## 4 Experiment and Analysis
### Corn Dataset Analysis  
This set comprises 80 Corn samples, and the wavelength range is 1100-2498 nm with 2 nm intervals. Each spectrum is a 700-dimensional vector ([[http://www.eigenvector.com/data/Corn/index.html](http://www.eigenvector.com/data/Corn/index.html)]([http://www.eigenvector.com/data/Corn/index.html](http://www.eigenvector.com/data/Corn/index.html)) (accessed on 13 January 2023)). In our experiments, the analysis focuses on moisture, oil, protein, and starch. The corresponding ranges for each parameter are as follows: moisture (9.377-10.993%), oil (3.088-3.832%), protein (7.654-9.711%), and starch (62.826-66.472%). After obtaining the parameters, the spectra are filtered. Then, the regression model is established using PLS. In the analysis of Corn data, the best mean RMSEP and prediction variances of FPLS, PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso are presented in Table 1. The numbers in parentheses next to RMSEP indicate the optimal number of components used in the respective regression model. According to Table 1, in moisture prediction, FPLS stands out with the lowest RMSEP value of 0.0977, indicating its high accuracy in predicting moisture content. This method also has a variance value of 0.0007, suggesting that its predictions are relatively stable and consistent. In contrast, methods such as MSC and SNV have higher RMSEP valuesof 0.2179 and 0.2174, respectively, indicating that their predictions may be less accurate compared to FPLS. Other methods, including PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, SGFilter, and Lasso, have RMSEP values that range from 0.1498 to 0.1840. These methods may have varying degrees of accuracy in predicting moisture content, depending on the specific dataset and conditions used for evaluation. FPLS and PLS have the same variance value of 0.0007, which is consistent with our previous analysis. According to Table 1, the RMSEP and variance results of these methods for oil, protein, and starch prediction are similar to the results of moisture. In conclusion, FPLS appears to be the best method for predicting moisture content. Figure 2(a)-d show that as the number of components increases, the RMSEP values for moisture, oil, protein, and starch prediction decrease. Regarding Lasso, it differs from the aforementioned methods; it is a variable selection method. In this figure, the horizontal axis represents the number of random experiments conducted for Lasso. Among these methods, FPLS exhibits a faster decline in RMSEP compared to other approaches. Furthermore, beyond a certain number of components, the RMSEP of FPLS becomes significantly smaller than that of other methods. Specifically, the number of components is observed to be 7 for moisture prediction, 5 for oil, and 8 for both protein and starch. These figures also validate the effectiveness of the FPLS method. Figure 3(a)-d show the CS (Cosine Similarity) between the responses and predictions for moisture, oil, protein, and starch with FPLS, PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso. The vertical axis represents the CS values. It can be observed that among these algorithms, FPLS has the highest CS. Furthermore, combining this with Table 1, it can be inferred that the RMSEP is small, and the CS between the predicted values and responses is high, indicating that the model possesses excellent predictive ability and generalization performance. Based on the analysis of Table 1, and Figures 3 and 4, the proposed FPLS method outperforms PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso in terms of RMSEP for moisture, oil, protein, and starch prediction. The magnitude responses of the learned filters in the Corn moisture analysis using FPLS are shown in Figure 5. The maximum number of components is 20, resulting in 20 deflation processes. Each time a deflation process is completed, a new filter is learned. Consequently, a total of 20 filters are obtained.