Application of kernel-based Fisher discriminant analysis to map landslide susceptibility in the Qinggan River delta, Three Gorges, China

摘要

Kernel machines are widely applied in classification because of many typical advantages, such as a good capacity to deal with high-dimensional data, good generation performance, few parameters to adjust, explainable results, etc. The kernel-based Fisher discriminant analysis (KFDA) is a typical kernel-based method based on the statistical discriminant analysis and it includes both the training and testing process. The model is trained by a dataset of environmental factors that cause landslide occurrence and target output values. Furthermore, the trained model is tested by a separate set of testing samples. This approach utilizes a kernel function to map data from the original feature space to a high-dimensional space, through which a nonlinear problem is converted into a linear one. A typical landslide study area, namely Qinggan River delta, situated in Three Gorges, China, is selected for this study and the following environmental factors are determined as independent variables of the model-lithology, elevation, normalized difference vegetation index (NDVI), slope, aspect, distance to rivers, plan curvature, and profile curvature. Judging from the accuracies of the training and testing samples, the sigmoid kernel performed better than the radial basis function kernel and the polynomial kernel. Using different ratios of landslide to non-landslide samples, the performance of KFDA is compared with the linear Fisher discriminant analysis (LFDA) and the logistic regression using a ROC/AUC validation. The results reveal that the average performance of KFDA for all ratios of samples is the most optimal with the mean AUC value as high as 0.911, while the mean AUC values of the logistic regression and LFDA are 0.867 and 0.089 respectively. Although the logistic regression performed slightly better than KFDA when the ratio of landslide to non-landslide samples was 2:1 and 3:1, its AUC values for other ratios of samples are much lower than the AUC values of KFDA. KFDA is more robust and less sensitive to different ratios of samples. The susceptibility map produced by KFDA shows that the regions around rivers are highly at risk to the occurrence of landslides in the study area.