Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data - Advanced Techniques in Knowledge Discovery and Data Mining - page 41

number N ∗ of hidden neurons is a major issue, especially for large scale
problems. Several top-down and bottom-up strategies have been developed
in the past [2.42] [2.15] [2.35] [2.30], employing and combining both super-
vised and unsupervised learning techniques. In a typical top-down strategy,
a large number of centers will be determined by vector quantization tech-
niques, e.g., Kohonen's self-organizing map. Fine-tuning of the network is
achieved by a following supervised learning step, e.g., using gradient descent.
Further network optimization and size reduction can be achieved by pruning
techniques.
On the other hand, in bottom-up approaches the network is generated
from scratch, thus completing a network-size tailored to the training data.
The RBF network proposed by Platt [2.42] and the restricted-Coulomb-energy
(RCE) network [2.46], [2.5] are significant examples of this category, as they
allow dynamic automatic topology construction tailored to the problem re-
quirements. This and an additional advantage of RBF-type networks make
them excellent candidates for the investigations in this work. They also allow
the concept of background classification (BC) to be implemented, which can
be generalized from multiclass to one-class classification (OCC). BC is im-
plemented by assigning the whole feature space to the selected background
class. Other class regions are established by placing kernel functions and ap-
propriately adjusting their widths during the learning process. Clearly, the
network loses the rejection capability associated with the appearance of data
far from the training samples. However, in cases like visual inspection or
semiconductor manufacturing, in contrast to the plethora of potential errors,
the desired condition can be described by su cient examples. Thus assign-
ing the background to such an error class can be advantageous. Initial ideas
can be found in the Nestor-learning-system (NLS) [2.5], [2.6], which com-
prises a special RBF model denoted by RCE network [2.46]. The concept has
been generalized to RBF networks in [2.20]. The special case of OCC, also
addressed in the literature as novelty filtering [2.19] or anomaly detection
[2.17], [2.31], [2.50], [2.33], is attractive because the classifier structure can
be generated just by presenting data from a normal process situation. This
is fortunate, as typically a lot of data from normal operation conditions are
available; however, the universe of potential deviations is hard to grasp in
terms of representative data samples actually covering all relevant regions in
the high-dimensional parameter space for appropriate class border definition.
Thus, in the following, a model for OCC will be briefly derived from
RBF-type networks for the regarded application domain.
The RCE Algorithm. The RCE network [2.46] is a special case of the RBF
network given earlier. Instead of smooth nonlinearities as, e.g., the Gaussian
function, a hard limiter or step function with a variable threshold parameter
is applied. Each RCE basis function is equivalent to a hypersphere, repre-
sented by a center t j and the threshold parameter, which has the meaning

of a radius R j . Each hypersphere is a liated to one of the classes of the