## 4 Experiment and Analysis
### Corn Dataset Analysis
For simplicity, only the filters learned from the deflation processes that resulted in the minimum RMSEP for moisture prediction are depicted in Figure 5. From this figure, it can be observed that one of the learned filter may be a low-pass, high-pass, band-pass, or band-stop filter. The characteristics of the filter are obtained based on the training samples. In subsequent experiments, for the  
Figure 4: Cosine Similarity between prediction results and response in moisture, oil, protein, and starch prediction using FPLS, PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, SGFilter, and Lasso. Figure 3: RMSEP values for the prediction of moisture, oil, and protein content in Corn samples using various methods, including FPLS, PLS, OSCPLS, VCPLS, PoPLS, LoPLS, DOSC, OPLS, MSC, SNV, and SGFilter, with 1 to 20 components each. sake of simplicity, we will no longer present the magnitude-frequency response of the learned filters. For moisture, oil, protein, and starch prediction, the initially learned filters for each target are \(h_{moisture}=[-0.7164,-0.6611,0.2228]\), \(h_{tail}=[0.2190,0.7080,0.6714]\), \(h_{protein}=[-0.1730,-0.9849]\), and \(h_{starch}=[-0.2478,0.0498,-0.9675]\). At this moment, \(\frac{w^{T}(Xh_{moisture})^{T}Y}{w^{T}X^{T}Y}=1.3331<N=3\), \(\frac{w^{T}_{i}(Xh_{total})^{T}Y}{w^{T}_{i}X^{T}Y}=2.5484<3\), \(\frac{w^{T}_{i}(Xh_{protein})^{T}Y}{w^{T}_{i}X^{T}Y}=1.3399<2\), and \(\frac{w^{T}_{i}(Xh_{total})^{T}Y}{w^{T}_{i}X^{T}Y}=1.3520<2\) are all consistent with our previous analysis in Section 3.3. The convergence behavior with respect to iteration numbers is presented in Figure 6, which simultaneously demonstrates the correlation between the projections of test samples from \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **RMSEP** & **CS** & **Lower RMSEP** & **Upper RMSEP** & **Lower CS** \\ \hline FPLS & 0.0977 & 0.9834 & 0.0052 & 0.5363 & 0.9691 \\ PLS & 0.1516 & 0.9343 & 0.0199 & 0.5531 & 0.9237 \\ OSCPLS & 0.1840 & 0.9347 & 0.0198 & 0.5529 & 0.8854 \\ VCPLS & 0.1498 & 0.8124 & 0.0533 & 0.6049 & 0.9256 \\ PoPLS & 0.1598 & 0.9576 & 0.0130 & 0.5448 & 0.9149 \\ LoPLS & 0.1516 & 0.9298 & 0.0212 & 0.5547 & 0.9237 \\ DOSC & 0.1837 & 0.9347 & 0.0198 & 0.5529 & 0.8858 \\ OPLS & 0.1533 & 0.9407 & 0.0180 & 0.5507 & 0.9219 \\ MSC & 0.2179 & 0.8760 & 0.0365 & 0.5758 & 0.8348 \\ SNV & 0.2174 & 0.8828 & 0.0346 & 0.5730 & 0.8356 \\ SGFilter & 0.1533 & 0.9344 & 0.0199 & 0.5530 & 0.9219 \\ Lasso & 0.1545 & 0.9344 & 0.0199 & 0.5530 & 0.9207 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Upper and lower boundaries of RMSEP and CS. In this experiment on Corn moisture prediction, the lower and upper bounds of RMSEP and the lower bound of CS are provided. In this table, “Lower RMSEP” and “Upper RMSEP” denote the respective lower and upper boundaries of RMSEP, while “Lower CS” signifies the lower boundary of CS. Figure 5: The filters learned during one iteration when analyzing the moisture content in the Corn dataset are depicted. The blue curve in the figure represents the magnitude frequency response of the filter. both PLS and FPLS models onto the weight vector \(w\) and their corresponding moisture content values.