## 3 Results and Discussion  
### Algorithm Comparison of the ML Model  
As the alloy phase formation mechanism is complex and nonlinear, certain nonlinear mapping was required to effectively improve the model's accuracy. Therefore, the RBF kernel was used for SVM, the Rectified Linear Unit as the activation function for BPNN, and the Adaptive Moment Estimation Optimizer as the optimizer to improve the nonlinear mapping capability of the model. Subsequently, the dataset containing 145 features was used as input parameters for LR, SVM, KNN, BPNN, AdaBoost, RF, XGBoost, GBDT, and LightGBM, respectively, and the alloy phase classes as output to train ML models to evaluate candidate algorithms. The evaluation indexes of the algorithm are accuracy, precision, recall, and F1-score under 10-fold to detect the classification performance of the algorithm, which are calculated as follows:  
\[\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FN}+ \text{FP}}, \tag{14}\]  
\[\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}}, \tag{15}\]  
\[\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}}, \tag{16}\]\[\text{F1}-\text{score}=\frac{2\text{Precision}\times\text{Recall}}{\text{Precision}+ \text{Recall}}, \tag{17}\]  
where TP and TN represent the correct classification; TP/TN is the number of correct classifications of positive/negative class; FP and FN represent misclassification; and FP/FN are the data misclassified as positive/negative class. As Figure 1 shows the confusion matrix of the classifiers fitted by the nine ML algorithms under 10-fold, the imbalance of the data makes each model to some extent less effective in classifying the HCP or BCC+FCC. Among them, the classification is particularly poor for BCC+FCC. For HCP prediction, EL algorithms such as RF, XGBoost, GBDT, LightGBM, etc., show overwhelming advantages over LR, KNN, SVM, and BPNN algorithms. Although the EL algorithms are still not ideal for the prediction of BCC+FCC, they have been improved to some extent compared to the traditional algorithms. This result may suggest that the EL algorithm suppresses the negative effects of data imbalances to some extent. Also, this result demonstrates the advantages of EL algorithms in dealing with sparse and redundant tabular data. Further, to select the optimal one from the EL algorithms, the accuracy, precision, recall, and F1-score of each algorithm were tested. In Table 1, LightGBM has the best prediction performance, with all the accuracy, precision, recall, and F1-score values exceeding 0.95. Therefore, LightGBM is used as the benchmark algorithm to construct the alloy phase classifier. However, due to data imbalance, the prediction accuracy of LightGBM for BCC+FCC is only 75.68%, which is much lower than the prediction accuracy of BCC, FCC, and HCP and has a negative impact on the accurate prediction of alloy phases. From the classification results of BCC+FCC in Figure 1g, five or thirteen BCC+FCC were misclassified as BCC or FCC, respectively, but none were misclassified as HCP. This may be due to the fact that most of the empirical parameters were used to distinguish between BCC, BCC+FCC, and FCC, while the phase transitions with empirical parameters followed the order BCC, BCC+FCC, and FCC. Also, this proves that the classification boundary between HCP and the other three phases is relatively clear, so that its classification accuracy reaches 91.45%, although there is a data imbalance in HCP. \begin{table}
\begin{tabular}{c c c c c} \hline
**ML Algorithm** & **Accuracy** & **Precision** & **Recall** & **F1-Score** \\ \hline LR & 0.7929 & 0.7846 & 0.7929 & 0.7848 \\ KNN & 0.7650 & 0.7622 & 0.7651 & 0.7624 \\ SVM-rbf & 0.7889 & 0.8219 & 0.7889 & 0.7834 \\ BPNN & 0.7967 & 0.7862 & 0.7899 & 0.7875 \\ AdaBoost & 0.6026 & 0.6910 & 0.6016 & 0.6182 \\ Random Forest & 0.9485 & 0.9478 & 0.9485 & 0.9477 \\ LightGBM & 0.9515 & 0.9508 & 0.9514 & 0.9507 \\ GBDT & 0.9465 & 0.9457 & 0.9465 & 0.9458 \\ XGBoost & 0.9445 & 0.9436 & 0.9445 & 0.9435 \\ \hline \end{tabular}
\end{table}