A novel landslide susceptibility prediction framework based on contrastive loss

Figures & data

Figure 1. Location of the study area.

Figure 2. Landslide condition factor maps excluding elevation factor; the elevation factor map is shown in Figure 1. The legends of the lithology map: (1) water (2) loose soil (3) soft clay (4) soft and hard sandstone–claystone lithofacies (5) moderately hard to weakly soft conglomerate–sandstone lithofacies (6) hard thick-bedded sandstones (7) weakly karstified carbonates (8) moderately karstified carbonate (9) medium-strength karstified carbonate (10) strongly karstified carbonates (11) hard lava rocks (12) hard metamorphic rocks.

Table 1. The description and data source of landslide condition factors used in this study.

Factor (abbreviation)	Description and data source
(1) Elevation	Global SRTM DEM data with a spatial resolution of 1 arc-second (https://earthexplorer.usgs.gov).
(2) Slope	Using elevation data to generate different geomorphic components using Arcgis 10.6 software
(3) Terrain Ruggedness Index (TRI)
(4) Curvature
(5) Plan Curvature
(6) Profile Curvature
(7) Topographic Position Index (TPI)
(8) Topographic Wetness Index (TWI)
(9) Aspect
(10) Maximum 20-months Cumulative Rainfall (Rainfall_20), (11) Maximum 10-months Cumulative Rainfall (Rainfall_10), (12) Maximum one-month Cumulative Rainfall (Rainfall_1), (13) Average Annual Rainfall (Rainfall_Aver)	The data are calculated based on the 1-km monthly precipitation dataset for China (1901–2020). The dataset is provided by National Tibetan Plateau Data Center (https://data.tpdc.ac.cn/zh-hans/data/faae7605-a0f2-4d18-b28f-5cee413766a2/) (Peng et al. 2019)
(14) Multi-year Monthly Average NDVI (NDVI) (15) Neighborhood Statistics of Local Mean by 5 × 5 pixel window for (14) (NDVI_5), (16) Neighborhood Statistics of Local Mean by 9 × 9 pixel window for (14) (NDVI_9), (17) Neighborhood Statistics of Local Mean by 13 × 13 pixel window for (14) (NDVI_13)	The data was generated by GEE based on the period 1986–2020. Considering the growing season of plants in Zigui County and the contamination of images by clouds and snow, the mean-monthly NDVI values were first calculated by monthly averaging from May to October, and then by averaging the NDVI values for the six months obtained. In order to better suppress noise, the neighborhood Statistics of Local Mean were calculated based on multi-year monthly average NDVI using the focal statistics tool of Arcgis 10.6.
(18) Distance to Fault (Fault)	The data was from a 1:50,000 geological map (http://www.ngac.org.cn/, last accessed on 08/10/2022).
(19) Lithology	The data was from a 1:1000,000 Engineering Geological Map (https://geocloud.cgs.gov.cn, last accessed on 20/10/2022).
(20) Distance to River (River)	The data was generated by OpenStreetMap (OSM). (http://download.geofabrik.de/asia/, last accessed on 12/30/2022)
(21) Distance to River in the Reservoir Control Reach (Reservoir)
(22) Distance to Road (Road)
(23) Mean of NDBI (NDBI_Mean) (24) Max of NDBI (NDBI_Max)	The data was generated by GEE based on the period 1986–2020. Mean of NDBI refers to the multi-year mean of NDBI. Considering that anomalies exist in the maximum value of NDBI caused by the image stripes noise, Max of NDBI refers to the 95th percentiles of the statistical NDBI histogram
(25) Distance to Mine (Mine)	Mine data was provided by the National Mineralogical Database (http://data.ngac.org.cn/, last accessed on 12/30/2022) and by visual interpretation of Google history images.

Table 2. The causes of selecting the landslide condition factors used in this study.

Abbreviation of factor	Causes of selecting the factors
Elevation	It is anticipated that there will be a positive correlation between increasing elevation and a higher frequency of landslides. (Larsen and Torres-Sánchez 1998)
Slope	Studies have indicated that slope angle exerts a significant influence on landslides, with steeper slopes exhibiting a greater propensity for landsliding. (ROTH 1983; C.-T.; C.-T. Lee 2013)
TRI	That TRI had the highest positive correlation with landslide occurrence. (Jebur, Pradhan, and Shafapour Tehrany 2014; Xu et al. 2022)
Curvature	Hill slopes with a concave curvature have been found to possess a slightly higher susceptibility to landslides as compared to their counterparts with a convex curvature. (Ohlmacher 2007)
Plan Curvature	Plan curvature is governed by water flow divergence/convergence, influencing downslope water flow, erosion, deposition, and landslide. (Cheng et al. 2022)
Profile Curvature	Profile curvature controls water flow convergence/divergence, shaping the likelihood of landslide on the slope. (Cheng et al. 2022)
TPI	The topographic position index provides a stronger sense of where landslide material may end up. (Emberson et al. 2022)
TWI	TWI is crucial to evaluate rainfall-induced pore water pressure and its influence on landslides, reflecting a key factor. (Rahali and Houda 2022)
Aspect	Aspect’s influence on landslides is rooted in contrasting vegetation and root cohesion arising from varied solar insolation levels. (Abancó et al. 2021)
Rainfall_20, Rainfall_10, Rainfall_1, Rainfall_Aver	Landslide is strongly related to rainfall event parameters (duration, intensity, total rainfall). (Berti et al. 2012)
NDVI, NDVI_5, NDVI_9, NDVI_13	Vegetation cover has both positive and negative impacts on landslides. The roots can reinforce soil shear strength, mitigating creep and erosion. However, increased coverage may elevate runoff and gully erosion, and root splitting may trigger landsliding. (Y. Gao and Zhang 2022; Y. Liu et al. 2012)
Fault	Faults introduce slope material discontinuity, making distance to faults a critical factor in landslide susceptibility assessment. (Çevik and Topal 2003)
Lithology	Each lithology contributes differently to the development of landslides. (C. Caiyan and Qiao 2009)
River	Rivers impact terrain erosion and water seepage, thus are critical factors in landslide analysis due to their distance. (Çevik and Topal 2003)
Reservoir	Below the water level, the shear strength of the sliding zone is reduced by reservoir impoundment. (Du, Yin, and Lacasse 2013)
Road	Field observations indicate a robust spatial association between landslides and roads. (McAdoo et al. 2018)
NDBI_Mean, NDBI_Max	NDBI reflects impermeable features, such as settlements and roads, which impact water runoff and slope stability. Consequently, high NDBI areas are susceptible to landslides. (V. D. Pham et al. 2020)
Mine	The principal factor contributing to diverse geological hazards, including landslides, is surface deformation caused by mining activities. (Z. Liu, Mei, and Sun 2022)

Figure 3. Detailed procedure of the PU-pullbaggingDT method.

Figure 4. Landslide susceptibility map of the study area: (a) PU-pullbaggingDT_valid47 (b) PU-pullbaggingDT_valid50 (c) PU-pullbaggingDT_valid52 (d) PU-baggingDT (e) AdaPU-RF.

Table 3. Accuracy results of different models for the PU dataset in Zigui county. The range [×-×] refers to cells whose output scores fall within this range. “PCT” is an abbreviation for percentage, and “PCT of cells” refers to the cells within the score range [×-×] that occupy a percentage of all cells within Zigui county. Test_R_PA refers to the percentage of correct predictions in the testing set within the score range [×-×]. valid47, valid50, and valid52 refer to the selected validation accuracy threshold of 47/52, 50/52, and 52/52, respectively.

Model		AdaPU-RF(%)	PU-baggingDT(%)	（ours）PU-pullbaggingDT(%)
				valid47	valid50	Valid52
Testing set (351 raster cells)	Test_PA	51.79 ± 2.80	67.98 ± 0.61	79.93 ± 1.79	83.90 ± 1.45	87.37 ± 0.75
	Right_AUC	89.21 ± 0.44	78.66 ± 0.04	78.75 ± 0.13	78.51 ± 0.15	78.32 ± 0.04
	Left_AUC	52.79 ± 2.05	78.60 ± 0.04	78.74 ± 0.13	78.50 ± 0.15	78.31 ± 0.04
Training set and validation set (526 raster cells)	Train_PA	84.87 ± 0.76	100.00 ± 0.00	100.00 ± 0.00	100.00 ± 0.00	100.00 ± 0.00
	Right_AUC	93.54 ± 0.40	100.00 ± 0.00	97.59 ± 0.13	97.29 ± 0.23	97.70 ± 0.11
	Left_AUC	77.53 ± 0.61	100.00 ± 0.00	97.59 ± 0.13	97.29 ± 0.23	97.7 ± 0.11
[0.80–1.00]	PCT of cells	14.49 ± 0.58	4.05 ± 0.01	12.95 ± 0.15	13.30 ± 0.14	13.31 ± 0.05
	Test_R_PA	50.03 ± 1.72	26.84 ± 0.42	48.66 ± 0.64	49.85 ± 0.49	49.64 ± 0.44
[0.60–0.80)	PCT of cells	0.57 ± 0.14	12.91 ± 0.02	17.98 ± 1.11	22.16 ± 1.46	25.20 ± 0.52
	Test_R_PA	0.97 ± 0.86	29.86 ± 0.33	24.91 ± 0.72	27.08 ± 1.07	29.19 ± 0.55
[0.40–0.60)	PCT of cells	0.92 ± 0.20	21.83 ± 0.06	17.70 ± 1.04	22.75 ± 1.71	28.71 ± 1.18
	Test_R_PA	1.37 ± 0.58	21.42 ± 0.38	12.71 ± 1.06	13.45 ± 0.51	14.19 ± 0.39
[0.20–0.40)	PCT of cells	2.46 ± 0.43	30.27 ± 0.11	28.70 ± 0.26	26.83 ± 1.53	26.03 ± 0.47
	Test_R_PA	2.96 ± 0.53	16.87 ± 0.33	10.29 ± 0.83	7.76 ± 0.99	6.29 ± 0.20
[0.00–0.20)	PCT of cells	81.57 ± 1.26	30.93 ± 0.12	22.67 ± 2.28	14.96 ± 2.06	6.76 ± 1.20
	Test_R_PA	44.67 ± 3.07	5.01 ± 0.29	3.43 ± 0.68	1.87 ± 0.14	0.7 ± 0.29

Figure 5. (a) The loss of D-TNN in different stage. (b) The Test_PA of D-TNN at the 30th/50th/70th epoch of stage 2. (c) The Test_Left_AUC of D-TNN at the 30th/50th/70th epoch of stage 2. (d) The Test_Right_AUC of D-TNN at the 30th/50th/70th epoch of stage 2.

Figure 6. The probabilistic classification results of all cells within Zigui county at the 30th/50th/70th epoch of stage 2 for D-TNN.

Table 4. Accuracy results of different models for the PU dataset in Zigui county. Test_Right_AUC and Test_left_AUC refer to the AUC results based on the testing set.

Epochs of iterations	Test_Right_AUC	Test_Left_AUC	Test_PA
500	78.68 ± 0.15	78.54 ± 0.14	67.12 ± 0.76
800	78.61 ± 0.05	78.55 ± 0.04	67.29 ± 0.75
1300	78.75 ± 0.05	78.71 ± 0.06	67.86 ± 0.49
1500	78.72 ± 0.08	78.69 ± 0.08	67.52 ± 0.36
1000(original parameter)	78.66 ± 0.04	78.60 ± 0.04	67.98 ± 0.61

Figure 7. The Right_AUC results of contrastive network for testing set were calibrated by PU-baggingDT.

Figure 8. The low accuracy results of PU-baggingDT for the testing set were calibrated using the contrastive network.

Figure 9. Impact of different validation accuracies on the accuracies of the contrastive network for the testing set.

Figure 10. Feature importance ranking of 25 conditioning factors, the abbreviations for the names are listed in Table 2.

Figure 11. Spearman correlation coefficient of 25 conditioning factors, the abbreviations for the names are listed in Table 2.

Table 5. Accuracy results of different models for the remaining 12 factors.

		AdaPU-RF	PU-baggingDT	（ours）PU-pullbaggingDT
				valid47	valid50	valid52
Testing set	Test_PA	49.69 ± 1.15	66.67 ± 0.40	82.81 ± 0.09	84.73 ± 0.12	88.59 ± 0.1
	Right_AUC	89.13 ± 0.33	77.59 ± 0.10	76.86 ± 0.06	76.84 ± 0.06	76.91 ± 0.07
	Left_AUC	48.51 ± 0.71	77.53 ± 0.11	76.85 ± 0.06	76.83 ± 0.06	76.90 ± 0.07
Training set and validation set	Train_PA	84.26 ± 0.25	100.00 ± 0.00	100.00 ± 0.00	100.00 ± 0.00	100.00 ± 0.00
	Right_AUC	93.76 ± 0.24	100.00 ± 0.00	97.35 ± 0.01	97.61 ± 0.01	98.25 ± 0.01
	Left_AUC	76.75 ± 0.92	100.00 ± 0.00	97.35 ± 0.00	97.61 ± 0.01	98.25 ± 0.01

Figure 12. Sampling positions of five randomly selected negative samples.

Table 6. Accuracy results of various machine learning models on five randomly selected negative samples.

		1	2	3	4	5
Test_PA (%)	SVM	70.09	59.83	66.38	62.68	70.09
	LR	69.8	64.1	66.67	64.96	68.09
	RF	68.66	66.38	63.25	62.96	67.24
	AdaBoost	66.67	66.67	71.23	68.09	67.24
	XGBoost	70.09	66.67	60.4	65.81	68.66
Left_AUC (%)	SVM	73.35	75.19	75.07	74.63	75.26
	LR	74.86	75.42	74.6	74.32	74.58
	RF	77.91	78.19	75.99	78.45	78.27
	AdaBoost	74.58	74.55	72.92	75.9	75.04
	XGBoost	76.07	77.76	74.5	78.35	77.82
Right_AUC(%)	SVM	73.38	75.21	75.08	74.66	75.3
	LR	74.88	75.42	74.6	74.33	74.59
	RF	78.17	79.44	77.79	78.62	78.63
	AdaBoost	75.05	74.86	78.39	78.07	75.35
	XGBoost	76.09	77.77	74.52	78.36	77.83
Train_PA (%)	SVM	75.86	70.91	78.14	77.76	82.32
	LR	78.33	72.05	73.95	72.62	78.14
	RF	98.1	98.1	98.67	98.48	98.29
	AdaBoost	89.54	81.75	80.42	78.71	81.56
	XGBoost	99.05	98.48	99.24	83.08	95.06
Search space	SVM	C: [0.1, 1, 10, 100, 1000]; gamma [10, 1, 0.1, 0.001, 0.0001]
	LR	Penalty: [L1, L2]; C [0.001.0.01.0.1.1.10, 100]
	RF	Number of trees: [10, 20, 30, …, 100] and [100, 150, 200, …, 500]
	AdaBoost	n_estimators: [10, 20, 30, …, 100] and [100, 150, 200, …, 500]; learning_rate :[0.125, 0.25, 0.5, 1, 2]
	XGBoost	n_estimators: [50, 100, 150, 200, 300]; max_depth: [3, 4, 5, 6, 7]; colsample_bytree: [0.4, 0.6, 0.8, 1]; min_child_weight: [1, 2, 3, 4]; learning_rate :[0.05, 0.1, 0,2, 0.3]

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Data availability statement

We present the codes openly available at https://github.com/ShubingOuyangcug/PU-pullbaggingDT to encourage reproducibility of the study.