# Variable Selection Using Adaptive Band Clustering and Physarum Network
## 4 Results and Discussion
### Sweet Orange Leaves Data Set  
The convergence diagram of the AP algorithm in the first round is shown in Figure 8. With the increase of the number of iterations, the fitness (net similarity) of quantized intermediate solutions gradually increases. When the number of iterations increases to 486, fitness no longer changes. The AP algorithm converges in the first round as well as in the other rounds. Figure 7: Diesel data (predicting viscosity content) wavelength selection result in the first round: (**a**) spectral responses vs. wavelengths, the 120 wavelengths selected by AP-PN are marked with circles; (**b**) times of selection (by GA-PLS) vs. wavelength identifier (1–120); (**c**) spectral response vs. wavelengths, the 25 wavelengths selected by AP-PN-GA-PLS are marked with circles; (**d**) scatter plot of predicted values vs. the measured values. \begin{table}
\begin{tabular}{c c c c c} \hline
**Method** & **Number of Input Wavelengths** & **Number of Selected Wavelengths** & **R** & **RMSEP(\%)** \\ \hline PLS & 401 & 401 & 0.9716 & 0.1370 \\ GA-PLS & 401 & 142 & 0.9739 & 0.1203 \\ PN-GA-PLS & 401 & 40 & 0.9727 & 0.1404 \\ AP-GA-PLS & 401 & 66 & 0.9722 & 0.1356 \\ AP-PN-GA-PLS & 401 & 26 & 0.9744 & 0.1167 \\ \hline \end{tabular}
\end{table} 
Table 5: The average values of the number of selected wavelengths, R, and RMSEP using PLS, GA-PLS, PN-GA-PLS, AP-GA-PLS, and AP-PN-GA-PLS (diesel data). The convergence diagram of the PN algorithm in the first round is shown in Figure 9. The \(D_{ij}\) represents the rate of change of the network continuity. With the increase of the number of the iterations, the \(D_{ij}\) gradually decreases. When the number of iterations increases to 132, all the \(D_{ij}\) are smaller than the threshold of stop. The PN algorithm converges in the first round as well as in the other rounds. The number of wavelengths selected by using AP-PN was 234 in the first round, which is illustrated in Figure 10a. These 234 wavelengths were input into GA-PLS. The times of each wavelength selected by GA-PLS is illustrated in Figure 10b. By using the 25 most selected wavelengths, the RMSECV can reach smallest value. These final 25 wavelengths selected by using AP-PN-GA-PLS are illustrated in Figure 10c. The scatter plot of the predicted value vs. the measured value is given in Figure 10d. The curve that fits the data points best is also given in Figure 10d. Figure 8: The convergence diagram of the AP algorithm (sweet orange leaves data) in the first round: Iterations vs. Fitness (net similarity) of quantized intermediate solutions. When the iteration is 486, the network is converged. Figure 9: The convergence diagram of the PN algorithm (corn data) in the first round: Iterations vs. \(D_{ij}\) (\(D_{ij}\) is the rate of change of the network continuity). When the iteration is 132, all the \(D_{ij}\) are smaller than the threshold of stop, and the network is converged. All five algorithms, i.e., PLS, GA-PLS, PN-GA-PLS, AP-GA-PLS, and AP-PN-GA-PLS, were tested in the ten rounds, and the average number of selected wavelength, RMSEP, and R are summarized in Table 6.  
It is seen from Table 6 that the PN-GA-PLS can achieve similar prediction performance (RMSEP = 1.3206%) as that of GA-PLS (RMSEP = 1.4998%) but with fewer wavelengths (49 vs. 125). This result confirms the conclusion in the literature [14]. However, the number of wavelengths selected or the prediction performance of PN-GA-PLS in this research is larger or better than those of PN-GA-PLS in the literature [14], as are those of the GA-PLS. These differences in the number of selected wavelengths or prediction performance are due to the way in which training sets, test sets, and the sub-spectral bands were selected. It is seen that AP-PN-GA-PLS can give the largest R (0.9220) and the smallest RMSEP (1.2436%) among PN-GA-PLS (R = 0.9110, RMSEP = 1.3206%), AP-GA-PLS (R = 0.9034, RMSEP = 1.4226%), GA-PLS (R = 0.9069, RMSEP = 1.4998%), and PLS (R = 0.9025, RMSEP = 1.4124%).