## 3 Results and Discussion
### Optimal Wavelengths Selection for Disease Detection of A. thaliana Leaves  
The procedure of reducing the data size through optimal wavelengths selection is generally considered important in HSI data analysis for a more robust classification model with a high computing efficiency [27; 36]. Figure 3 shows the optimal wavelengths selected by RF, SPA and SFS. The selection probability of each wavelength according to RF was displayed in Figure 3a. It can be found that the most of wavelengths with relatively higher selection probabilities were distributed near-infrared range, except for some in the red light region. The first selected wavelength was 747 nm with the highest selection probability of 93.6%. The selected wavelengths distributed in the near infrared range were related to the changes in tissue structure and internal chemical composition. In this study, diseased spots could be found in spectral images of near-infrared range as shown in Figure 2a, which was consistent with the results of the RF algorithm. Additionally, some wavelengths in the red light range could be due to the damage of chlorophyll after the infection of _S. scleroorum_. 16 optimal wavelengths selected by SPA for discriminating diseased leaves from healthy ones were shown in Figure 3b. The wavelengths in the blue and red light region associated with carotenoid and chlorophyll absorption, including 456, 464, 468, 474, 496, 631, 650, 667, 678, and 690 nm, were also selected by SPA. 710, 947, 1000, 1013, and 1023 nm were also considered as the sensitive wavelength due to the damage of mesophyll cell structure for SSR detection. Ten optimal wavelengths including those distributed in blue and red light (i.e. 455 nm, 469 nm, 667 nm, and 678 nm) were selected by SFS, which was similar with optimal wavelengths selected by SPA (Figure 3b). Compared with 452 full wavelengths, the optimal wavelengths chosen via RF, SFS, and SPA were decreased by 93.1%, 93.1% and 95.7%, respectively.  
Based on Figure 3, it could be observed that some selected wavelengths were close, indicating a high correlation between them. Therefore, it was necessary to further remove some selected wavelengths based on correlation analysis (CA). The Pearson's correlation coefficients between two sensitive wavelengths selected by RF, SPA, and SFS were calculated, and heat maps are shown in Figure 4. In this study, the correlation coefficient higher than 0.9 was regarded as a strong relationship between two wavelengths, one of which was removed based on the following criterion. The one with higher correlation coefficients with the rest wavelengths was discarded. Based on these criteria, three optimal wavelengths (458 nm, 660 nm, and 742 nm) from RF, four optimal wavelengths (456 nm, 678 nm, 710 nm, and 947 nm) from SPA and three optimal wavelengths (455 nm, 671 nm, and 747 nm) from SFS were finally selected respectively for establishing classification models for SSR detection (Table 1). The number of optimal wavelengths less than five indicated the feasibility to be applied for a rapid and low-cost SSR detection system in comparison with full wavelengths.  
Figure 3: (a) The selection probability of each wavelength for SSR detection by random frog (RF). (b) The selected wavelengths for SSR detection by successive projections algorithm (SPA) and sequential forward selection (SFS), respectively.