## 3 Results and Discussion
### Quantitative Analysis of the Sediment Using the PLSR Model  
A quantitative analysis of the metal components of sediment samples plays a significant role in the quality control and water quality management of rivers. Multivariate chemometric methods combined have recently been employed in combination with the LIBS technology in the field of soil analysis [12]. One of the multivariate chemometric methods, PLSR, was used to determine the elemental content in soil samples because it is an effective dimension-reduction method for LIBS data. Because soil is composed of various chemical components, which might increase the complexity of LIBS data [12], preprocessing of SG derivatives was employed to improve the results of the PLSR model. Optimally performing the preprocessing for LIBS analysis can effectively reduce the noise and enhance the prediction accuracy of the PLSR model. The SG derivative is a widely used preprocessing method that can effectively eliminate noise with the appropriate selection of the derivative and smoothing parameters, such as the derivative order, polynomial degree, and number of smoothing points (NSP). It is essential to select an appropriate NSP and polynomial order in the preprocessing process. Excessive smoothing can lead to the loss of information because the emission peak lines, which contain important information,  
Figure 5: Score (**a**) and loading (**b**) plots of first two PCs from the PCA on the LIBS spectra at the selected lines of sediment samples. can be regarded as noise. In this study, the simple first-order derivative and second-order polynomial with five points were employed. To determine the correlations between the samples, PLSR models were constructed by using a full cross-validation method on the averaged recorded spectra. The calibration and validation performance of the PLSR model was assessed using the \(R^{2}\), RMSEC, and RMSECV. For an ideal model, the \(R^{2}\) should be close to 1, whereas the RMSEC should be close to 0. Moreover, the RMSEC and RMSECV were proposed in order to assess the overall performance of the model. Lower RMSEC and RMSECV values indicate a better model quality. The number of PLS factors applied in the model presented the lowest RMSECV value. Twenty-eight analytical spectral data samples were selected to build the calibration model, and the same samples were used to test the cross-validation of the PLSR model with a leave-one-out strategy. Table 2 shows the performance of the PLSR model before and after the application of preprocessing with the SG derivative for the analysis of Cd, Cr, and Pb. The results output for the Cd and Pb analysis were significantly improved with respect to the \(R^{2}\) and RMSE from the application of the SG derivative. For the Cd analysis, the \(R^{2}\) values for calibration and cross-validation without the SG derivative were 0.9963 and 0.9406, respectively. The RMSE of calibration (RMSEC) and the RMSE of cross-validation (RMSECV) were 0.0063 and 0.0264, respectively. The \(R^{2}\) and RMSE were improved with the SG derivative smoothing method. The \(R^{2}\) values for calibration and cross-validation, the RMSEC, and the RMSECV with the SG derivative were 0.9989, 0.9670, 0.0035, and 0.0197, respectively. For the Cr analysis, the \(R^{2}\) values for calibration and cross-validation without the SG derivative were 0.9690 and 0.8574, respectively. The RMSEC and RMSECV were 7.9131 and 17.61650, respectively. However, the smoothing of the SG derivative did not improve the values of the \(R^{2}\) and RMSE. The \(R^{2}\) values for calibration and cross-validation were 0.9736 and 0.8136, respectively. The RMSEC and RMSECV decreased to 7.3066 and 20.1409, respectively. The results of the Pb analysis showed a similar trend to those of the Cr analysis. Without the SG derivative, the \(R^{2}\) values for calibration and cross-validation were 0.9718 and 0.6815, respectively. The RMSEC and RMSECV were 1.2379 and 4.3146, respectively. The \(R^{2}\) and RMSE were improved with the SG derivative smoothing method.