Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data - Advanced Techniques in Knowledge Discovery and Data Mining - page 42

application and gets activated if S ( is sit-

uated within the hypersphere. The RCE output layer is also modified from a
linear combination to an OR-like logic operation combining the hypersphere
responses to determine the overall classification.
The algorithm practically requires only two parameter settings, R max and
R min , for operation. The following situations can arise in classification:
•

|| x − t j || < = R j ), i.e., if pattern x

A pattern is uniquely classified by one or several hyperspheres of the same
class.

• No hypersphere is activated by the presented pattern. This defines a re-

jection mechanism, which can be controlled by setting R max in training.
A decision can be forced by, e.g., the nearest-neighbor rule. The rejection
mechanism is replaced if the background is a liated to one of the problem
classes in BC.

• Several hyperspheres of different classes are activated by the presented

pattern. The pattern is identified as ambiguous. A decision can be made
according to the a liation of the majority of the activated hyperspheres
or by the nearest-neighbor rule.

The iterative RCE training algorithm starts with an empty network and
presents all patterns of the training set until no more changes take place in
the following basic training steps:
•

If no hypersphere is activated by the presented pattern k ,itisstoredas
t J +1 with R J +1 = R max , where J denotes the current number of reference
vectors.

• A pattern is uniquely classified by one or several hyperspheres of the same

class. All radii are left unchanged, the pattern is not stored.

• Several hyperspheres of the same and different classes are activated by the

presented pattern. Radii of hyperspheres a liated to different classes will
be reduced until the pattern is no more included, or R j = R min is reached
for the regarded hypersphere j . The pattern is not stored.

• Only hyperspheres of different classes are activated by the presented pat-

tern. Radii of activated hyperspheres will be reduced until the pattern is
no more included or R j = R min is reached. In the first case, pattern k will
be stored with R J +1 = , i.e., the radius will extend just to the

center of the closest or nearest-neighbor hypersphere l . In the second case,
pattern k will not be stored.

|| t l − t J +1 ||

With the choice of R min , the storage of vectors close to class borders can
be suppressed, thus influencing network resubstitution and generalization
properties. Evidently, patterns once stored in the RCE network will never be
removed. Just the pattern radii will be reduced until R min is reached. This
means that the size and quality of the achieved network are determined by
the order of presentation of training vectors. A probabilistic presorting of
sample data for RCE (ProRCE) based on local probability estimation and
sorting of the training presentation order proportional to the probability has