Advanced Methods for the Analysis of Semiconductor Manufacturing Process Data - Advanced Techniques in Knowledge Discovery and Data Mining - page 54

Selected
intraclass
distances
Selected
interclass
distances
Fig. 2.15. Class compactness assessment.
The principal idea of intraclass and interclass distance computation for q ci
is illustrated in Fig. 2.15. The improved compactness q ci has a complexity of
O(N 2 ), is a nonparametric measure, and requires no parameters to be set by
the user. It shows a high sensitivity to changes in feature space, as these are
immediately mirrored by changes in distance, and, thus, in changes in q ci .
In comparison to the existing overlap measure q oi with equal sensitivity and
computational complexity, q oi is inferior, as it requires the parameter k to
be set. But q oi is superior with regard to normalization properties, returning
a value in [0,1], whereas q ci values depend on the distances in the data set
and only allow the observation of relative changes. For FS, an additional
normalization step for each selection or configuration is required for q ci .
These measures will serve in the following as feature space assessment or
ranking measures J. Information on the individual features' merit as well as
the current feature combinations' merit can be obtained by employing the
presented measures. Also, the results of different dimensionality reduction
methods, e.g., FS or FW, can be quantitatively compared and assessed [2.24].
Feature Selection Methods. The process of finding the appropriate co-
e cients c i in (Eq. 2.13) is an intricate optimization problem. Due to the
combinatorial complexity inherent to the problem of FS, the computational
effort of finding the best selection, i.e., feature combination, grows exponen-
tially. Thus, the global optimum solution for the selection process cannot be
found with polynomial complexity or effort, i.e., we have an NP-complete
problem (cf., e.g., [2.1]). Therefore, a complete or exhaustive search of all