## 3 Results and Discussion
### Continuum Regression Model  
The powers used in the investigated CR model ranged from 0.1 to 10 in logarithmically spaced intervals. The maximum numbers of LVs were 10 and 15 for the electronic nose and NIR datasets, respectively. The resulting CR prediction error surfaces are shown in Figure 7. A given number of LVs and a given value of \(\gamma\) corresponded to a specific height of the PRESS surface. Considering that there was only one MLR model on the right near the edge, the constant PRESS was identified as the number of LVs varied. In the \"MLR flat\" region where \(\gamma\) was small and the number of LVs was large, as \(\gamma\) decreased, the CR gave more importance to correlation (as opposed to the structure variance in predictor variables). That is, the data would converge to the MLR results much more quickly as the number of LVs increased. In contrast, the \"PCR mountain\" region where the number of LVs was few and \(\gamma\) was largely impaired the CR prediction ability greatly. In this context, the cross-validation procedure was used to find the valley located between these two extremes and containing a relatively low PRESS. From the CR PRESS surfaces of the electric nose data in the test set, the optimal model parameters were located in the region between MLR and PLSR. Specifically, the minimum PRESS was at \(\gamma=0.63\) and 8 LVs. This optimal CR model had an RMSEP of 1.6779, compared to 1.6692 for the best MLR \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Technique**} & \multirow{3}{*}{**Preprocessing Method**} & \multicolumn{5}{c}{**Classification Results**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Calibration Set**} & \multicolumn{2}{c}{**Prediction Set**} \\ \cline{3-8}  & & **F\({}_{1}\)** & **Accuracy** & **Kappa** & **F\({}_{1}\)** & **Accuracy** & **Kappa** \\ \hline \multirow{8}{*}{Electronic} & RAW & 0.9154 \(\pm\) & 0.9146 \(\pm\) & 0.8292 \(\pm\) & 0.9213 \(\pm\) & 0.9202 \(\pm\) & 0.8403 \(\pm\) \\  & & 0.0031 & 0.0032 & 0.0063 & 0.0053 & 0.0053 & 0.0107 \\  & MSC (mean) & 0.9014 \(\pm\) & 0.9012 \(\pm\) & 0.8023 \(\pm\) & 0.8866 \(\pm\) & 0.8885 \(\pm\) & 0.777 \(\pm\) \\  & & 0.0049 & 0.0048 & 0.0096 & 0.0099 & 0.0094 & 0.0187 \\ \multirow{2}{*}{Nose} & Mean-center & 0.9361 \(\pm\) & 0.9365 \(\pm\) & 0.873 \(\pm\) & 0.9249 \(\pm\) & 0.9253 \(\pm\) & 0.8507 \(\pm\) \\  & & 0.0037 & 0.0036 & 0.0073 & 0.0056 & 0.0054 & 0.0109 \\  & S-G 1 st and & 0.9442 \(\pm\) & 0.9444 \(\pm\) & 0.8888 \(\pm\) & 0.9298 \(\pm\) & 0.9307 \(\pm\) & 0.8613 \(\pm\) \\  & Mean-center & 0.0041 & 0.0041 & 0.0081 & 0.0054 & 0.0052 & 0.0103 \\ \hline \multirow{8}{*}{NIR} & RAW & 0.9667 \(\pm\) & 0.9655 \(\pm\) & 0.931 \(\pm\) & 0.9682 \(\pm\) & 0.9667 \(\pm\) & 0.9333 \(\pm\) \\  & MSC (mean) & 0.0016 & 0.0017 & 0.0034 & 0.0041 & 0.0044 & 0.0088 \\ \cline{1-1}  & MSC (mean) & 0.9985 \(\pm\) & 0.9985 \(\pm\) & 0.997 \(\pm\) & 0.9976 \(\pm\) & 0.9975 \(\pm\) & 0.995 \(\pm\) \\ \cline{1-1}  & Mean-center & 0.0008 & 0.0008 & 0.0016 & 0.0013 & 0.0014 & 0.0027 \\ \cline{1-1}  & Mean-center & 1 \(\pm\) & 0 & 1 \(\pm\) & 0 & 1 \(\pm\) & 0 & 1 \(\pm\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The discrimination results of PLS-DA models based on different preprocessing methods. Figure 7: Continuum regression (CR) prediction error surfaces based on the (**a**) electronic nose data and (**b**) NIRS data. model and 1.6861 for the 5-LV best PLS model. However, the minimum PRESS of the NIR data in the test set was found in the region between PCR and PLRS, which was at \(\gamma\) = 2.82 and 14 LVs. This optimal CR model had an RMSEP of 0.1285, compared to 0.4439 for the 4-PC best PCR model and 0.1706 for the 5-LV best PLS model. As the \(\gamma\)-value decreased to zero, at which point the CR model eventually converged to MLR, the algorithm prioritized the correlation between the predictors and the predicted variables while minimizing the importance of explaining the variance structure of predictor variables.