Biomedical Engineering Reference
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space to a comprehensible set of parameters. Instead, the training set is re-
tained in its entirety as a description of the object distribution. Thinning
methods can be used on the training set, but the result still does not usually
constitute a compact description of the object distribution. The method is also
rather slow if the training set has many examples. The most serious short-
coming of nearest-neighbor methods is that they are sensitive to the presence
of irrelevant parameters. Adding parameters that have random values for all
objects (so that it does not separate the classes) can cause these methods to
fail. Outliers are not easy to analyze and errors are likely to occur at decision
boundaries. Simple algorithms do not ensure optimality of classification. It
could be especially useful as a starting point for further optimization based
on better modeling of data. Simply put, it is “rough but quick” [134].
8.3.6 Decision Trees
Decision trees [135] can be used to identify and segment spectra when discrim-
inating rules are known or desired (Fig. 8.8). A binary tree consists of nodes
in which a single parameter is used as a discriminant. After a series of nodes
are traversed, leaf nodes of the tree are encountered in which all the objects
are labeled as belonging to a particular class. Decision trees can be axis par-
allel or oblique. Axis-parallel trees are called so because they correspond to
Fig. 8.8.
Schematic of a simple decision tree in which the vector of conditions is
used to partition data into one of the classes,
c
i
. The question at every node concerns
a particular property or element of the input vector
X
. Successive nodes are visited
until a terminal or leaf node is reached where the object is finally classified. Note
that different conditional questions can have different number of branches and also
that many leaf nodes can have the same class
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