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Fig. 4. The results of dimensionality reduction by Principal Component Analysis
(PCA), in a), and Non Parametric Linear Discriminant Analysis (NPLDA), in b).
As evident, the discrimination problem between the two classes healthy subject versus
lung cancer patient is better solved by NPLDA. This is probably due to the fact that
NPLDA is a supervised approach that takes into account the class membership of each
training sample and projects data in a way that maximizes the interclass distance and
minimizes the intraclass one; the approach is very different from PCA, which, as un-
supervised method, does not consider membership labels and projects the components
that maximize the variance information. On the other side, PCA plot is very useful
because it allows an exploration of data structure, emphasizing it and possible sensor
drift.
feed-forward neural network (usually multi-layer perceptrons), Kohonen Self Or-
ganizing Maps (SOM), Independent Component Analysis (ICA) and Sammon's
maps [10].
In the lung cancer diagnosis by the electronic nose application we evaluated
projection based both on PCA, LDA and NPLDA. As evident from Figure 4,
NPLDA is able to separate the projected features more clearly than PCA, which
plot shows a more evident samples overlap, due to the fact that PCA preserves
the original structure of the data, which includes odor variance and sensor drift,
without maximizing the class separability.
7 Classification
The objective of classification is to predict the class of an unknown input vector.
There are two main families of classification approaches: supervised and unsu-
pervised. The basic idea of supervised methods is to train the classifier providing
it a series of examples and the corresponding known classes, in order to learn the
relationship between feature data and classes. In unsupervised methods, the clas-
sifier learns to separate the different classes from the response vectors routinely,
without having any prior information on class membership.
 
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