Mapping the susceptibility to landslides based on the deep belief network: a case study in Sichuan Province, China

Abstract

A dataset of landslides from Sichuan Province in China, containing 1551 historical individual landslides, is a result of two teams’ effort in the past few years to map the susceptibility to landslides. Considering complex internal relations among the triggering factors, logistic regression (LR) and shallow neural networks, such as back-propagation neural network (BPNN), are often limited. In this paper, we make a straightforward development that the deep belief network (DBN) based on deep learning technology is introduced to map the regional susceptibility to landslides. Seven factors with respect to geomorphology, geology and hydrology are considered and verified through the collinearity test. A DBN model containing three pre-trained layers of restricted Boltzmann machines by stochastic gradient descent method is configured to obtain the susceptibility to landslides. Susceptibility results evaluated by DBN model are compared with those by LR and BPNN in the receive operator characteristic (ROC) analysis, showing that DBN has a better prediction precision, with a lower rate of false alarms and fake alarms. The case study also indicates different sensitivities of the triggering factors to the landslide susceptibility, that the factors of altitude, distance to drainage network and average annual rainfall have significant impact in mapping the susceptibility to landslides in the region. This research will contribute to a better-performance model for regional-scale mapping for the susceptibility to landslides, in particular, at the area where triggering factors show complex relations and relative independence.

Appendix: Weight calculation method

Each triggering factor contains several secondary categories. The area of all secondary categories $A_{ij}$ and the corresponding historical landslide area $a_{ij}$ were obtained with the statistical function of ArcGIS. Then, the area proportion of the categories $R_{ij}$ and the area proportion of the corresponding historical landslide area $r_{ij}$ can be calculated:

$$R_{ij} = A_{ij} /\mathop \sum \limits_{j = 1}^{m} A_{ij} \left( {i = 1,2, \ldots ,n;\quad j = 1,2, \ldots ,m} \right)$$

(15)

$$r_{ij} = a_{ij} /\mathop \sum \limits_{j = 1}^{m} a_{ij} \left( {i = 1,2, \ldots ,n;\quad j = 1,2, \ldots ,m} \right)$$

(16)

where m is the number of factor categories. Finally, the dimensionless relative weight of each category $I_{ij}$ is calculated according to the landslide density of each category $T_{ij}$:

$$T_{ij} = r_{ij} /R_{ij} \left( {i = 1,2, \ldots ,n;\quad j = 1,2, \ldots ,m} \right)$$

(17)

$$I_{ij} = T_{ij} /\mathop \sum \limits_{j = 1}^{m} T_{ij} \left( {i = 1,2, \ldots ,n;\quad j = 1,2, \ldots ,m} \right).$$

(18)

The weight of each category is recorded in Appendix Table 3.

Table 3 Classification and weight of the triggering factors