## 3 Proposed Methodology
### Preprocessing  
To ensure satisfactory accuracy, missing values must be handled in the preprocessing step depending on their distributions. [PERSON]'s MCAR (Missing Completely At Random) test was used in this study to confirm the randomization of missing values. The possibility of bias as a result of missing data is dependent on the mechanism that caused the data to be missing. The chi-square test of MCAR for multi-variate quantitative data is used to examine the analytical approaches used to correct the missingness and all the inference/computation work. In this study, the KNN Imputer method was employed to fill in the missing values.  
Many classification algorithms strive to collect only pure examples for learning and to make the boundary between each class as clear as possible to improve prediction. The majority of classifiers find it significantly more difficult to learn how to classify synthetic cases that are close to the boundary than those that are far from it. Based on these results, authors of one study presented an enhanced preprocessing method (A-SMOTE) for imbalanced training sets [27]. The SMOTE method is carried out in 3 stages, as explained below.  
Step A: Using Equation (1) synthetic instance is created.  
\[N=2*(r-z)+z \tag{1}\]  
where \(r\rightarrow\) majority class samples, z \(\rightarrow\) minority class samples and \(N\rightarrow\) newly created synthetic instance.  
Step B: The below-mentioned steps are carried out to remove the outlier; that is, noise.  
If, \(\hat{S}=\{\hat{S_{1}},\hat{S_{2}},\hat{S_{3}},\ldots\hat{S_{n}}\}\) is a new instance received by Step A, then we will calculate the distance among \(\hat{S_{i}}\) with original minority \(S_{m},\ Min_{Rap}\left(\hat{S_{i}},\ \hat{S_{m}}\right)\) defined using Equation (2).  
\[Min_{Rap}(\hat{S_{i}},\ \hat{S_{m}})=\sum_{k=1}^{z}\sum_{j=1}^{M}\sqrt{\left( \hat{S_{i}}^{(j)}-S_{mk}{}^{(j)}\right)^{2}} \tag{2}\]  
where  
\(Min_{Rap}(\hat{S_{i}},\ \hat{S_{m}})\rightarrow\) samples rapprochement and as per Equation (2), \(L\) is calculated using Equation (3).  
\[L=\sum_{i=1}^{n}(Min_{Rap}\ (\hat{S_{i}},\ S_{m})) \tag{3}\]  
Step C: Calculate distance between \(\hat{S_{i}}\), and every original majority \(S_{a}\), \(Maj_{Rap}(\hat{S_{i}},S_{a})\), described using Equation (4).  
\[Maj_{Rap}(\hat{S_{i}},S_{a})=\sum_{i=1}^{r}\sum_{j=1}^{M}\sqrt{\left(\hat{S_{ i}}^{(j)}-S_{al}{}^{(j)}\right)^{2}} \tag{4}\]  
\(Maj_{Rap}(\hat{S_{i}},S_{a})\rightarrow\) samples rapprochement and as per Equation (4), \(H\) is computed using Equation (5).  
\[H=\sum_{i=1}^{n}(Maj_{Rap}\ (\hat{S_{i}},\ S_{a})) \tag{5}\]  
Entropy is nothing but the measure of disorder. The following Equations (6) and (7) were used by [PERSON] to put this link between probability and heterogeneity.  
\[H(X)=-\sum(p_{i}*log_{2}p_{i}) \tag{6}\]  
\[\text{Entropy }(\ p)=-\sum_{i=1}^{N}p_{i}log_{2}p_{i} \tag{7}\]  
There are missing values in all the features except diagnostic class. In this study, the KNN Imputer method was employed to fill in the missing values. Since the dataset comprises 250 cases of the \"ckd\" class (62.5%) and 150 cases of \"notckd\" (37.5%), the dataset is uneven or unbalanced. The analysis of the features before and after application of the SMOTE technique is shown in Table 3.