## 2 Materials and Methods
### Method of Establishing the SSC Prediction Model
#### 2.3.2 The Method of Establishing the SSC Prediction Model  
(1) Selecting characteristic wavelengths  
Since hyperspectral images have a reflectivity of 256 wavelengths, that is, data with 256 channels, not only is the amount of data large, but the data also contain redundant information and collinearity information. It has been proved that not all bands have equal importance [29]. It is necessary to delete redundant wavelength variables and select characteristic wavelengths that are highly correlated with the measured indicators so as to simplify and optimize the model and enhance the robustness of the model. The method of selecting the characteristic wavelength employs the Successive Projections Algorithm (SPA), the Monte Carlo Uninformative Variable Elimination (MCUVE), and the combination of the two methods.  
* SPA is a forward variable selection method that obtains the subset of variables with minimal collinearity using the operation of projection in the vector space [30]. In this experiment, the number of spectral data samples \(N\) and the number of wavelengths, 256, can form a spectral matrix \(X_{N\times 256}\). SPA starts with one wavelength, calculates its projection on unselected wavelengths in each cycle, and then introduces the wavelength with the largest projection vector into the wavelength combination. The number of cycles is the number of selected characteristic wavelengths. Each newly selected wavelength has the smallest linear relationship with the previous wavelength. The algorithm models the results of each selection for prediction and analysis. If the predicted root mean square error (RMSE) of the modeling verification achieves the minimum value, the number of wavelengths selected at this time is the best [31].  
Figure 7: Selected RoI of hyperspectral images (different colors represent different RoIs).  
* MCUVE combines the Monte Carlo method with the Uninformative Variable Elimination (UVE) method, aiming to address the large amount of redundant information in the spectral data while making full use of the intrinsic correlation between samples and evaluating the contribution of the wavelength in the spectral data to the measured index. Based on the contribution of each wavelength, wavelengths with no information are eliminated [32].  
(2) Quantitative modeling and model evaluation  
Partial Least Square Regression (PLSR) is a multivariate statistical data analysis method which is mainly used for the regression modeling of multiple dependent variables with respect to multiple independent variables [33]. In the modeling process, the PLSR method integrates the characteristics of Principal Component Analysis, Canonical Correlation Analysis, and Linear Regression Analysis methods; thus, a more reasonable multivariate linear regression model can be established [34].  
After the regression model is established, the prediction effect of the model is measured using the following parameters: the main evaluation indicators are the coefficient of determination \(\text{R}_{\text{P}}^{2}\) of the test set and the root mean square error RMSEP of the test set, while the auxiliary evaluation indicators are the \(\text{R}_{\text{m}}^{2}\) of the modeling set and the RMSEM of the modeling set.