*2.5. Landslide Susceptibility*

The object-based random forest approach was employed to assess the susceptibility of the protected and non-protected forests to landslides by contributing the conditioning and triggering factors as well as historical landslide samples.

Spatially, the landslide samples are joined to the objects of predictor variables. An object where over 50% of its area was affected by landslides was indicated as a landslide-affected object (LAO) and otherwise as a non-affected landslide object (NLAO). Roughly 20% of the LAO and NLAO objects were randomly selected for determining the importance of variables that control landslide susceptibility and modeling the spatial probability of landslide using a classification and regression trees (CART) procedure of RF [96,97].

RF is an ensemble-learning algorithm that builds several decision trees during the process of model formation. The training of each tree was carried out by bootstrap sampling from the generated dataset; about two-thirds of the samples were used for training a decision tree (in bag samples) and the remaining one-third was used to test the accuracy of the formed tree (out of bag (OOB) samples).

Multiple RFs were built to determine the optimal number of variables that needed to be applied for every splitting in each tree of the forest [98] in both study areas (Figure 3a,b). The OOB prediction was computed using the majority vote obtained from the OOB data for each object. The OOB error of an object was computed from the OOB prediction of that object. The results over all of the objects

were used to calculate the error rate. The optimal performance of RF was determined with respect to the maximum area under the receiver operating characteristic (AUROC) [99,100] and the evaluating metrics of model performance such as sensitivity (Equation (1)), specificity (Equation (2)), precision (Equation (3)), and F-measure (Equation (4)) that were computed using the status of OOB errors including the objects that were labeled as LAO and also classified as LAO (TP); the objects that were labeled as NLAO and classified as NLAO (TN); the objects that were labeled as LAO but classified as NLAO (FN); and the objects that labeled as NLAO but classified as LAO (FP) [99,100].

$$\text{Sensitivity} = \frac{TP}{TP + FN} \tag{1}$$

$$\text{Specificity} = \frac{TN}{TN + FP} \tag{2}$$

$$\text{Precision} = \frac{TP}{TP + FP} \tag{3}$$

$$\text{F1} = 2 \times \frac{\text{Precision} \times \text{Sensitivity}}{\text{Precision} + \text{Sensitivity}} \tag{4}$$

RF calculates the importance of each variable in the classification through Gini importance or Permutation importance [101]. The importance of variables was determined depending on the internal Gini method [102] in this study. The probability value of assigning an object to the class LAO—depending on a specific threshold—was indicated as the susceptibility of that object to the landslide. All objects were scored depending on the optimal-trained model for calculating their susceptibility to landslide from zero (very-low probability) to one (very-high probability) in both protected and non-protected forests.

**Figure 3.** The optimal number of trees and the number of variables for splitting in each tree of the random forest based on the minimum misclassification error for mapping landslide susceptibility in the protected forest (**a**) and non-protected forest (**b**); the area under the ROC curve obtained from the out-of-bag error for testing the performance of random forest for mapping landslide susceptibility in the protected forest (**c**) and non-protected forest (**d**) in NE Iran.


**Table 1.** Conditioning factors for mapping landslide susceptibility used in NE Iran.


**Table 2.** Triggering factors for mapping landslide susceptibility used in NE Iran.
