## 2 Materials and Methods
### Classification Approach  
In order to classify the DR, a combination of SVM with DE algorithm was considered. The role of SVM is to classify the data, acting as classifier, while DE has the role of determining the best suited parameters of SVM, leading to maximum performance in terms of accuracy of classification. The mix of DE with SVM from the current work (which will be referred as sDE-SVM) is similar (but not identical) to the one used in [24] (called DE-SVM). From an optimization point of view, SVM parameters determination is not a very complex process as only a reduced number of parameters need to be optimized. The difficulty consists in the large number of resources consumed by the SVM itself. In this context, two variants of DE were used: one simple--referred to as sDE-SVM and one with a slightly more complex differentiation process referred to as DE-SVM. The results obtained in both cases are compared. The work flow of information between the database (which contains the patient information), DE and SVM is presented in Figure 1. The model, SVM, has as inputs a series of information related to the patients with DR. Parameters in SVM, that can have significant influence on the result accuracy, are optimized with DE. Consequently, the results in classification--changes or no changes in diabetic retinopathy--are provided by a model in optimal form. sDE-SVM and DE-SVM are based on two different variants of the DE algorithm, the basic mechanisms of DE and SVM remaining unchanged. For SVM, when given a set of N-dimensional points (\(x_{i}\), \(y_{i}\)), \(i=1\ldots N\) where \(x\) and \(y=\pm\) 1, the goal is to estimate a function \(f\), which respects the condition \(f(x)=y\). In order for the points to be linearly separable, a class of hyper planes (\(w\), \(b\)) defined by \(w^{*}\)\(x+b=0\) with the property \(y_{i}\) (\(x_{i}\)*\(w\) + b)--1 \(>\) 0 must exist. In this context, the implementation of SVM implies solving an optimization problem in the form:  
\[f(x)=\frac{\left\|x\right\|^{2}}{2} \tag{1}\]  
Figure 1: Workflow of the classification approach. with the following constraints:  
\[g_{i}(x)=y_{i}(w\cdot x_{i})-1\geq 0 \tag{2}\]  
For non-separable classes, the mapping of the input data into the feature space \(F\) is performed by a non-linear function and the kernel function has the following form:  
\[k(x,y)=\Theta(x)^{T}\Theta(y) \tag{3}\]  
The types of kernels considered in this work are linear, polynomial and radial basis function (RBF), these kernels being described by Equations (4)-(6), respectively. \[k(x_{i},y_{i})=x_{i}^{T}x_{j} \tag{4}\]  
\[k(x_{i},x_{j})=\left(\gamma x_{i}^{T}\cdot x_{j}+r\right)^{d},\ \gamma>0 \tag{5}\]  
\[k(x_{i}xj)=\exp\Bigl{(}-\gamma\cdot\|x_{i}-x_{j}\|^{2}\Bigr{)},\ \gamma>0 \tag{6}\]  
where \(\gamma\), \(d\) and \(r\) are the parameters of the kernels. In this work, the SVM implementation is provided by the LIBSVM library [25] in two variants: \(\varepsilon\)-SVM and \(\mu\)-SVM. The difference between the two consists in a different penalty parameter. On the other hand, DE is an optimization procedure, its scope being to determine the optimal solution \(x^{\star}\) to a known function \(f(x)=y\). The optimal solution can be either a minimum or a maximum, depending on the characteristics of the problem being solved. DE starts with a pool of potential solutions (which are first randomly generated using a random number generator). In this work, the initialization procedure is improved using the Opposition Based Principle (Equation (7)). \[x_{intermediatey_{i}}=rand()x_{i}=\left\{ \begin{array}{c}x_{intermediatey_{i}},\ if\Bigl{(}fit\Bigl{(}x_{intermediatey_{i}}\Bigr{)}\Bigr{)}<fit\Bigl{(}OBL \Bigl{(}x_{intermediatey_{i}}\Bigr{)}\Bigr{)}\\ OBL\Bigl{(}x_{intermediatey_{i}}\Bigr{)},\ otherwise\end{array} \right. \tag{7}\]  
where  
\[OBL(x_{i})=min_{i,j}+max_{i,j}-x_{i,j} \tag{8}\]  
and \(min_{i,j}\), \(max_{i,j}\) are the lower and the upper limit of the jth parameter of the xi solution, and fit represents the fitness function (mean squared error--MSE).