## 2 Materials and Methods
### Methods
#### 2.3.4 Model Evaluation  
Contamination between the data types can be verified and analyzed from the confusion matrix table, which is the table that brings the results from data type classification from any method to overlap with the area with the related fact data, and then compares the accuracy between them. The multi-class confusion matrix includes the following Figure 6[37]:The confusion elements for each class are shown by (Equations (6)-(9)):  
\[TP_{i}=c_{ii} \tag{6}\]  
\[FP_{i}=\sum_{l=1}^{n}c_{li}-TP_{i} \tag{7}\]  
\[FN_{i}=\sum_{l=1}^{n}c_{il}-TP_{i} \tag{8}\]  
\[TN_{i}=\sum_{l=1}^{n}\sum_{k=1}^{n}c_{lk}-TP_{i}-FP_{i}-FN_{i} \tag{9}\]  
True Positive (_TP_) was the actual value, and the predicted value should be the same. False Positive (_FP_) was the sum of the corresponding rows values except for the _TP_ value. False Negative (_FN_) was the sum of values of corresponding column except for the _TP_ value. True Negative (_TN_) was the sum of values of all columns and rows except the values of that class for which we calculate the values. After knowing the _TP_, _FP_, _FN_, and _TN_ values, check a _p_-value and Kappa coefficient index. A _p_-value was used to evaluate the significance of the results in comparison to the null hypothesis when carrying out statistical tests. The null hypothesis asserts that no link exists between the two variables under investigation (one variable does not affect the other). The alternative hypothesis asserts that the independent variable did influence the dependent variable, and the results are important in terms of corroborating the theory under investigation. Statistical significance is defined as a _p_-value less than 0.05 (usually 0.05). It shows significant evidence against the null hypothesis since the likelihood of the null being true is less than 5%. As a result, the null hypothesis is rejected, and the alternative hypothesis is accepted. [PERSON]'s Kappa coefficient, which is frequently used to measure reliability, may be used for training-testing reliability. The Kappa coefficient reflects the degree of agreement between the frequencies of two sets of data obtained on two distinct occasions in training-testing. The scale of Kappa value interpretation was shown in Table 4. [38]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Kappa** & **Interpretation** \\ \hline \(<\)0\% & No agreement \\
0.01–20\% & Slight \\
21–40\% & Fair \\
41–60\% & Moderate \\
61–80\% & Substantial \\
81–100\% & Perfect \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The scale of Kappa value interpretation. Figure 6: The multi-class confusion matrix. The accuracy of the model is based on the following Equations ((10)-(14)):  
\[Sensitivity=\frac{TP_{i}}{TP_{i}+FN_{i}} \tag{10}\]  
\[Specificity=\frac{TN_{i}}{TN_{i}+FP_{i}} \tag{11}\]  
\[Positive\;prediction\;value=\frac{TP_{i}}{TP_{i}+FP_{i}} \tag{12}\]  
\[Negative\;prediction\;value=\frac{TN_{i}}{TN_{i}+FN_{i}} \tag{13}\]  
\[Accuracy=\frac{TP+TN}{TP+FN+FP+TN} \tag{14}\]  
The ratio of correctly identified positives to the total number of positive samples is known as sensitivity, or actual positive rate or recall. Sensitivity is a crucial metric to assess and compare classifiers with since it indicates the correct classification rate of the class. The ratio of properly categorized negatives to the total number of negative samples is specificity. Specificity is similar accuracy because the number of occurrences is less. The ratio of correctly identified positives to the total number of samples labelled as positives is the precision or positive predictive value. The ratio of correctly identified negatives to the total number of samples classified as negatives is called fallout, sometimes known as the false-positive rate. It is a rate that complements specificity and shows the percentage of \"false alarms.\"  
The capacity of a classification test to accurately identify or exclude an outcome is measured by accuracy (ACC), and it is the proportion of correct predictions to total samples.