## 4 Materials and Methods
### Discriminant Analysis (DA)  
Discriminant Analysis (DA) is one of dependency statistical analysis techniques in Multivariate Analysis. It means that in DA, there are dependent and independent variables being analyzed, where the value of the dependent variable depends on the values of the independent variables. In DA, there is only one dependent variable, but there are more than one independent variables. DA can be used if the dependent variable is categorical (in nominal or ordinal scale), and the independent variables are metric (in interval or ratio scale). A categorical dependent variable means the corresponding variable consists of certain categories. DA is used to classify an object into one of the statistically independent groups or categories based on the values of the independent variables. Classification process in DA is mutually exclusive, that is, if an object is classified into one particular group, it will not be classified into another group. In DA, discriminant function(s) will be formulated. A discriminant function is used to classify an object into a group or category based on the value of the discriminant function itself. The values of the independent variables of an object will be inputted in the function. Then, the obtained value of the function, which is called the discriminant value, will determine in which group an object belongs. For k categories, k-1 discriminant functions have to be formulated. Based on the amount of the categories of the dependent variable, there are two types of DA, which are two-group discriminant analysis and Multiple Discriminant Analysis (MDA). Two-group discriminant analysis is a type of DA where the dependent variable consists of two categories. While MDA is another type of DA where the dependent variable consists of more than two categories. Based on the type of the discriminant function, there are also two types of DA, which are Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA). LDA is a classification method used to find the optimum linear combination of features to separate two or more groups of objects [21]. QDA can be considered as a direct extension of LDA. There are some differences between LDA and QDA. First, the discriminant function in LDA is a linear combination of the independent variables. While the discriminant function in QDA is in the form of quadratic function. Second, in LDA, every covariance matrix of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Hemoglobin** & **Hematocrit** & **WBC** & \
\begin{tabular}{c} **Platelet** \\ **Count** \\ \end{tabular} & **Neutrophil** & **Lymphocyte** & **Monocyte** &
\begin{tabular}{c} **Severity** \\ **Level** \\ \end{tabular} \\ \hline Minimum value & 8.5 & 30.3 & 1000 & 6000 & 22 & 12.1 & 0 & 0 \\ \hline
1 st quartile & 12.6 & 38.4 & 2330 & 93,000 & 55 & 20.7 & 3 & 0 \\ \hline Median & 13.9 & 40.6 & 3100 & 119,000 & 64 & 25 & 10 & 1 \\ \hline Mean & 13.9 & 41.3 & 3178 & 126,188 & 61.7 & 28 & 9.5 & 0.6 \\ \hline
3 rd quartile & 15.4 & 45 & 4000 & 161,000 & 73 & 34 & 14 & 1 \\ \hline Maximum value & 17.8 & 52.3 & 6900 & 278,000 & 84 & 68 & 23 & 2 \\ \hline \end{tabular}
\end{table} 
Table 1: Dengue patients’ data summary. every independent variable has to be the identical. While in QDA, every covariance matrix of every independent variable can be different. The third difference, the decision curve in LDA is in the form of a straight line, while the decision curve in QDA is in the form of a quadratic curve [22]. Assume that observations \(X_{j}^{(k)}\) of a group \(k\) are random vectors of size \(p\) sampled from a Gaussian distribution \(\mathcal{N}\left(\mu^{(k)},\Sigma^{(k)}\right)\), for all \(j\in\{1,\ \ldots,\ N\}\).