## 3 Results and Discussion
### Model Monitoring Results and Analysis  
#### 3.4.1 Evaluation Criteria  
In this study, the random forest model, PT-Former model, and _kNDVI_-PT-Former model were used to build and compare the models of the data on vegetation change monitoring in grassland desertification ecological restoration. By inputting the dataset of vegetation change characteristics, the results of monitoring vegetation change by the above three models are obtained. Subsequently, the accuracy of the above models is evaluated. The semantic segmentation evaluation index is mainly used to measure the classification accuracy of each pixel in the image and the accuracy of the segmentation area. Common metrics include Pixel Accuracy (_PA_), Class Pixel Accuracy (_CPA_), Mean Pixel Accuracy (_MPA_), Intersection over Union (_IoU_), Mean IoU (_mIoU_), etc. [31; 32]. Figure 8: Some datasets are shown: (**a**) remote sensing imageldataset, (**b**) remote sensing imageldataset, (**c**) _kNDVI_ dataset, (**d**) label dataset. This study mainly uses the _CPA_ and the _IoU_ to evaluate the accuracy of the model. 1. CPA Class Pixel Accuracy is a commonly used evaluation index in semantic segmentation tasks. It measures the accuracy of the model's pixel-level prediction for each category. It refers to the proportion of pixels in each pixel of the image that the model correctly classifies as a specific category of pixels. The formula is as follows. \[CPA_{i}=\frac{TP_{i}}{TP_{i}+FP_{i}+FN_{i}}\] (10) The following are used in the formula. \(TP_{i}\): The model correctly predicts the number of pixels of class \(i\). \(FP_{i}\): The model incorrectly predicts the number of background pixels of class \(i\). \(FN_{i}\): The model incorrectly predicts the number of class \(i\) pixels as the background class. 2. IoU Intersection over Union is a commonly used evaluation index in semantic segmentation, which measures the degree of overlap between prediction results and real annotations. The higher the _IoU_ value, the more accurate the prediction results of the model. The formula is as follows. \[IoU=\frac{TP}{TP+FP+FN}\] (11) The following are used in the formula. \(TP\) (True Positive): Correctly predict the number of pixels for the target class. \(TN\) (True Negative): Correctly predict the number of pixels for the background class. \(FP\) (False Positive): False prediction is the number of background pixels of the target class. \(FN\) (False Negative): Error prediction is the number of target pixels of the background class. 3. Loss Function In machine learning and deep learning, the loss function (or cost function) quantifies the discrepancy between the predicted output and the true target. It serves as the optimization objective during model training, guiding parameter updates via gradient descent or other optimization algorithms. The formulation of the hybrid loss function is given as follows: \[L_{hybrid}=L_{BCD}+\lambda L_{Dice}\] (12) where \(\lambda\) is the coefficient defined in the hybrid loss function. To explain the concepts of BCE loss and Dice loss, we consider the predicted change map \(\hat{Y}\) and the reference map \(Y\) as sets of pixels, represented, respectively, as \(\hat{Y}=\{\hat{y}_{i},\,i=1,\,2,\,\ldots,\,N\}\) and \(Y=\{y_{i},\,i=1,\,2,\,\ldots,\,N\}\). Here, \(\hat{y}_{i}\) denotes the probability of change in the \(i\)th pixel, while \(y_{i}\) represents the reference value of the \(i\)th pixel. In this context, a value of 0 indicates an unchanged pixel, whereas a value of 1 signifies a changed pixel. The total count of pixels in the change map is denoted by \(N\). The combined objective function of these two loss functions can be formulated as  
\[L_{BCD}=-\frac{1}{N}\sum_{i=1}^{N}y_{i}log_{2}\hat{y}_{i}+(1-y_{i})log_{2}(1- \hat{y}_{i}) \tag{13}\]  
\[L_{Dice}=1-\frac{2\sum_{i=1}^{N}y_{i}\hat{y}_{i}}{\sum_{i=1}^{N}y_{i}+\hat{y}_{ i}} \tag{14}\]
4. Cross-ValidationCross-validation is a common method for evaluating the generalization ability and stability of a model.