# Prediction of Diabetes Using Statistical and Machine Learning Modelling Techniques
## 3 Methodologies
### Models Overview
SVR is less popular than SVM, but it has been verified that it is a valuable technique in estimating the real value of a function [24]. One of the most useful features of SVM is that the complexity of its computation does not rely on the dimensional parameters of the input space. Moreover, SVR shows better generalisation ability, with high performance and accurate prediction. Fundamentally, SVR is a linear approach with one output, dealing with a high-dimensional feature space established by nonlinear mapping of the N-dimensional input vector into a K-dimensional feature space (K > N) utilising the function \(\varphi(\mathbf{x})\). The learning process is moved to the minimisation of the error function, which is defined by the so called \(\epsilon\)-insensitive loss function \(L_{\epsilon}(d,y(x))\):  
\[L_{\epsilon}(d,y(x))=\left\{ \begin{aligned} &|d-y(x)|-\epsilon,\;\;for\;|d-y(x)| \geq\epsilon\\ & 0,\;\;for\;|d-y(x)|<\epsilon\end{aligned} \right. \tag{4}\]  
where \(\epsilon\) is the assumed accuracy; \(d\) is the destination; \(x\) is the input vector; and \(y(x)\) is the actual output under the effect of \(\mathbf{x}\). The actual output of the SVR is defined by  
\[y(x)=\sum_{j=1}^{K}\omega_{j}\varphi_{j}(x)+b=w^{T}\varphi(x)+b \tag{5}\]  
where \(w=[\omega_{0},\omega_{1},\ldots,\omega_{K}]^{T}\) is the weight vector; and \(\varphi(x)=\left[\varphi_{0}(x),\varphi_{1}(x),\ldots,\varphi_{K}(x)\right]^ {T}\) is the basis function vector. 4. Adaptive Neuro-Fuzzy Inference Model  
The ANFIS model is a combined model of fuzzy systems and ANN [25]. The main parts of the FIS are fundamental rules, which contain the choices of fuzzy logic rules \"If-Then\", a set of membership functions, and the fuzzy logic inference procedures from the fundamental rules to obtain the output. In order to map the inputs with the outputs, two common fuzzy inference systems (FIS) can be employed in different applications: Mamdani and Sugeno inference systems. The fuzzy rules in the two inference models give different results, therefore their actions of defuzzification and combination are also different. However, the Sugeno system is believed to be computationally more efficient than the Mamdani; in the former, the resultant parameter is a linear equation or constant coefficient. Supposing that we have a system including two inputs, x and y, and the output is f, and the based rule has two fuzzy if-then rules, then the description of rules for the linear equation Sugeno FIS can be presented as rule 1 (R1) and rule 2 (R2):  
\[\text{R1}:\text{ if }x\text{ is }A_{1}\text{ and }y\text{ is }B_{1}\text{ then }f_{1}=p_{1}x+q_{1}y+r_{1} \tag{6}\]  
\[\text{R2}:\text{ if }x\text{ is }A_{2}\text{ and }y\text{ is }B_{2}\text{ then }f_{2}=p_{2}x+q_{2}y+r_{2} \tag{7}\]  
where \(A_{i}\) and \(B_{i}\) are the membership functions of each input \(x\) and \(y\); and \(p_{i},q_{i}\) and \(r_{i}\) are the linear parameters in the resulting part of the Sugeno fuzzy inference system. The ANFIS model can be considered successful due to the strength of its results. Moreover, as with other machine learning techniques and as a neural network, ANFIS has a high ability to generalise. On the other hand, there are some limitations of the ANFIS model regarding the type, number, and position of membership functions [26]. 5. Artificial Neural Networks Model  
Neural Network and ANN are mathematical models based on the concept of Artificial Intelligence, which simulates the biological neuronal activity of the human brain. This modelling approach is a valuable tool that simulates the functionality of the human brain when dealing with complex relations between the inputs and outputs in any system [27]. There are many types of ANN architectures, the most common of which is Multilayer Perceptron (MLP), which is commonly used for prediction. It comprises three layers: an input layer, hidden layers, and an output layer.