# Variable Selection Using Adaptive Band Clustering and Physarum Network
## 4 Results and Discussion  
### Corn Data Set  
The convergence diagram of the AP algorithm run in the first round is shown in Figure 2. With the increase in the number of iterations, the fitness (net similarity) of quantized intermediate solutions \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\lambda\) & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\ \hline Number of groups & 234 & 234 & 234 & 234 & 234 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The relationship between \(\lambda\) and the number of groups (orange leaves data). gradually increases. When the number of iterations increases to 562, fitness no longer changes. The AP algorithm converges in the first round as well as in the rest of the rounds. The convergence diagram of the PN algorithm run in the first round is shown in Figure 3. The \(D_{ij}\) represents the rate of change of the network continuity. The convergence condition of the PN algorithm is that all the rates of change of the network continuity are smaller than a threshold (0.001). Figure 3 shows the relationship of one of the rates of change of the network continuity and iterations. With an increase in the number of iterations, the \(D_{ij}\) gradually decreases. When the number of iterations increases to 10, all the \(D_{ij}\) are smaller than the threshold of stop. The PN algorithm converges in the first selection as well as in the rest of the rounds. There were 184 wavelengths selected by the AP-PN in the first round, which are illustrated in Figure 4a. These 184 wavelengths were input into the GA-PLS. The times of each wavelength selected by GA-PLS are illustrated in Figure 4b. By using the 16 most selected wavelengths, the root mean  
Figure 3: The convergence diagram of the physarum network (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 10, all the \(D_{ij}\) are smaller than the threshold of stop, and the network converges. Figure 2: The convergence diagram of the affinity propagation (AP) algorithm (corn data) in the first round: Iterations vs. Fitness (net similarity) of quantized intermediate solutions. When the iteration is 562, the network is converged. square errors of cross-validation (RMSECV = \(\sqrt{\sum\limits_{i=1}^{n}{{{{\left({{\widetilde{y}_{i}}-y_{i}}\right)}^{2}}/{n}}}}\), where \(\widetilde{y}_{i}\) represents the predicted value of the concentration of the \(i\)-th sample in the cross validation set, \(y_{i}\) represents the measured value of the concentration of the \(i\)-th sample in the cross validation set, and \(n\) is the number of cross validation sets) can reach the smallest value. These final 16 selected wavelengths found by using AP-PN-GA-PLS are illustrated in Figure 4c. The scatter plot of the predicted value vs. the measured value is given in Figure 4d. The curve that fits the data points best is also given in Figure 4d. The AP-PN-GA-PLS selected 16 wavelengths in the first round, which are shown in Figure 4c. All five algorithms, i.e., PLS, GA-PLS, PN-GA-PLS, AP-GA-PLS, and AP-PN-GA-PLS, were tested on the ten rounds, and the average number of selected wavelengths, RMSEP, and Rare summarized in Table 4.  
It is seen from Table 4 that the PN-GA-PLS can achieve similar prediction performance (RMSEP = 0.0597%) as that of GA-PLS (RMSEP = 0.0431%) but with fewer wavelengths (35 vs. 67). 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. AP-PN-GA-PLS can achieve a similar prediction performance (RMSEP = 0.0397%) as that of PN-GA-PLS (RMSEP = 0.0597%) but with fewer wavelengths. The number of selected wavelengths of AP-PN-GA-PLS and PN-GA-PLS was 25 and 35, respectively.