Pattern Classification Techniques for Lung Cancer Diagnosis by an Electronic Nose - Computational Intelligence in Healthcare: Advanced Methodologies - page 398

weights of the network in order to classify the data correctly. For each data
point, a winner neuron is detected as the one closest to the desired value
and the weights of its connections are consequently adapted. The main ad-
vantage of LVQ is that it creates prototypes that are easy to interpret for
experts in the field.
- Probabilistic Neural Networks (PNN) : PNN is a parallel implementation of
the Bayes statistical technique and is a four layer feed-forward MLP. By re-
placing the sigmoid activation function with an exponential function (Gaus-
sian), a PNN can compute nonlinear decision boundaries that approach the
Bayes optimal. The decision requires an estimate of the probability den-
sity function (pdf) for each class. The only adjustable parameter in PNN
is the kernel width, which determines the degree of interpolation that oc-
curs in determining the pdf. The main drawback of PNN is that it is lim-
ited to applications involving relatively small datasets; large datasets would
indeed lead to large network architectures and would increase the rate of
misclassification.

Support Vector Machine (SVM). SVM are linear classifiers in high dimen-
sional spaces. The basic idea behind the SVM paradigm is that, if we define a
map (usually nonlinear) from the input space to a feature space H ,thesample
S can be separated by a hyperplane in H even if a separating hyperplane does
not exist in X . In the subset of all the S -separating hyperplanes the optimal sep-
arating hyperplane must be detected: it is the hyperplane which maximizes the
distance between the hyperplane and the closest between the positive and the
negative cluster. A hyperplane in the feature space is the image of a nonlinear
function in the input space, whose shape depends on the kernel function. Deter-
mining the optimal separating hyperplane is a quadratic programming problem.
However, mapping the input space to a feature space may make this problem
computationally hard. The important advantage of the support vector classi-
fier is that it offers a possibility to train generalizable, nonlinear classifiers in
high-dimensional spaces using a small training set. Moreover, since a quadratic
programming problem is convex, every local solution is also global (unique if the
Hessian is positive definite). On the other hand, the training phase of a SVM
can be computationally intensive, but it is also amenable to parallelization and
always yields the optimal solution.

Fuzzy logic. Fuzzy logic is a form of multi-valued logic derived from fuzzy set
theory conceived by Lotfi Zadeh [14]. It provides a generalization of the tradi-
tional forms of logic and set membership. In contrast with binary sets having
binary logic, also known as crisp logic, in fuzzy set theory the set member-
ship values can be between 0 and 1, that is, the degree of truth of a state-
ment can range between 0 and 1 and is not constrained to the two truth values
{ as in classic propositional logic. Indeed, in classical set the-

ory an object either belongs to a set or it does not. Probability explains how
events occur in random space, while fuzzy logic includes situations where there
is imprecision due to vagueness rather than randomness. Probability deals with

true (1) ,false (0) }