## 4 Experimental Results and Discussion
### Investigation of Classification Performance  
To evaluate the performance of the proposed method under different training conditions, we selected \(n_{i}(n_{i}=5,20,50,100,200)\) samples per class for training, and 1-NN classifier was utilized to classify the remaining samples. Each experiment was repeated ten times, the averaged OA with standard deviations (STDs) and kappa coefficient (\(K\)C) of all DR methods on Indian Pines and PaviaU datasets are shown in Tables 1 and 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **5** & **20** & **50** & **100** & **200** \\ \hline RAW & 43.6 \(\pm\) 2.8 (0.372) & 54.9 \(\pm\) 1.7 (0.495) & 60.1 \(\pm\) 1.4 (0.552) & 63.6 \(\pm\) 0.9 (0.588) & 66.9 \(\pm\) 0.6 (0.622) \\ PCA & 43.4 \(\pm\) 2.7 (0.370) & 54.9 \(\pm\) 1.6 (0.495) & 60.2 \(\pm\) 1.2 (0.553) & 63.9 \(\pm\) 0.8 (0.591) & 67.0 \(\pm\) 0.6 (0.622) \\ LDA & 32.5 \(\pm\) 4.8 (0.253) & 51.6 \(\pm\) 1.9 (0.459) & 64.4 \(\pm\) 1.2 (0.599) & 71.0 \(\pm\) 0.5 (0.672) & 74.4 \(\pm\) 0.7 (0.706) \\ LPP & 43.6 \(\pm\) 3.7 (0.372) & 54.5 \(\pm\) 1.8 (0.491) & 59.7 \(\pm\) 1.2 (0.546) & 62.7 \(\pm\) 1.0 (0.578) & 65.8 \(\pm\) 0.5 (0.609) \\ MFA & 44.1 \(\pm\) 4.0 (0.377) & 57.1 \(\pm\) 1.6 (0.520) & 66.8 \(\pm\) 1.9 (0.625) & 70.8 \(\pm\) 1.1 (0.669) & 72.0 \(\pm\) 1.0 (0.680) \\ RIDE & 41.7 \(\pm\) 1.1 (0.622) & 60.9 \(\pm\) 1.5 (0.561) & 69.8 \(\pm\) 1.4 (0.659) & 74.6 \(\pm\) 0.7 (0.711) & 78.4 \(\pm\) 0.6 (0.751) \\ DHLP & 44.1 \(\pm\) 3.8 (0.377) & 57.2 \(\pm\) 2.1 (0.522) & 68.9 \(\pm\) 1.2 (0.649) & 73.8 \(\pm\) 0.8 (0.702) & 77.6 \(\pm\) 0.7 (0.741) \\ SCCE & 30.2 \(\pm\) 4.5 (0.230) & 69.7 \(\pm\) 1.0 (0.658) & 76.3 \(\pm\) 0.9 (0.730) & 79.1 \(\pm\) 0.5 (0.760) & 82.9 \(\pm\) 0.6 (0.801) \\ LPNPE & 60.2 \(\pm\) 3.5 (0.594) & 74.0 \(\pm\) 1.4 (0.706) & 79.3 \(\pm\) 0.7 (0.759) & 81.6 \(\pm\) 0.6 (0.791) & 84.2 \(\pm\) 0.6 (0.817) \\ SSRHE & **65.6 \(\pm\)** 2.3 (0.615) & **74.8 \(\pm\)** 1.2 (0.711) & **80.0 \(\pm\)** 1.0 (0.765) & **82.9 \(\pm\)** 1.0 (0.803) & **86.7 \(\pm\)** 1.0 (0.829) \\ \hline \hline \end{tabular} Note that the best results of a row are marked in bold.  
\end{table} 
Table 1: Classification results using different methods with different classifiers for the Indian pines dataset. (OA \(\pm\) STDs (%) (\(K\)C)). Figure 9: OAs with different embedding \(d\): (**a**) Indian Pines dataset; and (**b**) Pavia U dataset. As shown in Tables 1 and 2, for all methods, the OA and _K_C greatly improved and the STDs decreased with the increasing of training samples, because a large number of training samples usually provide more useful information for training. The spatial-spectral combined methods, SSCE, LPNPE and SSRHE, produced better classification results than the spectral-based methods, because they exploit the spatial and spectral information in HSI to improve the representation ability of extracted features. Among these spectral-based methods, DHLP presented better classification performance under most training conditions, since it applies the hypergraph learning model to discover the intrinsic complex relationship between samples. Compared with all the other methods, SSRHE had better discriminant performance with different proportions of training samples on two HSI datasets, especially with small size of training set. SSRHE utilizes the hypergraph framework to discover the complex multivariate relationships between interclass samples and intraclass samples, and computes two spatial neighborhood scatters to reveal the spatial correlation between each pixels in HSI, which further enhances the discriminating power of low  
According to Tables 3 and 4, SSRHE obtained better classification results than other methods in most classes, and it achieved the best OA, AA and KC on two HSI datasets. This indicates that SSRHE possessed stronger ability to reveal the intrinsic complex geometric relations between samples and extract more useful the spatial-spectral combined features for classification.