# Comparative Analysis of Machine Learning Methods and a Physical Model for Shallow Landslide Risk Modeling

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area Profile

^{2}, of which the slope area and channel area are approximately 1805.5 km

^{2}, accounting for 65.3% of the total area. According to statistics, there are 3649 erosion gullies above 500 m. The area has a temperate continental semiarid climate with sufficient sunlight and an average annual temperature of 10 °C. The annual precipitation is 400–600 mm. The rainfall distribution is uneven, and the precipitation from July to September accounts for more than 50% of the total annual precipitation. The main soil type is silty loam. The silty loam has a loose soil texture and displays poor resistance to erosion. The former vegetation mainly consisted of secondary forest and grassland.

#### 2.2. Frequency Ratio Analysis of Environmental Factors

#### 2.3. The Principle of the Machine Learning Methods

- (1)
- RF can be understood as the organic integration of bagging (bootstrap aggregating) ensemble learning and the decision tree algorithm. The basic idea is to construct multiple decision trees by randomly selecting training samples, and the output category is determined by the mode or average of the predicted values of these single decision trees. That is, the prediction results of unknown samples are determined by the principle of majority voting, and the information of multiple decision trees is integrated to improve the accuracy of classification and the stability of the model. Its expression is as follows:

_{Gkhj}is the decreasing value of the Gini index of the k factor at the j node of tree h. P

_{k}is the importance of the k underlying environmental factor.

- (2)
- SVM is a supervised learning method. The basic idea is to map the samples in the input space to a high-dimensional feature space through nonlinear transformation. Then, the optimal classification surface in the feature space that linearly separates the samples is obtained. Based on a set of linearly separable vectors xi (i = 1, 2..., n), including 10 environmental factors and their corresponding output class yi, the landslide classification is distinguished by the maximum clearance of the n-dimensional hyperplane. Its expressions are as follows:

_{i}is the Lagrange multiplier.

- (3)
- Log is a kind of generalized linear regression analysis model that fits a logical function to forecast the probability of an event occurring. Its expression is as follows:

#### 2.4. The Principle of the SINMAP Model

_{s}is the soil cohesion (N/m

^{2}), C

_{r}is the plant root cohesion (N/m

^{2}), θ is the slope gradient (°), ρ

_{s}is the density of wet soil (kg/m

^{3}), ρ

_{w}is the water density (kg/m

^{3}), g is the gravity acceleration (9.81 m/s

^{2}), D is the vertical depth of soil lead (m), and φ is the soil internal friction angle (°). The vertical depth (m) of D

_{w}is determined from the soil isobaric surface.

#### 2.5. Dataset

- (1)
- The machine learning method dataset

- (2)
- The dataset of the SINMAP model

#### 2.6. Model Performance Evaluation and Validation

## 3. Results

#### 3.1. Frequency Ratio Analysis of Environmental Factors

^{2}·h·a), 1393.73–1421.86 MJ·mm/(hm

^{2}·h·a) and 1308.17–1330.65 MJ·mm/(hm

^{2}·h·a), with FRn values of 1.0, 0.97 and 0.95, respectively.

#### 3.2. Multicollinearity Analysis

#### 3.3. Analysis for the Model Results

#### 3.3.1. Model Performance and Validation

#### 3.3.2. Mapping and Comparison of the Sensitivity of Shallow Landslides

## 4. Discussion

#### 4.1. Characteristics of Environmental Factors for Shallow Landslides

#### 4.2. Difference in Sensitivity Mapping of Shallow Landslides Predicted by the Models

#### 4.3. Limitations and Implications of This Study

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Study area and shallow landslide points. (

**a**): the Loess Plateau; (

**b**): Dongzhiyuan; (

**c**) and (

**d**): shallow landslide.

**Figure 2.**Foundational environmental factors of shallow landslides in Dongzhiyun. (

**a**): DEM; (

**b**): Slope Gradient; (

**c**): Slope Aspect; (

**d**): Topograpghic Relief; (

**e**): Plane Curvature; (

**f**): Profile Curvature; (

**g**): TWI; (

**h**): SPI; (

**i**): STI; (

**j**): Rainfall Erosivity; (

**k**): NDVI; (

**l**): Land Use Type.

**Figure 4.**Relationships between shallow landslides and environmental factors. (

**a**): DEM; (

**b**): Slope Gradient; (

**c**): Slope Aspect; (

**d**): Topograpghic Relief; (

**e**): Plane Curvature; (

**f**): Profile Curvature; (

**g**): TWI; (

**h**): SPI; (

**i**): STI; (

**j**): Rainfall Erosivity; (

**k**): NDVI; (

**l**): Land Use Type.

**Figure 5.**The ROC curves of the model predicting landslide susceptibility. Note: (

**a**) is the ROC curve generated by the training set data; (

**b**) is the ROC curve generated by the validation set data.

**Figure 6.**Model prediction classification map of landslide susceptibility. (

**a**): RF model; (

**b**): SVM model; (

**c**): Logistic model; (

**d**): SINMAP model.

**Figure 8.**Comparison of local prediction results between the RF model and the Log model. Note: (

**a**) represents the prediction result of the RF model; (

**b**) represents the prediction result of the Log model.

Class | Stability Index Using Factor Safety | Characteristics |
---|---|---|

1 | <0.5 | Very High Susceptibility |

2 | 0.5–1.0 | High Susceptibility |

3 | 1.0–1.25 | Moderate Susceptibility |

4 | 1.25–1.5 | Low Susceptibility |

5 | >1.5 | Very Low Susceptibility |

Environmental Factor Type | Factor | Data Sources | Data Resolution | Classification Method |
---|---|---|---|---|

Topographic and Geomorphic Factors | DEM | ALOS Satellite | 12.5 m | Natural Break |

Slope Gradient | ||||

Slope Aspect | ||||

Topographic Relief | ||||

Plane Curvature | ||||

Profile Curvature | ||||

Hydrological Environmental Factors | TWI | |||

SPI | ||||

STI | ||||

Rainfall Erosivity | Geospatial Data Cloud | 30.0 m | ||

Land Cover Factors | NDVI | |||

Land Use Type | National Earth System Science Data Center | Equal Interval |

ρ_{s}(kg·m ^{−3}) | T/R (m) | C (N·m ^{−2}) | φ (°) | |||
---|---|---|---|---|---|---|

entry 1 1350 | min | max | min | max | min | max |

100 | 3000 | 0.35 | 0.54 | 15 | 25 |

Factors | Collinearity Statistics | |
---|---|---|

VIF | TOL | |

DEM | 2.36 | 0.42 |

Slope Gradient | 1.81 | 0.55 |

Slope Aspect | 1.08 | 0.93 |

Plane Curvature | 1.36 | 0.73 |

Profile Curvature | 1.36 | 0.73 |

TWI | 1.58 | 0.64 |

STI | 1.42 | 0.70 |

Rainfall Erosivity | 2.84 | 0.35 |

NDVI | 1.50 | 0.67 |

Land Use Type | 1.05 | 0.95 |

Model | Accuracy Parameters | ||
---|---|---|---|

Sensitivity | Specificity | Accuracy | |

RF | 92.03% | 85.99% | 84.85% |

SVM | 87.87% | 76.60% | 82.23% |

Log | 83.71% | 66.75% | 79.38% |

SINMAP | 81.21% | 59.98% | 70.59% |

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## Share and Cite

**MDPI and ACS Style**

Feng, L.; Guo, M.; Wang, W.; Chen, Y.; Shi, Q.; Guo, W.; Lou, Y.; Kang, H.; Chen, Z.; Zhu, Y.
Comparative Analysis of Machine Learning Methods and a Physical Model for Shallow Landslide Risk Modeling. *Sustainability* **2023**, *15*, 6.
https://doi.org/10.3390/su15010006

**AMA Style**

Feng L, Guo M, Wang W, Chen Y, Shi Q, Guo W, Lou Y, Kang H, Chen Z, Zhu Y.
Comparative Analysis of Machine Learning Methods and a Physical Model for Shallow Landslide Risk Modeling. *Sustainability*. 2023; 15(1):6.
https://doi.org/10.3390/su15010006

**Chicago/Turabian Style**

Feng, Lanqian, Mingming Guo, Wenlong Wang, Yulan Chen, Qianhua Shi, Wenzhao Guo, Yibao Lou, Hongliang Kang, Zhouxin Chen, and Yanan Zhu.
2023. "Comparative Analysis of Machine Learning Methods and a Physical Model for Shallow Landslide Risk Modeling" *Sustainability* 15, no. 1: 6.
https://doi.org/10.3390/su15010006