## 2 Methodology
### Model Construction Using ML  
By revealing the implicit relationship between target features and alloy phases, ML can help to understand the formation mechanism of the HEAs and accelerate the discovery of new alloys. Generally, it is very difficult to choose the best algorithm for alloy phase prediction because the features used, the model hyperparameters, and the dataset distribution are various. Building the alloy phase prediction model requires testing a large number of algorithms so as to select the best algorithm for the model. In this work, we will test the fitting effects of 9 algorithms--Logistic regression (LR), SVM, K-Nearest Neighbors (KNN),Back Propagation Neural Network, Adaptive Boosting (AdaBoost), eXtreme Gradient Boosting (XGBoost), Gradient Boosting Decision Tree (GBDT), Light Gradient Boosting Machine (LightGBM), and Random Forest (RF)--and take the algorithm with the highest accuracy as the benchmark algorithm for model construction.  
Feature engineering is to remove redundant features and noises, reduce the risk of model overfitting, and improve model accuracy and interpretability. In addition, the use of data pre-processing, such as data dimensionality reduction, can change the data distribution and cause the data to lose interpretability, and therefore should be avoided in the feature engineering process. Further, because the feature set includes a large quantity of features, it is crucial to select the most suitable features according to whether to effectively perform feature engineering. Through both Embedded and Wrapper modes, feature selection can be performed, and the selected features can be made relevant to ML modeling. The Embedded mode incorporates feature selection into the model training and evaluates the weight coefficient of individual features based on the specific model so as to find out the features with the greatest contribution to the model. Wrapper mode directly takes the accuracy of the model as the evaluation criterion of the feature subset and searches the feature set through a certain search strategy to obtain the optimized model accuracy. The common algorithms of Wrapper are Sequential Forward Selection (SFS), recursive feature elimination (RFE), etc. However, these algorithms are often greedy, and the prediction results of the selected features are not as accurate as those of the features selected through the global optimization algorithm. Genetic algorithm (GA), a search algorithm based on the principle of biological evolution, can find the optimal solution in a large-scale search space by simulating the biological genetic and natural selection processes in nature. Compared with SFS, RFE, and other search strategies, GA has better global search capability, which makes it easier to converge to the global optimal solution. However, being a global optimization algorithm, GA requires a large amount of computational resources when feature selection is performed in a dataset with a large feature set. Therefore, this work will combine Embedded and Wrapper modes to quickly select the best combination of features for modeling while reducing the use of computational resources. To avoid overfitting or underfitting, we use the 10-fold cross-validation method (10-fold) to ensure the generalization of the model in the process of algorithm selection, feature selection, and hyperparameter optimization for ML modeling. The 10-fold divides the original dataset into 10 subsets of equal size, 9 of which are used as the training set and 1 as the test set, and then rotates each of these 10 subsets as the test set until each subset is used once as the test set. The performance on each test set is recorded and finally averaged as the performance metric of the model. A 10-fold method can better utilize the dataset for model performance evaluation and avoid overfitting, resulting in more accurate evaluation results.