# Evaluation of Conditioning Factors of Slope Instability and Continuous Change Maps in the Generation of Landslide Inventory Maps Using Machine Learning (ML) Algorithms

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## Abstract

**:**

## 1. Introduction

#### Conditioning Factors of Terrain Stability

## 2. Study Area

^{2}in the central zone in the State of Guerrero in México; it consists of a mountainous region with elevations ranging from 280 m to 3540 m above mean sea level and slopes greater than 40° (Figure 1).

## 3. Materials and Methods

- Dataset. The first step consists of acquiring primary data: ASTER images, Digital Elevation Model (DEM), geological-mining charts, aerial photographs, and field data. Derived maps were generated from Principal Component 1 (PC1) in principal component analysis (PCA), normalized difference vegetation index (NDVI), cloud masks, slope angle (S), aspect (A), lithology (L), and ground truth (GT) samples. Dinamica EGO 5 was used to generate the NDVI images; the PCA images were obtained using ArcMap 10.3.
- Automatic change detection. At this stage, two change detection methods were applied, linear regression (LR) and image differencing (Diff), to the maps derived from the ASTER images. Three maps of continuous change were generated: LR applied to PC1 (LR-PC1), LR applied to NDVI (LR-NDVI), and Diff applied to PC1 (Diff-PC1). This process was performed with Dinamica EGO 5.
- Supervised classification. In this stage, the k-nearest-neighbor (KNN), stochastic gradient descent (SGD), support vector machine (SVM), and AdaBoost classifiers were applied using the previously obtained continuous change maps (LR-PC1, LR-NDVI, and Diff-PC1) and the factors of slope stability (S, A, and L) considered. The process was repeated and complemented by incorporating the factors into the classification, one by one, and combining them. All classification algorithms, so as the accuracy evaluation metrics, were run using the scikit-learn version 0.22.1 for Python 3.6.5 programming language.
- Accuracy assessment. In this stage, the inventory maps obtained by supervised classification were evaluated by confusion matrices, omission and commission errors, and metrics such as the Kappa concordance coefficient (k), accuracy (ACC), precision, recall, and F1 score. Python’s Georasters library version 0.5.20 was used to read the derived satellite images, including its metadata, and generate the maps after the classification stage.

#### 3.1. Dataset

#### 3.2. Ground Truth

^{2}(two ASTER pixels) were given priority to characterize small landslides in greater detail.

- 2/3 of the GT samples (21,640 pixels) were used for the training stage of the classification models to identify landslides/non-landslides;
- 1/3 of the GT samples (10,822 pixels) were reserved for assessing the accuracy of the classifier methods in detecting landslides.

#### 3.3. Automatic Change Detection

#### 3.3.1. Linear Regression

_{2}result from a linear function of the pixel values (X) of the initial-date image f

_{1}. Thus, it is possible to perform a regression from ${Y}_{I,J}^{K}\left({f}_{2}\right)$ to ${X}_{I,J}^{K}\left({f}_{1}\right)$ by least squares [59,60,61] to obtain the parameter gradient m and Y-intercept b of the regression line and generate a model equation in the form ${Y}^{\prime}=mX+b$.

#### 3.3.2. Image Differencing

_{1}from the final-date image f

_{2}, pixel-by-pixel, shown in Equation (2).

#### 3.4. Supervised Classification

- First, the algorithm undergoes a learning process by generating knowledge from the association between known input and output data;
- Second, the corresponding output values are estimated based on new input data.

#### Classifiers

- A subset of training data is randomly generated from the original training dataset, each of which is assigned equal weights;
- The misclassified data are given greater weight, whereas correctly classified data still have the same weight;

#### 3.5. Experimental Description

- The spectral images analyzed correspond to the best continuous change images produced by the change detection method in the previous stage, as described in Ramos-Bernal et al. (2015) [16] and Ramos-Bernal et al. (2018) [18], corresponding to LR for PC1 and NDVI images, and Diff for PC1 images. Those images were selected based on relevant differences in sites where landslides occurred during the analyzed period.
- The combinations of maps with the S, A and L factors were included in the landslide detection process, generating 40 landslide and non-landslide maps.

#### 3.6. Accuracy Assessment

## 4. Results

#### 4.1. Supervised Classification

#### 4.2. Accuracy Assessment

## 5. Discussion

#### 5.1. Visual Analysis

#### 5.2. Accuracy Assessment

#### 5.3. Conditioning Factor Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Landslides registered in the State of Guerrero. (

**a**) Massive landslide in La Pintada community. Source: Adaptation https://www.jornada.com.mx/2013/09/24/ciencias/a03a1cie (accessed on 25 May 2021). (

**b**) Landslide in Jaleaca de Catalán and (

**c**) landslide in El Tule ravine in Chilpancingo, the capital city of the State of Guerrero. Source: Adaptation in Google Earth and El Sur, 2017. https://suracapulco.mx/aun-no-reubican-a-20-familias-que-perdieron-su-casa-tras-un-deslizamiento-de-tierra-en-la-capital/(accessed on 25 May 2021).

**Figure 4.**Explanatory factors of hillside land instability: (

**a**) slope angle (S), (

**b**) aspect (A), and (

**c**) lithology (L).

**Figure 6.**Continuous change maps obtained by automatic change detection methods. (

**a**) Diff-PC1, (

**b**) LR-PC1, and (

**c**) LR-NDVI.

**Figure 7.**Landslide inventories generated by KNN using combinations (

**a**) C1, (

**b**) C2, (

**c**) C3, (

**d**) C4, (

**e**) C5, (

**f**) C6, (

**g**) C7, and (

**h**) C8.

**Figure 8.**Landslide inventories generated by SGD using combinations (

**a**) C1, (

**b**) C2, (

**c**) C3, (

**d**) C4, (

**e**) C5, (

**f**) C6, (

**g**) C7, and (

**h**) C8.

**Figure 9.**Landslide inventories generated by SVM with RBF Kernel using combinations (

**a**) C1, (

**b**) C2, (

**c**) C3, (

**d**) C4, (

**e**) C5, (

**f**) C6, (

**g**) C7, and (

**h**) C8.

**Figure 10.**Landslide inventories generated by SVM with linear kernel using combinations (

**a**) C1, (

**b**) C2, (

**c**) C3, (

**d**) C4, (

**e**) C5, (

**f**) C6, (

**g**) C7, and (

**h**) C8.

**Figure 11.**Landslide inventories generated by AdaBoost using combinations (

**a**) C1, (

**b**) C2, (

**c**) C3, (

**d**) C4, (

**e**) C5, (

**f**) C6, (

**g**) C7, and (

**h**) C8.

**Figure 12.**Close-up of the maps obtained by the AdaBoost classifier on the area where the largest landslide occurred: (

**a**) Red band. Results of landslide detection using combinations (

**b**) C1, (

**c**) C2, (

**d**) C3, (

**e**) C4, (

**f**) C5, (

**g**) C6, (

**h**) C7, and (

**i**) C8.

**Figure 13.**Details on landslide region classification when applying (

**a**) KNN, (

**b**) SGD, (

**c**) SVM RBF kernel, (

**d**) SVM linear kernel, and (

**e**) AdaBoost using combination C1 (LR-PC1, LR-NDVI, and Diff-PC1).

Images | Input Classification | |||||||
---|---|---|---|---|---|---|---|---|

LR-PC1 | * | * | * | * | * | * | * | * |

LR-NDVI | * | * | * | * | * | * | * | * |

Diff-PC1 | * | * | * | * | * | * | * | * |

Slope angle (S) | * | * | * | * | ||||

Aspect (A) | * | * | * | * | ||||

Lithology (L) | * | * | * | * | ||||

Combination | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 |

Classifiers | Parameters |
---|---|

KNN | N_neighbors = 5, weights = “uniform”, algorithm = “auto”, leaf_size = 30, p = 2, metric = “minkowski”, mertric_params = None, n_jobs = None, Kwargs |

SGD | Loss = “hinge”, penalty = ”l2”, alpha = 0.0001, l1_ratio = 0.15, fit_intercept = True, max_iter = 1000, tol = 0.001, shuffle = True, verbose = 0, epsilon = 0.1, n_jobs = _None, random_state = 0, learning_rate = “optimal”, eta0 = 0.0, power_t = 0.5, early_stopping = False, validation_fraction = 0.1, n_iter_no_changes = 5, class_weight = None, warm_start = False, average = False |

SVM RBF kernel | C = 10, kernel = “rbf”, degree = 3, gamma = “auto_deprecate”, coef0 = 0.0, shrinking = True, probability = False, tol = 0.001, cache_size = 200, class_weight = None, verbose = False, max_iter = −1, decision_fuction_shape = “ovr”, random_state = 0. |

SVM linear kernel | Penalty = “l2”, loss = “squared_hinge”, dual = True, tol = 0.0001, C = 1.0, multi_class = ”ovr”, fit_intercept = True, intercept_scaling = 1, class_weight = None, verbose = 0, random_state = None, max_iter = 1000 |

AdaBoost | Base_estimator = None, n_estimators = 50, learning_rate = 1.0, algorithm = “SAMME.R”, random_state = 0 |

Method | Equations |
---|---|

Kappa concordance coefficient | $k=\left(n{{{\displaystyle \sum}}^{\text{}}}_{i=1,n\text{}}{X}_{ii}-{{{\displaystyle \sum}}^{\text{}}}_{i=1,n}\text{}{X}_{i+}\text{}{X}_{+i}\right)/\left({n}^{2}-{{{\displaystyle \sum}}^{\text{}}}_{i=1,n}\text{}{X}_{i+}\text{}{X}_{+i}\right)$ $k$ is the Kappa coefficient of agreement, $n$ is the sample size, ${X}_{ii}$ is the observed agreement, and ${X}_{i+}$ ${X}_{+i}$ is the expected agreement in each category $i$. |

Accuracy | $ACC=\frac{TP+TN}{TP+TN+FP+FN}$ $TN$ corresponds to true-negative pixels; FP represents False-Positive pixels; TP represents true-positive pixels, and FN represents False-Negative pixels. |

Precision | $Precision=\frac{TP}{TP+FP}$ $FP$ represents False-Positive pixels, and TP represents True-Positive pixels. |

Recall | $Recall=\frac{TP}{TP+FN}$ $TP$ represents True-Positive pixels, and $FN$ represents false-negative pixels. |

F_{1} score | ${F}_{1}\text{}score=\frac{2\xb7Precision\xb7Recall}{Precision+Recall}$ |

Method | Combination | Precision | Recall | F1 Score | Accuracy | Kappa | Omission Error | Commission Error |
---|---|---|---|---|---|---|---|---|

KNN | C1 | 0.94 | 0.90 | 0.92 | 0.93 | 0.850 | 7.324 | 7.569 |

C2 | 0.97 | 0.93 | 0.95 | 0.96 | 0.911 | 4.274 | 4.527 | |

C3 | 0.97 | 0.92 | 0.94 | 0.94 | 0.888 | 5.372 | 5.700 | |

C4 | 0.96 | 0.93 | 0.95 | 0.95 | 0.899 | 4.927 | 5.092 | |

C5 | 0.98 | 0.94 | 0.96 | 0.96 | 0.927 | 3.480 | 3.714 | |

C6 | 0.98 | 0.95 | 0.97 | 0.97 | 0.937 | 3.043 | 3.252 | |

C7 | 0.97 | 0.93 | 0.95 | 0.95 | 0.907 | 4.479 | 4.718 | |

C8 | 0.99 | 0.95 | 0.97 | 0.97 | 0.944 | 2.658 | 2.860 | |

SGD | C1 | 0.91 | 0.82 | 0.86 | 0.88 | 0.751 | 11.884 | 12.657 |

C2 | 0.93 | 0.92 | 0.92 | 0.93 | 0.857 | 7.083 | 7.165 | |

C3 | 0.85 | 0.87 | 0.86 | 0.87 | 0.732 | 13.414 | 13.366 | |

C4 | 0.89 | 0.84 | 0.87 | 0.88 | 0.751 | 12.253 | 12.567 | |

C5 | 0.96 | 0.9 | 0.93 | 0.94 | 0.873 | 6.075 | 6.470 | |

C6 | 0.93 | 0.91 | 0.92 | 0.92 | 0.846 | 7.650 | 7.712 | |

C7 | 0.96 | 0.62 | 0.75 | 0.81 | 0.606 | 15.232 | 20.211 | |

C8 | 0.95 | 0.91 | 0.93 | 0.94 | 0.875 | 6.083 | 6.324 | |

SVM RBF kernel | C1 | 0.93 | 0.87 | 0.9 | 0.91 | 0.818 | 8.823 | 9.232 |

C2 | 0.96 | 0.9 | 0.93 | 0.94 | 0.870 | 6.268 | 6.628 | |

C3 | 0.95 | 0.88 | 0.91 | 0.92 | 0.839 | 7.708 | 8.193 | |

C4 | 0.93 | 0.87 | 0.9 | 0.91 | 0.817 | 8.853 | 9.272 | |

C5 | 0.96 | 0.9 | 0.93 | 0.94 | 0.876 | 5.891 | 6.322 | |

C6 | 0.96 | 0.9 | 0.93 | 0.93 | 0.867 | 6.411 | 6.791 | |

C7 | 0.95 | 0.88 | 0.91 | 0.92 | 0.840 | 7.684 | 8.164 | |

C8 | 0.96 | 0.9 | 0.93 | 0.94 | 0.872 | 6.077 | 6.532 | |

SVM linear kernel | C1 | 0.93 | 0.87 | 0.9 | 0.91 | 0.817 | 8.830 | 9.268 |

C2 | 0.98 | 0.78 | 0.87 | 0.88 | 0.767 | 9.718 | 12.020 | |

C3 | 0.95 | 0.82 | 0.88 | 0.9 | 0.789 | 9.539 | 10.803 | |

C4 | 0.90 | 0.91 | 0.91 | 0.91 | 0.821 | 8.952 | 8.912 | |

C5 | 0.97 | 0.76 | 0.85 | 0.88 | 0.750 | 10.412 | 12.890 | |

C6 | 0.97 | 0.85 | 0.9 | 0.91 | 0.825 | 7.944 | 9.010 | |

C7 | 0.84 | 0.86 | 0.85 | 0.85 | 0.709 | 14.550 | 14.472 | |

C8 | 0.73 | 0.97 | 0.83 | 0.81 | 0.627 | 15.866 | 18.157 | |

AdaBoost | C1 | 0.93 | 0.93 | 0.93 | 0.93 | 0.861 | 6.934 | 6.945 |

C2 | 0.98 | 0.97 | 0.98 | 0.98 | 0.956 | 2.163 | 2.208 | |

C3 | 0.97 | 0.94 | 0.96 | 0.96 | 0.922 | 3.806 | 3.969 | |

C4 | 0.95 | 0.96 | 0.95 | 0.96 | 0.914 | 4.317 | 4.294 | |

C5 | 0.98 | 0.97 | 0.98 | 0.98 | 0.956 | 2.162 | 2.208 | |

C6 | 0.98 | 0.98 | 0.98 | 0.98 | 0.965 | 1.767 | 1.772 | |

C7 | 0.98 | 0.97 | 0.97 | 0.97 | 0.947 | 2.609 | 2.651 | |

C8 | 0.98 | 0.98 | 0.98 | 0.98 | 0.962 | 1.920 | 1.894 |

**Table 5.**Landslide detection ratio by classification method for each layer combination. The mean ratio and the standard deviation are also included.

Method | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | Std. Dev. | Mean |
---|---|---|---|---|---|---|---|---|---|---|

KNN | 1.14 | 2.83 | 2.68 | 2.73 | 3.46 | 4.39 | 3.40 | 4.81 | 1.13 | 3.18 |

SGD | 0.78 | 4.47 | 5.81 | 1.87 | 1.81 | 4.99 | 0.29 | 2.85 | 2.03 | 2.86 |

SVM RBF kernel | 0.82 | 1.04 | 0.73 | 0.81 | 0.82 | 0.97 | 0.73 | 0.79 | 0.11 | 0.84 |

SVM linear kernel | 0.80 | 0.38 | 0.63 | 1.2 | 0.44 | 0.56 | 11.76 | 25.09 | 8.96 | 5.11 |

AdaBoost | 1.56 | 2.00 | 1.59 | 1.60 | 2.12 | 2.13 | 1.38 | 2.14 | 0.31 | 1.82 |

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**MDPI and ACS Style**

Ramos-Bernal, R.N.; Vázquez-Jiménez, R.; Cantú-Ramírez, C.A.; Alarcón-Paredes, A.; Alonso-Silverio, G.A.; G. Bruzón, A.; Arrogante-Funes, F.; Martín-González, F.; Novillo, C.J.; Arrogante-Funes, P.
Evaluation of Conditioning Factors of Slope Instability and Continuous Change Maps in the Generation of Landslide Inventory Maps Using Machine Learning (ML) Algorithms. *Remote Sens.* **2021**, *13*, 4515.
https://doi.org/10.3390/rs13224515

**AMA Style**

Ramos-Bernal RN, Vázquez-Jiménez R, Cantú-Ramírez CA, Alarcón-Paredes A, Alonso-Silverio GA, G. Bruzón A, Arrogante-Funes F, Martín-González F, Novillo CJ, Arrogante-Funes P.
Evaluation of Conditioning Factors of Slope Instability and Continuous Change Maps in the Generation of Landslide Inventory Maps Using Machine Learning (ML) Algorithms. *Remote Sensing*. 2021; 13(22):4515.
https://doi.org/10.3390/rs13224515

**Chicago/Turabian Style**

Ramos-Bernal, Rocío N., René Vázquez-Jiménez, Claudia A. Cantú-Ramírez, Antonio Alarcón-Paredes, Gustavo A. Alonso-Silverio, Adrián G. Bruzón, Fátima Arrogante-Funes, Fidel Martín-González, Carlos J. Novillo, and Patricia Arrogante-Funes.
2021. "Evaluation of Conditioning Factors of Slope Instability and Continuous Change Maps in the Generation of Landslide Inventory Maps Using Machine Learning (ML) Algorithms" *Remote Sensing* 13, no. 22: 4515.
https://doi.org/10.3390/rs13224515