## 4 Experimental Results and Discussion
### Parameters Selection  
For the proposed SSRHE algorithm, there are four important parameters: spatial neighborhood size \(T\), weighted coefficient \(\varphi\), tradeoff parameters \(\alpha\) and \(\beta\). To select the optimal parameters, we performed some parameters selection experiments on the Indian Pines and PaviaU datasets. In each experiment, we randomly selected five samples from each class as training set and the remaining samples were used for testing.  
To explore the effect of tradeoff parameters \(\alpha\) and \(\beta\), we turned them with a set of \(\{0,0.01,0.05,0.1,0.2,\cdots,0.9,1\}\). Figures 6 and 7 show the classification accuracies with respect to \(\alpha\) and \(\beta\) on two datasets. As shown in Figure 6, an increasing \(\alpha\) produced subtle change of OAs under a fixed \(\beta\). The OAs first varied slightly and then declined significantly with the increase of \(\alpha\) on Indian Pines dataset, since a too large \(\alpha\) led to the algorithm losing the property of spatial-domain in HSI and the obtained features might fail to represent the intrinsic structure of hyperspectral image. For PaviaU dataset, the OAs first increased with increasing \(\alpha\) and \(\beta\), and then tended to decline. To balance the influence of spectral and spatial information for classification, we set parameters \(\alpha=0.3\) and \(\beta=0.7\) for the Indian Pines dataset, and \(\alpha=0.2\) and \(\beta=0.5\) for PaviaU dataset based on the results presented in Figures 6 and 7.  
Figure 6: The OAs of SSRHE with different \(\alpha\) and \(\beta\) on Indian Pines dataset.  
The parameters \(T\) and \(\varphi\) have a significant influence on the discrimination of SSRHE. The former is defined to determine the size of spatial neighborhood and the latter is exploited to adjust the compactness of the interclass neighbors. To analyze the influence of two parameters for SSRHE, we performed two experiments with respect to \(T\) and \(\varphi\), and the corresponding experimental results on two HSI datasets are shown in Figure 8. In Figure 8a, it is clear that the OAs first quickly increased with the growth of \(T\) on two dataset because a larger spatial neighborhood was beneficial to preserving more useful spatial-domain information in HSI. However, if the value of \(T\) was too large, it might bring pixels from other classes into training model, as well as greatly increase computational complexity. According to the results in Figure 8a, the size of spatial neighborhood \(T\) was set to 7 for Indian Pines dataset and 15 for PaviaU dataset. As shown in Figure 8b, with the increasing of \(\varphi\), the OAs improved until reaching a peak value due to further enhancing the compactness of intraclass samples in the embedding space. While \(\varphi\) kept increasing, the OAs declined since too large \(\varphi\) weakened the ability to extract between-class features. Therefore, we set \(\varphi=50\) for the Indian Pines dataset and \(\varphi=60\) for the PaviaU dataset.  
Figure 8: OAs with respect to parameters \(T\) and \(\varphi\) on different datasets: (**a**) the OAs of \(T\); and (**b**) the OAs of \(\varphi\).  
Figure 7: The OAs of SSRHE with different \(\alpha\) and \(\beta\) on PaviaU dataset.