## 2 Materials and Methods
### Methods  
#### 2.3.1 Maximum Entropy Classifier (MaxEnt)  
In the permafrost degradation area, the traditional permafrost mapping methods, such as frost number model [56], Stefan formula [57], and GIPL model [58], are not suitable for the high resolution of 30m. With the continuous development of image-processing technology, there are more and more research on the mapping of permafrost using machine learning methods [1].  
In this study, the sample had two aspects of particularity. First, the observation data of permafrost were limited in spatial distribution. The distribution was relatively concentrated, and it was mainly located in accessible places. Secondly, there were only two types of samples observed, i.e., samples with permafrost and samples without permafrost. For the above two reasons, common classification algorithms, such as RF and SVM, are prone to under-fitting or over-fitting in the pre-experiment. MaxEnt is a one-class classification specialized in studying species distribution. The principle of maximum entropy requires that the selected probability model must meet the existing fact, i.e., the constraint conditions. The uncertain part is equal possibility, and the equal possibility is represented by the maximization of entropy [59]. This is a good fit for the above two particularities of the sample.  
MaxEnt is frequently used to simulate species distribution probability utilizing environmental data from several \"background\" information in addition to confirmed presence locations [60; 61]. In addition to species distribution prediction, some scholars have applied it to one-class classification [62], such as the simulation of tree species distribution [63], tree species classification [64], and extraction of fire-burned land [65]. Pernafrost has special environmental attributes, and it proliferates or degenerates with changes in climate and environment [66]. In this study, MaxEnt was applied to map the distribution of permafrost in the study area.  
The receiver operating characteristic (ROC) curve is used for analysis during the creation of the classification model, and the area under the curve (AUC) is used to assess the model's accuracy [60; 67]. The true positive rate, which is the ratio that both exists and is expected to exist, serves as the ordinate on the ROC curve, while the false positive rate, which is the ratio that neither exists nor is expected to exist, serves as the abscissa. AUC has a range of 0 to 1. The more closely the AUC value approaches 1, the more accurate the model is. The distance from the random distribution increases as the AUC value grows. The association between environmental factors and the expected geographic distribution of species increases with the increase in the AUC value. The better ability of the model to predict outcomes is shown by a higher AUC value [68]. Failure (0.5-0.6), poor (0.6-0.7), fair (0.7-0.8), good (0.8-0.9), or excellent (0.9-1.0) are the four performance categories for the model [21].  
In this study, the permafrost prior data were divided into \"samples with permafrost\" and \"samples without permafrost\", and they were taken as input samples to train the classification. A total of 75% of the samples were randomly selected as the training data, and the remaining 25% of the samples were used as the test data. The environmental characteristic variables considered in the classification included LST1, LST2, LST3, DEV, SR, NDVI, and NDWI. After the model was classified, the continuous data covering the study area was output, and an estimated probability value was ascribed to each pixel in the study area to evaluate the PP existence on that point [62]. This probability can range from 0 to 1. Figure 3 shows the technical flowchart of this study.