## 4 Research Methodology
### Preprocessing  
Reviewing the maximum values, they appear to be extremely high; for example, (A5), the maximum value of insulin cannot be 850. As a result, it is an outlier. Box plots can be used to verify our assumptions about such outliers, as shown in Figure 3.  
The preprocessing step in the proposed algorithm contains outlier rejection (P), imputing missing values (Q), the standardization process (S), and the selection of features.  
When an observation deviates from the other observations in the data, it is called an outlier [50]. The classifiers are affected by the distribution of the data and are sensitive; thus, the data deviating from the distribution need to be rejected. We used the IQR technique to remove outliers. The mathematical formulation for outlier rejection is described mathematically as in Equation (4).  
\[\mathrm{P}(I)\ =\left\{\begin{array}{ll}I&if\ \mathrm{Q}_{1}-1.5*\mathrm{IQR}\ \leq I\leq\ \mathrm{Q}_{3}+1.5*\mathrm{IQR}\\ Reject&Otherwise\end{array}\right. \tag{4}\]  
where \(I\) denotes the enrolled feature vector (FV) instances in the dimension space M, such as \(I\in\mathrm{R}_{\mathrm{M}}\). \(\mathrm{Q}_{1}\) represents the 1 st quartile, \(\mathrm{Q}_{3}\) represents the 3 rd quartile and the IQR are the range of interquartile of the applied attributes, knowing that \(\mathrm{Q}_{1}\), \(\mathrm{Q}_{3}\), and the IQR belongs to \(\mathrm{R}_{\mathrm{M}}\). It is important to process the data by filling in the missing or blank values after outlier rejection, as this affects the classifiers with incorrect predictions. After the data became continuous without entering outliers, the null and absent values were processed by the average values of the enrolled features, as shown in Equation (5) [51].  
\[\mathrm{Q}(I)\ =\ \left\{\begin{array}{ll}mean(I),&if\ I=null/missed\\ I,&otherwise\end{array}\right. \tag{5}\]  
Figure 3: Boxplot showing features (A1, A2,..., A8) and outliers.  
The Z-score normalization was performed based on rescaling parameters such that the normal distribution with zero mean and one variance were achieved. As shown in Equation (6), the term standardization (S) refers to the process of reducing the skewness of the data distribution.  
\[\mathrm{S}(A)\ =\ \frac{I-\overline{I}}{\sigma} \tag{6}\]  
where the enrolled FV (\(l\), \(\overline{l}\)) \(\in\) R\({}_{\mathrm{M}}\), where \(\overline{I}\)\(\in\) R\({}_{\mathrm{M}}\) is the mean, and the standard deviation is \(\sigma\)\(\in\) R\({}_{\mathrm{M}}\).  
The statistical analyses in Figure 4 show that the correlation of the features with the intended results is enhanced after imputing the missing outlier rejection values, wherever the correlation coefficient has improved significantly, particularly for A3, A4, and A5. The benefit of feature selection is an improved correlation. The classifiers' accuracy increases as the dimension of the feature increases. However, as the domain of the feature increases without increasing the sample size, the efficiency of the classifiers needs to be improved. In machine learning, such a scenario is known as overfitting. The space of the feature becomes denser and denser because of the curse of dimensionality, forcing the classifiers to be overfitted and lose functional generalizability [52].  
Figure 4: Boxplot of the feature distribution with (**a**) existing and (**b**) rejected outliers, so the first row is for features A1, A2, A3, and A4, and the second row is for features A5, A6, A7, and A8 (from left to right). (**a**) The appearance of a data outlier. (**b**) After outlier rejection.  
However, feature standardization is unlikely to provide a guarantee of significant improvement in many ML models, such as the NB model. The correlation's confusion matrix combines the results of outlier rejection and imputation of missing values. The confusion matrix that represents the correlation of features based on the applied PIDD dataset before and after processing is shown in Figure 5.