## 2 Materials and Methods
### Data Analysis
#### 2.4.4 Discriminant Model and Performance Evaluation  
Partial least squares discrimination analysis (PLS-DA), as a supervised discriminant analysis method, is a high-dimensional linear discriminant analysis model using partial least squares regression (PLSR) [24]. In addition, PLS-DA is an algorithm based on the relationship between spectral data and sample characteristics. It converts the data of the calibration set into latent variables to determine the sample label of the prediction set. Therefore, the number of latent variables (LV) is a key parameter of PLS-DA. A too-small number of latent variables will result in too low model accuracy, while too many latent variables will lead to overfitting. This study chooses ten-fold cross-validation to determine the optimal number of latent variables.  
The key of least squares support vector machine (LSSVM) is to find all the support vectors from which the optimal separation hyperplane can be obtained [25]. LSSVM uses the least-squares linear system as a loss function instead of the quadratic planning method as a loss function of the SVM and changes the inequality constraint in the SVM to an equation constraint, which significantly simplifies the calculation of the Lagrange multiplier alpha. SVM is a quadratic programming (QP) problem, while LSSVM is a problem of solving linear equations. LSSVM has two important parameters that affect the model's ability to generalize, namely the penalty coefficient (c) and kernel range (\(\sigma\)). In general, the requirements of the model accuracy and complexity on the parameters (c, \(\sigma\)) are contradictory. In practice, the grid method should be used to select the optimal model parameters.  
Random forest (RF) is a classifier that uses several trees to train and predict, it is a special bagging method that uses decision trees as a model in bagging. Random forest randomizes the use of variables (columns) and data (rows) to generate many classification trees, each of them is an independent judgment branch, they are independent of each other [26]. Random forest improves the prediction accuracy without significant increase in the amount of calculation, and is insensitive to multivariate linearity. The missing data and unbalanced data are more robust, which can effectively predict the role of up to thousands of variables. When a new object is classified and discriminated based on certain attributes, each tree in the random forest will give their own classification choice, and then \"vote\", by means of which the overall output of the forest will be the classification option with the most votes. Compared with a single decision tree algorithm, it produces a better classification effect, and is not prone to overfitting.  
Extreme learning machine (ELM) or \"over-limit learning machine\" is a model based on a feed-forward neural network (FNN) machine learning system or method for solving supervised and unsupervised learning problems [27]. ELM is deemed to be a unique FNN or an enhancement to the FNN and its backpropagation (BP) algorithm. The traditional neural network learning algorithm needs to be set in a lot of parameters in the training model, while the ELM only needs to be set in the number of hidden layer neurons (L) and the excitation function. The process of algorithm execution does not need to be iterated and the input weights and hidden element offsets are randomly generated. The connection weight (\(\beta\)) between the hidden layer and the output layer generates the only solution by calculating the equations. Therefore, ELM improves the learning speed of the forward neural network without being trapped into the local minimum value or overfitting.  
The reliability and accuracy of the predictive model performance are assessed by the correct classification rate (CCR), which is calculated as follows:  
\[CCR=\frac{TP}{P} \tag{2}\]  
In Formula (2): CCR represents the correct classification rate, TP represents the number of correctly classified samples, and P represents the total number of samples.