## 3 Methodology and Principle
### Partial Least-Squares Regression (PLS)  
Partial least squares (PLS) method has been widely used in many fields such as data analysis, parameter estimation, system identification, regression modeling and prediction [16; 17]. PLS is a new multivariate statistical method, which integrates principal component analysis, multivariate correction analysis, canonical correlation analysis and linear regression analysis. It provides a multiple linear regression modeling method, overcoming the shortcomings of traditional regression analysis method which can not describe  
Figure 2: (a) is the reflectance spectra of 10,084 sampling point of lunar mare processed by MSC, and (b) is the 14,141 sampling point of lunar highland processed by MSC.  
the multicollinear relationship of variables. PLS can achieve regression modeling, data structure optimization, correlation analysis of two groups of variables, which obviously improves the reliability of data analysis and the accuracy of calculation process [18; 19]. PLS method not only pay close attention to the information on the independent variables, and pay attention to the relationship between dependent and independent variables [20]. PLS can decompose and filter the data information in the system, identify the system information and noise, eliminate the redundant information among the data, and extract the comprehensive variable with the strongest explanatory power to the dependent variable. PLS can establish the model with higher accuracy when the number of sample points is less than the number of variables, which has the advantages that traditional regression analysis methods do not have.  
PLS indirectly reflects the linear relationship between independent variables and dependent variables by establishing the regression model of latent variables of independent variables about latent variables of dependent variables. In the final model, all original independent variables will be included, and the regression coefficient of each independent variable in the regression model will be easier to explain [21]. The basic principle is as follows.  
The p-independent variable matrix \(X=\{x_{1},\ldots,x_{p}\}\) and q-dependent variable matrix \(Y=\{y_{1},\ldots,y_{q}\}\) of n samples are decomposed. Components \(u_{1}\) and \(v_{1}\) are extracted from X and Y. \(u_{1}\) is a linear combination of \(x_{1},\ldots,x_{p}\) and \(v_{1}\) is a linear combination of \(y_{1},\ldots,y_{q}\). When extracting these two components, \(u_{1}\) and \(v_{1}\) should carry as much variation information as possible in their respective data tables, and the correlation degree of \(u_{1}\) and \(v_{1}\) can reach the maximum, which ensures that \(u_{1}\) and \(v_{1}\) represent matrix X and Y as well as possible and independent variable component \(u_{1}\) has the strongest explanatory power for dependent variable component \(v_{1}\). After extracting the first components \(u_{1}\) and \(v_{1}\), partial least squares regression is applied to the regression of X to \(u_{1}\) and Y to \(v_{1}\), respectively. When the regression equation reaches the required precision, the algorithm will be terminated. Otherwise, the residual information after X and Y are interpreted by \(u_{1}\) and \(v_{1}\) respectively will be used for the next round of component extraction, so that the cycle can be completed until the required precision is reached. If the \(r\) components \(u_{1},\ldots,u_{r}\) are extracted from the independent variable matrix X, the partial least squares regression will establish the regression equation of the dependent variable matrix Y and \(u_{1},\ldots,u_{r}\), and then be expressed as the regression equation of the dependent variable matrix Y and the independent variable matrix X.