## 3 Proposed Method
### Regional Adaptive Weight Representation  
Pixels in HSIs that are spatially close to each other usually belong to the same category of ground objects. In practice, due to complex geographical and climatic conditions, ground objects in the same category may exhibit different spectral characteristics, and ground objects in different categories may exhibit the same spectral characteristics. This issue means that the features of the pixel's own spectrum do not fully reflect the unique feature information of the category to which it belongs. Considering the spatial significance of pixels, the spectral information of spatially neighbor points can be used to compensate for the shortage of its own spectrum, which does not fully reflect the category information. This approach not only makes the spectral features of similar features more similar, but  
Figure 1: The overall framework of the proposed SSAMMA.  
also makes the spectral differences between dissimilar pixels increase. The conventional algorithm generally uses the average weight of fixed neighborhood pixels as the spectral feature value of the pixels, which has the following disadvantages: The fixed near-neighbor region is not suitable for pixels on the boundary of spatially dissimilar ground objects. The calculation of weights in the fixed region is not adaptively adjusted according to the distance from the central pixel. Thus, pixels further from the center pixel and pixels closer to it are given the same weight, resulting in ineffective use of spatial information. In view of this issue, an improved region adaptive weight representation method was proposed in this study that uses the super-pixel segmentation technique, which is expressed as follows. The SLIC algorithm was used to segment the HSI to obtain \(k\) adaptively sized super-pixel image blocks \(\{S_{1},S_{2},\cdots,S_{k}\}\). The pixels in any image block \(S_{i}\) after segmentation were represented as \(\{x_{1},x_{2},\cdots,x_{N_{i}}\}\), where \(N_{i}\) is the total number of pixels in the \(i\) pixel block. For any pixel \(x_{i}\) in any pixel block, its pixel value \(x_{i}\) after regional adaptive weight representation could be expressed via Equation (2).  
\[x_{i}^{\prime}=\frac{\sum_{j=1}^{N_{i}-1}w_{ij}x_{j}}{N_{i}-1}+\gamma x_{i} \tag{2}\]  
where \(\gamma\) is the real parameter, and the adaptive weight \(w_{ij}\) is the weight representation between pixel points \(x_{i}\) and \(x_{j}\). We supposed that the spatial coordinates of two pixels \(x^{\prime}\) and \(y^{\prime}\) are denoted as \((a,b)\) and \((c,d)\), respectively. The pixel values are denoted as \(x_{i},y_{i}\). Then, \(w_{ij}\) can be expressed via Equation (3).  
\[w_{ij}=\frac{(1-\lambda)}{d_{ij}}+\lambda S_{ij} \tag{3}\]  
where \(d_{ij}\) is the Euclidean distance between the spatial coordinates of two pixels \(x^{\prime}\) and \(y^{\prime}\), i.e., \(d_{ij}=\sqrt{(a-c)^{2}+(b-d)^{2}}\). The choice of \(\lambda\) depends on the specific application and the data characteristics. \(S_{ij}\) denotes the cosine similarity of the spectral features between two pixels \(x^{\prime}\) and \(y^{\prime}\), i.e., \(S_{ij}=\sum\limits_{i=1}^{N_{i}}x_{i}y_{i}/\sqrt{\sum\limits_{i=1}^{N_{i}}x_{i} ^{2}}\cdot\sqrt{\sum\limits_{i=1}^{N_{i}}y_{i}^{2}}\).