## 4 Experimental Results and Analysis
### Parameter Analysis
#### 4.4.2 Spatial Window Size p and the Number of Near Neighbors k  
The efficient use of the spatial features of HSIs is essential to improve the classification accuracy. Therefore, in the construction of multi-manifold graphs in spatial dimensions, two parameters are extremely important: the spatial window size p and the number of near neighbors k. The spatial window size determines the degree of the spatial feature utilization of pixels. Twenty samples are selected as training samples in each category of both the IP and PU datasets, and the other samples are used as test samples. The variation ranges of parameters p and k are set as {5, 7, 9, \(\ldots\), 19} and {3, 4, 5, \(\ldots\), 10}, respectively. Figure 7 shows the classification results after dimensionality reduction obtained by setting different parameters p and k on the two datasets. In Figure 7, it can be observed that as the number of near neighbors k increases, the classification accuracy fluctuates around a fixed value on both datasets when the spatial window size p is fixed. The increase in the number of near neighbors k leads to a variable feature extraction effect on the spatial near-neighbor graph, which has an impact on the classification results. When k is fixed, the classification effect on both datasets first increases and then fluctuates around a fixed value as the spatial window size p increases. More spatial features can be captured when the spatial window size p is gradually increased. However, when the spatial window is too large, the spatial window may capture some spatial features that interfere with the dimensionality reduction effect.  
4.3 Balancing Spectral Information Parameters \(\alpha\) and Spatial Information Parameters \(\beta\)  
In order to evaluate the effects of balancing spectral information parameters \(\alpha\) and spatial information parameters \(\beta\) on the dimensionality reduction performance, 20 samples from each category were selected as training samples on both datasets. The variation range of \(\alpha\) and \(\beta\) was {0, 0.1, 0.2, \(\ldots\), 1}. The comparison between the dimensionality reduction effect obtained on two datasets is shown in Figure 8. In Figure 8, it can be seen that when the parameter \(\alpha\) is a fixed value, the classification accuracy of the model gradually increases and stabilizes with the increasing parameter \(\beta\). As the parameter \(\beta\) continues to increase, the intra-manifold maps in the spatial and spectral domains occupy an increasingly important weight in the whole near-neighbor map. In addition, when the parameter \(\beta\) is fixed, the classification accuracy of the model gradually increases and fluctuates about a fixed value as the parameter \(\alpha\) increases. As a larger \(\alpha\) indicates a stronger separation of data between inter-manifold data, it occupies an increasingly important weight in the whole near-neighbor graph. Considering the comprehensive model performance and model complexity, \(\alpha\) = 0.6 and \(\beta\) = 0.7 were chosen as the two parameters used in the experiment.  
Figure 7: Classification accuracy under different values of spatial window size p and the number of near neighbors k: (**a**) IP dataset; (**b**) PU dataset.