# Improving Spatial Agreement in Machine Learning-Based Landslide Susceptibility Mapping

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}of land (estimated using data from WorldPop [29] and UNHCR [30]).

^{2}[31,33]. Any catastrophic landslide will cause significant damage to human lives and assets. Hence, an accurate assessment of landslide susceptibility is paramount for developing a plan for landslide risk management.

#### 2.2. Landslide Inventory Mapping

#### 2.3. Landslide Conditioning Factor

_{s}and β indicates the specific catchment area (m

^{2}/m) and slope gradient, respectively [43].

_{2}O), Bhuban formation (Miocene, Tb), Dupi Tila formations undivided (QTdd), valley alluvium and colluvium (ava), Girujan clay (Pleistocene and Neogene, QTg), Tipam Sandstone (Neogene, Tt), Boka Bil formation (Neogene, Tbb), beach and dune sand (csd), marsh clay and peat (ppc), Dupi Tila formation (Pleistocene and Pliocene, QTdt), and Dihing formation (Pleistocene and Pliocene, QTdi) (Figure 4i). Primary-level parameters such as soil type and soil texture are essential predictors of landslides. These parameters determine the amount of moisture content indicating the degree of stability of the soil [25,37,47,48]. Soil type and soil texture data were collected from the Bangladesh Agricultural Research Council [49].

#### 2.4. Multi-Collinearity Analysis of Landslide Conditioning Factors

#### 2.5. Landslide Susceptibility Modelling

#### 2.5.1. Pre-Processing

#### 2.5.2. Hyperparameter Optimization

#### 2.5.3. Machine Learning Models

- (1)
- K-Nearest Neighbor (KNN)

- (2)
- Multi-Layer Perceptron (MLP)

- (3)
- Random Forest (RF)

_{b}(x). The RF uses bootstrap aggregating where the weak learners train parallelly [31].

_{b}(x) is the function for bth weak learner.

- (4)
- Support Vector Machine (SVM)

^{(M−1)}dimensional in R

^{M}. A hyperplane in R

^{2}is a line, a hyperplane in R

^{3}is a plane, and so on. This hyperplane functions as a decision boundary, which determines the label of a sample (i.e. landslide or non-landslide). The margin around the hyper lane indicates that value exceeding 1 denotes a positive sample (landslide), and a value equal to −1 denotes a negative sample (non-landslide). If X (X

_{1}, X

_{2}, ………, X

_{n}) is the vector of landslide affecting factor and Y

_{j}(Y

_{1}, Y

_{2}) is the vector of landslide (1) or non-landslide (0) event, the optimal hyperplane can be found by solving Equation (4) [26].

_{i}is the positive real constant, and k(X, X

_{i}) is the Kernel function. To classify the binary events (landslide or non-landslide), the condition to solve Equation (4) was assumed as below:

_{i}) is the total number of factors that affects landslide.

#### 2.5.4. Performance Evaluation Methods

#### 2.6. Evaluation of Spatial Agreement and Optimizing Prediction Map

_{0}is the intercept of the model, θ

_{i}(i = 1, 2, …, n) indicates the regression coefficient of independent variables, and x

_{i}(i = 1, 2, …, n) represents the n number of independent variables. Validation of the resultant combined model was performed by developing the ROC curve by using the 40% testing data.

## 3. Results

#### 3.1. Landslide Susceptibility Modelling

#### 3.1.1. Landslide Prediction

#### 3.1.2. Evaluation of Models’ Performance

#### 3.2. Spatial Agreement of Various Methods

#### 3.3. Aggregated Landslide Susceptibility Mapping

^{2}) of 0.80 indicates a very good model performance. In relation to the estimated regression coefficients, the RF model had the highest degree of agreement with the landslide inventory, followed by the MLP, SVM, and KNN. The pattern of influence of various models in predicting landslides corresponds to their level of accuracy in terms of their respective AUC values (Figure 7).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location map of Cox’s Bazar district in Bangladesh; and (

**b**) the sub-districts of Cox’s Bazar district. Digital Elevation Model (DEM) source: [28]

**Figure 2.**The process of evaluating spatial agreement among various machine learning technique-based landslide susceptibility maps and optimizing the landslide prediction map. LSM = landslide susceptibility maps; KNN = K-Nearest Neighbor; MLP = Multi-Layer Perceptron; RF = Random Forest; SVM = Support Vector Machine.

**Figure 3.**Landslide inventory map of this study. Data source: [11].

**Figure 4.**Landslide conditioning factors. SPI = Stream Power Index. NDVI = Normalized Difference Vegetation Index.

**Figure 5.**Landslide susceptibility maps obtained by four machine learning algorithms: (

**a**) K-Nearest Neighbor (KNN), (

**b**) Multi-Layer Perceptron (MLP), (

**c**) Random Forest (RF), and (

**d**) Support Vector Machine (SVM).

**Figure 6.**Landslide susceptible area obtained using five models: K-Nearest Neighbor (KNN), Multi-Layer Perceptron (MLP), Random Forest (RF), Support Vector Machine (SVM), and combined model. Blue dots indicate the proportion of people exposed to ‘high’ and ‘very high’ susceptible zones.

**Figure 7.**Receiver operating characteristic (ROC) curves of the five models: K-Nearest Neighbor (KNN), Multi-Layer Perceptron (MLP), Random Forest (RF), Support Vector Machine (SVM), and combined model.

**Figure 8.**Correlogram to show the agreement between the five landslide susceptibility models: K-Nearest Neighbor (KNN), Multi-Layer Perceptron (MLP), Random Forest (RF), Support Vector Machine (SVM), and combined model.

**Figure 9.**(

**a**) Combined landslide susceptibility map of Cox’s Bazar district, (

**b**) ratio of landslide susceptible zones (high and very high) in various sub-districts (Upazila), and (

**c**) landslide susceptibility in the Rohingya refugee camps of Ukhia sub-district.

No. | Conditioning Factor | Spatial Resolution | Variable Type | Data Source | Variance Inflation Factors (VIF) |
---|---|---|---|---|---|

1 | Aspect | 30 m | Continuous | Estimated from the Digital Elevation Model (DEM) | 1.02 |

2 | Elevation | ″ | ″ | DEM [28] | 2.77 |

3 | Curvature | ″ | ″ | Estimated from the DEM | 1.57 |

4 | Slope | ″ | ″ | ″ | 2.83 |

5 | Stream Power Index (SPI) | ″ | ″ | ″ | 1.60 |

6 | Distance to stream | ″ | ″ | ″ | 1.15 |

7 | Land cover | ″ | Discrete | Landsat Operational Land Imager (OLI) (https://earthengine.google.com) | 1.13 |

8 | Normalized difference vegetation index (NDVI) | ″ | Continuous | ″ | 1.24 |

9 | Geology | ″ | Discrete | [46] | 1.06 |

10 | Soil type | ″ | ″ | [49] | 1.13 |

11 | Soil texture | ″ | ″ | ″ | 1.06 |

12 | Distance to road | ″ | Continuous | [52] | 1.10 |

**Table 2.**Hyperparameters, search range, and optimal values of the machine learning-based landslide susceptibility models.

Classifier | Hyperparameter | Remark | Search Range | Optimal Value |
---|---|---|---|---|

K-Nearest Neighbor | Metric | Distance metric to use | Euclidean, Manhattan | Manhattan |

Number of neighbors | Number of neighbors used for prediction | 3, 5, 11, 19 | 5 | |

Weights | Weight function used in prediction | Uniform, distance | Distance | |

Support Vector Machine | C value | Inverse regularization strength | 10^{−3}, 10^{−2}, 10^{−1}, 1, 10^{1}, 10^{2}, 10^{3} | 10^{3} |

Kernel | Functions for transforming inputs | Polynomial, radial basis function, sigmoid | Radial basis function | |

Gamma | Kernel coefficient | 10^{−3}, 10^{−2},10^{−1}, 1 | 10^{−3} | |

Multi-Layer Perceptron | Hidden layer Size | Number of hidden units | 10, 15, 20, 25, 30, 35, 40, 45 | 20 |

Activation function | Nonlinearity for squeezing output to desired range | Identity, logistic, hyperbolic tangent, rectified linear unit | Rectified linear unit | |

Learning rate | Specifies if learning rate is constant or variable | Constant, adaptive | Constant | |

Alpha | L2 penalty/regularization term | 10^{−4}, 10^{−3}, 10^{−2}, 10^{−1} | 10^{−4} | |

Random Forest | Number of estimators | Number of trees in the random forest | 200, 300, 400, 500 | 500 |

Maximum features | Maximum features to be considered | Auto, square root, logarithm (base = 2) | Auto | |

Maximum depth | Maximum depth of internal trees | 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 | 10 | |

Criterion | Function for measuring quality of split | Gini, entropy | Entropy |

**Table 3.**Performance evaluation indicators of the machine learning based landslide susceptibility models.

Model | Overall Accuracy | Precision | F1-score | Recall | |||
---|---|---|---|---|---|---|---|

Non-Landslide | Landslide | Non-Landslide | Landslide | Non-Landslide | Landslide | ||

KNN | 0.9069 | 0.9227 | 0.9227 | 0.9015 | 0.9015 | 0.8811 | 0.8811 |

MLP | 0.9545 | 0.9547 | 0.9547 | 0.9528 | 0.9528 | 0.9508 | 0.9508 |

RF | 0.9663 | 0.9633 | 0.9633 | 0.9652 | 0.9652 | 0.9672 | 0.9672 |

SVM | 0.9406 | 0.9385 | 0.9385 | 0.9385 | 0.9385 | 0.9385 | 0.9385 |

Variables (Landslide Susceptibility Models) | Coefficient | p-Value |
---|---|---|

Intercept | −5.84 | <2.2e^{−16 ***} |

KNN | 0.64 | 0.34 |

MLP | 3.52 | 2.67e^{−09 ***} |

RF | 5.01 | 8.449e^{−09 ***} |

SVM | 2.02 | 0.01205 ^{*} |

Significance codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘▪’ 0.1 ‘ ’ 1. Coefficient of determination R ^{2}: 0.80Log-Likelihood: −178.42 |

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## Share and Cite

**MDPI and ACS Style**

Adnan, M.S.G.; Rahman, M.S.; Ahmed, N.; Ahmed, B.; Rabbi, M.F.; Rahman, R.M.
Improving Spatial Agreement in Machine Learning-Based Landslide Susceptibility Mapping. *Remote Sens.* **2020**, *12*, 3347.
https://doi.org/10.3390/rs12203347

**AMA Style**

Adnan MSG, Rahman MS, Ahmed N, Ahmed B, Rabbi MF, Rahman RM.
Improving Spatial Agreement in Machine Learning-Based Landslide Susceptibility Mapping. *Remote Sensing*. 2020; 12(20):3347.
https://doi.org/10.3390/rs12203347

**Chicago/Turabian Style**

Adnan, Mohammed Sarfaraz Gani, Md Salman Rahman, Nahian Ahmed, Bayes Ahmed, Md. Fazleh Rabbi, and Rashedur M. Rahman.
2020. "Improving Spatial Agreement in Machine Learning-Based Landslide Susceptibility Mapping" *Remote Sensing* 12, no. 20: 3347.
https://doi.org/10.3390/rs12203347