## 2 Materials and Methods
### Classification Models
#### 2.3.3 M-SSL Model for Tree Classification Based on Multisource Images
The learning process of the M-SSL model is implemented as Algorithm 1, where, K-Means denotes a clustering algorithm that is widely used with GPU, and \(c_{m}\) denotes the \(k_{m}\) prototype set (center of the cluster) [37]. In Equation (12), \(\varnothing\) represents the parameter of the encoder, the momentum encoder in the same cluster \(c\) is represented as \(\{W_{i}^{\prime}\}_{z=1}^{Z}\), \(\alpha\) is the smoothing parameter, which plays a role in restriction \(\varnothing\), and the default value is set to 10. In addition, Adam is employed to make the parameters in the query encoder update. \[\varepsilon^{\prime}=0.999*\varepsilon^{\prime}+0.001*\varepsilon \tag{11}\]  
\[\varnothing=\frac{\sum_{z=1}^{Z}||w_{z}^{\prime}-c||_{2}}{Zlog(Z+\alpha)} \tag{12}\]The proposed M-SSL is similar to the original ContrastNet model with several differences. First, M-SSL treats features extracted from HSI and MSI as input, rather than a single source dataset. Second, more attention was paid to the fusion of the two kinds of features rather than to the \"contrast\" part in the structure of M-SSL directly. Third, two types of special characteristics employ DCAM [38] to emphasize the discriminative characteristics and weaken ineffective characteristics. Because of that, through the attention mechanism, DCAM encourages feature interaction, in which, the depthwise correlation layer further enhances the correlation to integrate the features of HSI and MSI. The whole structure of M-SSL is shown in Figure 4, where, the expectation maximization (EM) is used to train the multisource supervised network. In the E-step, the VAE features of HSI and MSI are crossed to fuse into the momentum encoder by DCAM, and then \(C^{m}\) and \(\mathcal{D}^{m}\) are calculated, respectively. In the M-step, according to the updated features and variables, \(L_{ProNCE}\) is calculated, and then the query encoder and the average momentum encoder are updated by backpropagation Equations (11) and (12). Similarly, all convolution calculation in the multi-source pretext task consists of a convolution layer and a batch normalization layer. After the cross-fusion of DCAM, the AAE and VAE features of 512 HSI and 512 MSI are divided into 4 \(\times\) 4 \(\times\) 64 blocks. First, 128 feature maps are extracted, and the spatial information is completely retained. Then, the feature map is mostly fed from a supervised network. Since the previous process implementing feature extraction, M-SSL completes the downstream task of tree species classification, which only needs to pay attention to feature fusion and contrast learning. The structure of the projection head is adopted in M-SSL, the output of which is used for training, and the features in front of the head are used for testing. The projection head is used as a nonlinear transformation as \(g(. )\), and the embedded variable \(w\) is the transformation of the contrast feature \(z\), as shown in Equation (13). \[w=g(z) \tag{13}\]  
In the training part, \(w\) is used to supervise the update of M-SSL parameters, and in the testing part, \(z\) is used for the downstream task of tree species classification. In this way, the contrastive features extracted will assimilate more original ones. In the test part, only the query encoder extracts the features that could save much testing time for the multi-source supervised network in Figure 5. Ultimately, the features learned with the M-SSL model from multi-source images are fed into the Softmax classifier to output the classification map of tree species. Detailed experimental settings are shown in the next section.