining - page 51

Sketch of class boundary by Voronoi tesselation

Fig. 2.13. Class separability assessment.

A very simple parametric measure for overlap computation was introduced
in [2.49]. The class specific distributions are modeled by Gaussian functions
and an overlap of two-class regions, denoted by ω i und ω j ,canbecomputed
from the respective mean values µ i , µ j

and standard deviations σ i , σ j by

|µ i − µ j |

q x l ij =

1) σ j .

(2.16)

( N i − 1) σ i +( N j −

The merit of a feature for the separation of one class from all others is given
by

L

1
L −

q x l i = q x l ij . (2.17)

1

j = i

Also, the merit of a single feature to distinguish all classes could be computed
by

L

1
L

q x l = q x l i . (2.18)

i =1

However, practical experience has shown that the global summation can be
misleading in some cases. A feature can, for instance, be excellent for certain
class separations and meaningless for most others but have a summation value
that outperforms other features that are good everywhere in feature space.