## 3 Proposed Method
### Endmember Network  
In the traditional blind unmixing process, an unsupervised unmixing task can be accomplished by adding an abundance non-negativity constraint (ANC) and abundance sum-to-one constraint (ASC) to the network; however, the accuracy and robustness will be limited and no clear physical meaning can be assigned to the endmembers. Therefore, the EN learns the physical properties of endmembers by using pure or relatively pure pseudo-endmember bundles as the input. Inspired by [50], the endmember bundles required for the EN can be obtained via the following steps. Based on [51; 52; 53], the spectral characteristics of adjacent pixels are highly correlated, which indicates that pure spectral pixels are more likely to appear in areas with uniform spatial distributions. First, the HSI is randomly divided into partially overlapping blocks, with the number of partitions set according to [52]. Then, the number of endmembers is automatically estimated using the HySime algorithm, and the endmembers are extracted from each block via VCA. Finally, the repeated endmembers are removed using the K-means clustering algorithm, and the extracted endmembers are aggregated into K clusters. According to the experiment, the K value should be set to about 20% of the pixels in the HSI. The participation of the extracted endmember bundles in unmixing can both clarify the physical meaning of unmixing and effectively reduce the influence of SV on the whole-network unmixing process, which is more conducive to the accurate estimation of the abundances in the HSI. The endmember bundle input extracted by this method is defined as \(\left\{\mathrm{x}_{\mathrm{i}}\right\}_{\mathrm{i=1}}^{\mathrm{P_{e}}}\in \mathbb{R}^{\mathrm{B}}\), with B bands consisting of \(\mathrm{P_{e}}\) pixels, the pure abundance \(\left\{\mathrm{y}_{\mathrm{i=1}}^{\mathrm{N_{e}}}\right\}\in\mathbb{R}^{ \mathrm{C}}\) has C categories and the ith endmember of the lth EN is defined as \(\mathrm{t}_{\mathrm{i}}^{\mathrm{(l)}}\), which is expressed as  
\[\mathrm{t}_{\mathrm{i}}^{\mathrm{(l)}}= \begin{cases}\mathrm{g}\left(\mathrm{ W}_{\mathrm{EN}}^{\mathrm{(l)}},\mathrm{B}_{\mathrm{EN}}^{\mathrm{(l)}}, \mathrm{x}_{\mathrm{i}}\right),&1=1\\ \mathrm{g}\left(\mathrm{W}_{\mathrm{EN}}^{\mathrm{(l)}},\mathrm{B}_{\mathrm{EN}}^ {\mathrm{(l)}},\mathrm{t}_{\mathrm{i}}^{\mathrm{(l-1)}}\right),&1=2,\ldots, \mathrm{k}\end{cases}  \tag{1}\]  
Figure 1: Network architecture of the proposed efficient attention-based convolutional neural network (EACNN). where \(g(\cdot)\) is the nonlinear activation function. \(W_{EN}\) and \(B_{EN}\) represent the weights and biases of each layer. As shown in Figure 1, the EN convolution layer uses the \(1\times 1\) convolution core. After each output of the convolution layer, a batch normalization (BN) layer is used. The output of the BN layer is  
\[t_{BN_{i}}^{(I)}=\alpha\hat{x}_{i}^{(I)}+\beta \tag{2}\]  
where \(\hat{E}_{i}^{(I)}\) is the z-score of \(E_{i}^{(I)}\) and \(\alpha\) and \(\beta\) represent the parameters for network learning. After the first convolution layer, a dropout layer is used to effectively alleviate overfitting, remove noise and diminish the SV to a certain extent to enhance the generalization ability of the model. The output of the dropout layer is denoted as \(E_{D_{i}}^{(I)}\). An effective convolutional attention module is used for unmixing. As shown in Figure 2, the EC BAM consists of two attention modules, namely, the efficient channel attention and spatial attention modules. First, efficient channel attention produces the input. To effectively aggregate the spatial feature information, it is implemented using a fast 1D convolution of size k, where the kernel size k represents the coverage of local cross-channel interactions and is confirmed using an adaptive method.