# Add projections
## 7 Results and Discussion of Data Classification
\begin{table}
\begin{tabular}{c c} \hline \hline
**ML Models** & **Parameters** \\ \hline Logistic Regression & random\_state = 0 \\  & solver = liblinear\({}^{\prime}\) \\  & penalty = l2 \\ \hline  & kernel = \({}^{\prime}\)bf\({}^{\prime}\) \\ Support Vector Machine (SVM)-Model-1 & random\_state = 0 \\  & probability = True \\  & C = 1 \\ \hline  & kernel = \({}^{\prime}\)poly\({}^{\prime}\) \\  & degree = 8 \\ Support Vector Machine (SVM)-Model-2 & random\_state = 0 \\  & probability = True \\  & C = 1 \\ \hline  & n\_estimators = 200 \\ Random Forest & criterion = \({}^{\prime}\)entropy\({}^{\prime}\) \\  & random\_state = 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model parameters for Logistic regression, SVM and Random Forest algorithms. For SVM, we have experimented with the polynomial kernel transformation of degree = 3 and observed the accuracy of 0.75, whereas with degree = 8 the accuracy is 0.78. However Radial-basis function (RBF) gave the similar accuracy equals to 0.78 when regularization parameter C value is 1.0. Based on this observation, we can say that polynomial kernel with degree = 3 underperformed when compared to RBF because the characteristics of the data distribution falls in the radial basis curve. Despite the lower accuracy, the non-linear polynomial kernel SVM-model with degree = 3 is preferred rather than degree = 8 as it is difficult to generalize the model with higher polynomial degree. With these results, we can determine the best model for the Mg-alloy dataset, but before making the decision, we also calculated one of the important metrics Receiver Operating characteristics (ROC) and the Area under curve (AUC)-ROC. ROC curves are very helpful to understand the balance between true-positive rate and false positive rates. For calculating Receiver Operating Characteristic Curve (ROC), the probabilities are predicted for the independent variables of the test dataset (33 rows) and only positive probability is considered to calculate the ROC_AUC scores. The True positive and False positive rates are calculated which forms an input to plot the roc-curve. The Area under curve (AUC) for ROC is calculated for all the three models and tabulated in Table 5, and ROC curve plots are shown in Figure 7.  
Table 5 shows the ROC-AUC scores for all three models. The ROC-AUC values range from 0 to 1. The models with ROC_AUC score close to 1 has better performance compared to others. From Table 5, we observe that SVM-Model-2 and Random Forest have outperformed compared to the other two models. The AUC_ROC value for SVM-model-2 is high as equal as Random Forest but we do not prefer the SVM-Model-2, as this model is built using polynomial kernel with a higher degree = 8 which is difficult to generalize the model. Despite that, the SVM model with polynomial kernel of degree = 3 is preferred, achieving an AUC_ROC value of 0.818. Hence, we can consider Random Forest and SVM with polynomial kernel of degree = 3 as the best classification models for the Mg-alloy dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ML Models** & **Precision** & **Recall** & **F1-Score** & **Accuracy** \\ \hline Logistic Regression & 0.71 & 0.73 & 0.73 & 0.73 \\ \hline SVM-Model-1 & 0.78 & 0.79 & 0.79 & 0.79 \\ \hline SVM-Model-2 & 0.80 & 0.79 & 0.77 & 0.79 \\ \hline Random Forest & 0.88 & 0.88 & 0.88 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance Metrics of Mg-alloy dataset on the independent test data (33 rows) using the parameters from Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**ML Models** & **ROC-AUC Score** \\ \hline Logistic Regression & 0.603 \\ \hline Support Vector Machine (SVM)-Model-1 & 0.777 \\ \hline Support Vector Machine (SVM)-Model-2 & 0.835 \\ \hline Random Forest & 0.835 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ROC-AUC values for Logistic regression, SVM and Random Forest models.