C. Support Vector Machines (SVMs) 
According to (Müller et al, 2001)], the classification problem can be formally stated as estimating a function f: R
N**{-1, 1} based on an input-output training data generated from an** 
independently, identically distributed unknown probability distribution P(x,y) such that f **will be** able to classify previously unseen (x**,y) pairs. The best such function is the one that minimises** 
the expected error (risk) which is given by 

 ∫
$$R[f]=\int l(f(x),y)d P(x,y)$$
where l **represents a loss function (Müller et al, 2001). Since the underlying probability** distribution P **is unknown, equation (2) cannot be solved directly. The best we can do is to find** 
an upper bound for the risk function (Vapnik, 1995), (Müller et al, 2001) which is given by 

$$R[f]=R[f]_{c o u p}+\sqrt{\frac{h\left(\ln\frac{2n}{h}+1\right)-\ln\left(\frac{\delta}{4}\right)}{n}}$$
 n
$$(2)$$

$$({\boldsymbol{3}})$$
$$\quad(4)$$

where h ∈N
+ is the Vapnik-Chervonenkis (VC) dimension of f ∈ F and δ **> 0 holds true for** 
all. The VC dimension of a function class F is defined as the largest number h **of points that can** 
be separated in all possible ways using functions of that class (Vapnik, 1995). The empirical error *R[f]*emp **is a training error given by** 

 ∑+
$$R[f]_{e m p}=\frac{1}{n}\sum_{i=1}^{n}l(f(x_{i}),y_{i})$$
Assuming that the training sample is linearly separable by a hyperplane of the form f(x) = (w.x) + b **(5)** 
where w is an adjustable weight vector and b **is an offset, the classification problem looks like** 
figure 2 (Müller et al, 2001) 