Modeling of landslides susceptibility prediction using deep belief networks with optimized learning rate control

Figures & data

Figure 1. Algorithm flow and Dropout architecture: (a) algorithm flow; (b) dropout architecture.

Figure 2. Landslide inventory map of study area.

Figure 3. Environmental factors for landslides. (a) DEM, (b) Slope, (c) aspect, (d) MAP, (e) distance to road, (f) topographic roughness, (g) lithology, (h) TWI, (i) NDVI, (j) NDBI, (k) MNDWI, (l) total surface radiation.

Table 1. Parameters of LRC model.

Parameter	Values
Number of input features	12
Number of output features	5
Number of iterations	400
Dropout	0.5
Learning rate $\epsilon$	1
Initial value of the momentum learning rate $\rho$	0.5

Table 2. Prediction experimental results of changing the number of RBM layers and nodes.

Number of RBM layers	Number of nodes in each RBM layer	Accuracy (%)
1	20	78.82
2	20, 40	82.61
3	20, 40, 40	87.39
4	20, 40, 40, 80	90.82
5	20, 40, 40, 80, 40	92.57
6	20, 40, 40, 80, 40, 20	92.76
7	20, 40, 40, 80, 40, 20, 20	92.84
8	20, 40, 40, 80, 40, 20, 20, 20	92.93

Figure 4. Landslide susceptibility maps: (a) LRC-DBN, (b) RF, (c) LR, (d) SVM.

Table 3. Statistical results of landslide susceptibility prediction.

Models	Area ratio (%)
	Extremely high	High	Medium	Low	Extremely low
LRC-DBN	14.51	11.25	12.97	18.91	42.36
RF	11.08	15.48	20.17	26.24	27.03
LR	10.38	15.22	23.45	24.93	26.02
SVM	15.25	17.33	17.94	21.62	27.86

Table 4. Landslide prediction performance.

Models	LRC-DBN	RF	SVM	LR
TP	1067	1029	985	947
TN	1073	989	945	940
FP	389	475	517	522
FN	397	433	479	517
PPR (%)	86.14	78.14	74.12	72.73
NPR (%)	85.33	80.34	75.79	72.93
TA (%)	84.28	79.19	74.92	72.83

Figure 5. ROC curves for each landslide susceptibility prediction model.

Figure 6. Loss and accuracy curves with number of iterations.

Table 5. One-way interpretable results for landslide susceptibility prediction based on slope.

		Number of landslides	Q2
Slope intervals (°)	[0–11.2]	284	0.071
	[11.2–16.4]	365	0.071
	[16.4–19.1]	467	0.334
	[19.1–24.7]	506	0.591
	[24.7–27.5], [49.6–64)	578	0.713
	[27.5–49.6]	726	0.902

Table 6. One-way interpretable results for landslide susceptibility prediction based on distance to road.

		Number of landslides	Q2
Distance to road intervals (m)	[0–500]	558	0.071
	[500 − 1000]	495	0.470
	[1000 − 1500]	386	0.397
	[1500 − 2000]	118	0.484
	[2000 − 10,000)	3	0.543

Table 7. Interpretable result of interaction between altitude and slope.

Probability of landslide occurrence		Altitude intervals (m)
		[397–794.6]	[794.6–803.9], [1293.2 − 1421)	[803.9–829.7], [1107.1 − 1293.2]	[829.7–845.2], [1033.6 − 1107.1]	[845.2–894.7], [998.5 − 1033.6]	[894.7–998.5)
Slope intervals (°)	[49.6–64)	0.175	0.481	0.475	0.693	0.778	0.913
	[24.7–27.5], [27.5–49.6]	0.181	0.4	0.429	0.634	0.652	0.862
	[16.4–19.1], [19.1–24.7]	0.158	0.272	0.306	0.525	0.475	0.758
	[11.2–16.4]	0.112	0.127	0.124	0.264	0.28	0.493
	[0–11.2]	0.102	0.102	0.102	0.114	0.122	0.253
	[24.7–27.5]	0.104	0.104	0.104	0.104	0.105	0.185

Table 8. Interpretable result of interaction between topographic roughness and TWI.

Probability of landslide occurrence		Topographic roughness intervals (m)
		[0–12.5]	[12.5–19.7]	[19.7–24.6]	[24.6–28.3]	[28.3–31.7]	[31.7–91]
TWI intervals	[2.4–3.9]	0.195	0.24	0.398	0.533	0.634	0.892
	[3.9–5.2], [5.2–6.9]	0.183	0.267	0.362	0.561	0.658	0.785
	[6.9–10.4], [10.4–27.1)	0.164	0.199	0.265	0.434	0.458	0.562

Data availability

Data sharing is not applicable to the article no datasets were generated or analyzed during the current study.