Heterogeneous transfer learning considering feature representation and environmental consistency for landslide spatial prediction

ABSTRACT

The difficult, time-consuming, and imbalanced acquisition of landslide inventories in complex and heterogeneous large areas often results in limited predictive performance for most statistical landslide spatial prediction methods. Although partial transfer learning methods have produced reliable predictive results and successfully implemented knowledge transfer between data-rich and data-scarce areas, most of these methods generally only extract inadequate environmental features and lack the ability to interpret when, what, and how to effectively transfer knowledge to other regions with limited data. In this paper, a heterogeneous transfer learning method considering feature representations and environmental consistency, which features robustness, similarity, and transferability, is proposed for landslide spatial prediction. Specifically, we trained a stacked autoencoder (SAE) to extract more nonlinear features among environmental factors, and added an environmental similarity criterion to the transfer adaptation boosting (TrAdaBoost) algorithm to minimize feature dissimilarities and avoid negative transfer in different scenarios. To evaluate the robustness of the proposed method, we first selected two target areas (Lushan County and Luding County, China) and a source area (Wenchuan County, China) as case study areas. Then, we directly combined the source area and target area as an additional dataset without considering transfer learning to validate the significance and necessity of the proposed method. The area under the receiver operating characteristic curve (AUC) of the two target regions for the proposed method were 0.920 and 0.972, respectively, which were greater than those of the traditional TrAdaBoost (0.909 and 0.969, respectively), SAE (0.790 and 0.937, respectively), and random forest (0.915 and 0.966, respectively) methods. Furthermore, the AUC values of the SAE (0.851 and 0.900) and random forest (0.890 and 0.935) models based on the expanded datasets were also lower than those of the proposed method. Therefore, the experimental results show that the proposed method can be generalized well due to its efficient utilization and high adaptability. Moreover, the proposed method can not only be applied to emergency rescue and disaster prevention but can also offer a promising way to improve landslide predictions of models with incomplete landslide inventories.

GRAPHICAL ABSTRACT

KEYWORDS:

• Landslide spatial prediction
• transfer learning
• environmental consistency
• feature representation
• random forest

1. Introduction

Climate change is expected to increase the duration, frequency, and intensity of extreme weather events, such as heavy precipitation and heat waves, subsequently affecting landslide occurrences and threatening human lives and property (Chowdhuri et al. 2020, 2021; Froude and Petley 2018; Gariano and Guzzetti 2016; Seneviratne et al. 2012). In addition, strong earthquakes are also a main cause of landslide occurrences, which cause slope instability and generate a large number of loose deposits, leading to landslides and debris flows under the further action of heavy rainfall. Landslide spatial prediction (LSP), which refers to the spatial probability of landslide occurrence, is therefore extremely valuable for landslide prevention and mitigation (Chen et al. 2024; Huang et al. 2020a; Reichenbach et al. 2018; Ruidas et al. 2021, 2022, 2023; Yao et al. 2023, 2024).

In recent decades, an increasing number of LSP methods have been proposed to generate LSP results for different areas (Chen et al. 2022; Huang et al. 2020a; Jia et al. 2021; Lin et al. 2021; Ouyang et al. 2024; Pham et al. 2019b; Van Den Eeckhaut et al. 2011; Wang et al. 2022), including random forests (Chowdhuri et al. 2022; Sun et al. 2020), frequency ratios (Huang et al. 2022a; Pal and Chowdhuri 2019), convolutional neural networks (Panahi et al. 2021; Zhao et al. 2021), Bayesian generalized linear models (Pal et al. 2022), analytic hierarchy processes (Moragues et al. 2021; Pal, Das, and Malik 2019), support vector machines (Pham and Prakash 2019; Pham et al. 2019a), artificial neural networks (Chen et al. 2017), and U-Net convolutional networks (Bhuyan et al. 2023). These methods are generally classified into three categories: knowledge-driven, physically-driven, and data-driven methods (Corominas et al. 2014). Data-driven methods are much more convenient and high efficiency when expert knowledge and detailed geotechnical parameters are difficult to obtain in large areas (Corominas et al. 2014; Park et al. 2019; Zhao et al. 2023b), the accuracy of which is strongly correlated with the richness of the landslide inventory and the selection of environmental factors. However, data-driven methods also exhibit significant limitations in data-scarce regions and heterogeneous environments due to the problem of landslide inventory shortages (Ai, Sun, and Chen 2022; Al-Najjar et al. 2021; Chen et al. 2020; Hong et al. 2019; Huang et al. 2022a). Specifically, some regions with high altitudes, hidden features, and dense vegetation cover may hinder the investigation of landslide, and limited or imbalanced landslide data may occur, leading to inaccurate LSP results (Zeng et al. 2022). Although field investigation, visual interpretation of satellite or aerial images, identification of low-altitude unmanned aerial vehicle images, and semantic segmentation methods are used to generate accurate landslide inventory maps, these approaches are time-consuming, labor-intensive, expensive, and overlap in practical applications (Dai et al. 2022; Steger et al. 2017; Wang, Wang, and Zhang 2022; Zhao et al. 2023a). Thus, there is a challenge in how to achieve effective sharing and application between limited landslide inventories in different regions. Whenever feasible, it is essential to consider knowledge transfer or sharing between data-rich and data-limited regions when constructing LSP models. This contributes to enhancing the reuse efficiency of landslide data and the robustness of the model (Chen et al. 2020; Wang, Wang, and Zhang 2022; Zhu et al. 2020, 2022). However, many studies have overlooked the opportunity to learn general and transferable knowledge from similar environments. Instead, they directly utilize limited or unbalanced landslide inventories for LSP in heterogeneous environments (Conoscenti et al. 2016; Hong et al. 2019; Wang et al. 2022). Consequently, there is a need to develop transferable LSP methods that overcome the limitations of data deficiency.

As such, transfer learning has received much more attention due to its great potential in solving limited-data problems and facilitating knowledge transfer between the source domain and the target domain (Xu et al. 2022). For instance, an integrated deep learning and transfer learning method was proposed to generate LSP results in Hong Kong and achieved high prediction accuracy (Wang, Goetz, and Brenning 2022). The transfer adaptation boosting (TrAdaBoost) algorithm based on instance transfer was adopted to transfer useful information from different areas to improve the performance of an LSP model. Unsupervised transfer learning based on domain adaptation was applied to address the challenge of model transfer (Wang, Goetz, and Brenning 2022; Wang, Wang, and Zhang 2022). A spatial case-based reasoning method and its improvements were developed to improve the transferability and prediction accuracy of the model compared with other machine learning methods (Zhao et al. 2021, 2023b). However, in the construction of an LSP model, most transfer learning methods do not consider intrinsic differences in matching landslide datasets between the source and target domains and have directly expanded the entire landslide dataset in other areas to train the LSP model, which ignores intrinsic heterogeneity among different environmental characteristics and can lead to negative transfer due to its excessive transferability. Some studies have shown that the homogeneous distribution of landslide data is crucial for the performance of transfer learning methods. Therefore, there are still gaps regarding how to represent environmental characteristics and how to filter transferable landslide inventories in data-rich regions.

Thus, in this study, the key objective is to propose a heterogeneous transfer learning method that considers feature representation and environmental consistency to improve the robustness and transferability of an LSP model. In contrast to previous studies, we first trained a stacked autoencoder (SAE) to extract more representations of nonlinear features in an unsupervised manner, and an environmental similarity criterion was implemented to filter valuable landslide inventories. Then, the LSP results were predicted by three traditional machine learning methods, and their performances were evaluated and compared across two target study areas. Finally, the importance of feature representation and environmental consistency was further discussed, followed by the presentation of some future work.

2. Study area and data

Wenchuan County, Lushan County, and Luding County, which are located in Sichuan, China, were used as the source area and two target areas, respectively. The reasons for selecting these areas are their specific geographic locations, experience with intense earthquakes, and frequent occurrence of geological disasters (Zhao and Chen 2023; Zhao et al. 2021). This section provides a brief introduction to the study areas, landslide inventories, and corresponding environmental factors.

2.1. Source and target areas

Wenchuan County, with an area of approximately 8,820 km², is in the northwestern plateau region of Sichuan Province, China. This region is situated in the Longmenshan tectonic belt on the eastern margin of the Qinghai Tibet Plateau and mainly comprises magmatic rocks, including granite, diorite, and gabbro (Wang et al. 2021). The area is characterized by three main faults: the Longmenshan Fault, Central Fault, and Houshan Fault (Wang et al. 2021). On 12 May 2008, an 8.0-magnitude earthquake with a focal depth of more than 20 km struck Wenchuan County, triggering extensive collapses, landslides, and debris flows, which severely disrupted the local economy and transportation infrastructure (Cui et al. 2021; Qi et al. 2010; Zhang et al. 2022). Consequently, the abundant landslide inventory in this area can serve as the source area for our study.

Lushan County is situated in the northeastern part of Ya’an, at the western edge of the Sichuan Basin in China. It features altitudes ranging from 527 m to 5,289 m, with an average annual rainfall of approximately 102 mm. Lushan County experienced a series of powerful earthquakes (Ms ≤ 7.0) on 20 April 2013, and 1 June 2022. These earthquakes altered the internal forces acting on the mountain slopes, resulting in frequent landslides in the study zone.

Luding County lies in a transitional zone between the western Sichuan Plateau and Sichuan Basin, located in southeastern Ganzi, Sichuan, China. The terrain varies from high in the west to low in the east and is shaped by river and glacial erosion, resulting in alpine and canyon landforms. Geological features, including faults and folds, are prominent in Luding County, and are characterized by active tectonic movements. The region has experienced numerous earthquakes, with 22 earthquakes above Ms 6.0 and 8 earthquakes above Ms 7.0 since 1700. Following the 2008 Wenchuan earthquake and the 2013 Lushan earthquake, the Kulun stress in the Xianshuihe fault zone notably increased, increasing the risk of major seismic events. On 5 September 2022, Luding County was struck by a Ms 6.6 earthquake, with a depth of 16 km and a maximum intensity of IX degrees. The earthquake resulted in injuries, casualties, and extensive damage to roads, bridges, and infrastructure. Consequently, it is important for decision-makers to quickly produce reliable landslide susceptibility map. Figure 1 displays the geographic location and landslide distribution of the source and target areas, respectively.

Figure 1. Locations of the study areas and landslide distributions. (a) The geographic location of the three study areas in Sichuan Province. (b) Wenchuan County as a source area. (c) Lushan County as a target area. (d) Luding County as a target area.

2.2. Data used

A comprehensive landslide inventory and relevant environmental factors are pivotal in elucidating the relationships between landslide occurrences and environmental conditions. The proposed method primarily emphasizes the representation and consistency of environmental factors, thus focusing on earthquake-induced landslides rather than those triggered by multiple events. Accordingly, we curated and filtered 5,447 historical earthquake-induced landslides in Wenchuan County, 353 in Lushan County, and 5,007 in Luding County based on historical records, field surveys, and remote sensing image interpretation (Huang et al. 2024). These landslides predominantly occurred in 2008, 2013, and 2022 in Wenchuan, Lushan, and Luding Counties, respectively. Table 1 outlines the specifics of landslides in each study area, encompassing attributes such as name, type, volume, time, triggering conditions, and locations. Moreover, an equal number of non landslide samples were randomly selected from landslide-free areas to balance the overall sample distribution in both the source and target areas (Pham et al. 2019a).

Table 1. Details of landslides in the three study areas.

Study area	Year	Number	Earthquake magnitude	Type
Wenchuan County (Source area)	2008	5,447	8.0	Earthquake-induced landslides
Lushan County (Target area)	2013	353	6.1	Earthquake-induced landslides
Luding County (Target area)	2022	5,007	6.8	Earthquake-induced landslides

The selection of landslide-related environmental factors is crucial for the development of an effective LSP model that encompasses geological, topographic, hydrological, climatic, and triggering factors (Zhao et al. 2021). These factors not only influence landslide occurrence but also contribute to the spatiotemporal distribution of landslides. Despite the absence of a consensus on a definitive set of factors, our selection was informed by previous literature and the environmental context of both the source and target areas. Elevation, slope, aspect, distance to roads, rivers, faults, and earthquakes, land use, lithology, and peak ground acceleration (PGA) were identified as pertinent landslide-related environmental factors. Elevation, aspect, and slope data were derived from the ASTER Global Digital Elevation Model at a spatial resolution of 30 m × 30 m. Lithology and fault data were sourced from the 1:500,000 geological map of China, while river and road data were obtained from the 1:1000,000 national basic geographic information dataset. The land use data were derived from Landsat images via the Google Earth Engine platform, and the earthquake data were collected from the United States Geological Survey. Moreover, determining the appropriate spatial resolution and mapping unit for LSP is paramount. To this end, we considered the resolution of conditioning factors, data availability, landslide volume, and insights from previous studies (Abbaszadeh Shahri et al. 2019; Ba et al. 2018; Chang et al. 2020; He et al. 2021; Huang et al. 2024; Huang et al. 2020a; Pham et al. 2019a; Youssef et al. 2015). Thus, all the data layers were uniformly resampled and reclassified to raster layers with a spatial resolution of 30 m × 30 m. Figures 2, 3, and 4 illustrate the landslide-related environmental factors in both the source and target areas, providing a visual representation of the data for analysis and interpretation.

Figure 2. Landslide-related environmental factors in Wenchuan County.

Note: Land use and lithology were reclassified 12 and 16 categories, respectively, according to related studies and platforms (land use: from the Google Earth Engine platform; lithology: from a geographic information dataset of China), including barren land, water bodies, roads, woodlands, wetlands, mixed forests, sand and soil, sandstone, magmatic rocks, etc.

Figure 3. Landslide-related environmental factors in Lushan County.

Note: Land use and lithology were reclassified 8 and 53 categories, respectively, according to related studies and platforms (land use: from the Google Earth Engine platform; lithology: from a geographic information dataset of China), including barren land, farmlands, roads, woodlands, water bodies, sand and soil, sandstone, magmatic rocks, etc.

Figure 4. Landslide-related environmental factors in Luding County.

Note: Land use and lithology were reclassified 8 and 17 categories, respectively, according to related studies and platforms ((land use: from the Google Earth Engine platform; lithology: from a geographic information dataset of China). These included barren land, water bodies, ice and snow, construction roads, woodlands, sand and soil, sandstone, magmatic rocks, etc.

3. Methodology

3.1. Frequency ratio analysis

Frequency ratio (FR) analysis is a popular and traditional method for LSP (Lee, Ryu, and Kim 2007; Pal and Chowdhuri 2019; Vakhshoori and Zare 2016) and is employed to assess the influence of predisposing factors on landslide susceptibility (Chowdhuri et al. 2021; Pal, Das, and Malik 2019; Ruidas et al. 2021, 2022). Calculating the FR value enables the estimation of the likelihood of landslide occurrence within a target area under the influence of these factors. Typically, a higher FR indicates a greater probability of landslide occurrence, while a lower FR suggests a diminished correlation (Chang et al. 2020). The FR value can be calculated as:

(1) $\mathit{F}{R}_{\mathit{ij}}=\frac{\mathit{L}{\mathit{A}}_{\mathit{ij}}/{\sum }_{j=1}^n\mathit{L}{A}_{\mathit{ij}}}{\mathit{F}{A}_{\mathit{ij}}/{\sum }_{j=1}^n\mathit{F}{A}_{\mathit{ij}}}$(1)

where $\mathit{L}{A}_{\mathit{ij}}$,$\mathit{F}{A}_{\mathit{ij}}$, and $\mathit{F}{R}_{\mathit{ij}}$ are the number of landslides, number of grid pixels, and frequency ratio value in the i^th subclass of the j^th environmental factor, respectively. In addition, n denotes the number of subclasses in the i^th influencing factor.

3.2. Kullback-leibler divergence analysis

To meet the requirements of a transfer learning method and avoid negative transfer in different scenarios, we used the Kullback-Leibler (KL) divergence method to describe similarities between the source area and target area in terms of the distributions of two variables (Kullback and Leibler 1965). The equation for KL is as follows:

(2) $\mathit{KL}(\mathit{P}||\mathit{Q})=\int \mathit{P}(\mathit{x})log\frac{\mathit{P}(\mathit{x})}{\mathit{Q}(\mathit{x})}\mathit{dx}$(2)

where $\mathit{P}(\mathit{x})$ and $\mathit{Q}(\mathit{x})$ represent the probability distributions of the two variables. The $\mathit{KL}(\mathit{P}||\mathit{Q})$ value is greater than or equal to 0. Smaller KL values represent greater similarities between two independent variables.

3.3. Framework of the proposed transfer learning method

The purpose of this paper is to propose a transfer learning method that considers feature representation and environmental consistency to improve the robustness and transferability of LSPs. The framework of the proposed method is shown in Figure 5. The procedure can be divided into three steps: environmental feature representation in source and target areas, environmental similarity criterion creation, and instance-based transfer learning.

Figure 5. The framework of the proposed transfer learning method.

3.3.1. Environmental feature representation

The initial step involves acquiring a compressed representation of environmental factors through unsupervised learning, thereby enhancing feature representation within a lower-dimensional space. The stacked autoencoder (SAE), a specialized form of a multilayer perceptron, serves this purpose. In this study, the SAE model was utilized not only for reconstructing the features of landslide-related environmental factors but also for mitigating the simplistic use of original data (Nam and Wang 2020). Moreover, the middle layer, characterized by a lower dimension, aids in preventing overfitting and facilitates dimension reduction scenarios (Charte et al. 2018; Hinton and Salakhutdinov 2006). The SAE model comprises multiple autoencoders, in which the output of each layer connects to the input of the preceding layers, configured as 80-50-2-50-80 (refer to Figure 5). Five hidden layers, employing the rectified linear unit (ReLU) function, are utilized in the middle layer for encoding the input and decoding the output. The model underwent 8,000 training steps with a batch size of 32. An adaptive learning rate, implemented through the Adam optimizer, was utilized to refine the model weights. Consequently, this process yields a new feature representation of landslide-related environmental factors in both the source and target areas, which is essential for subsequent steps.

3.3.2. Environmental similarity criterion creation

The primary objective of this step is to discern and filter pertinent knowledge within the source area, recognizing that not all samples within the source area may be suitable for transfer (Jiang and Zhai 2007). The process of transferring knowledge from the source area to the target domain entails inherent uncertainties regarding what, when, and how this knowledge is effectively transferred. Given the insights gleaned from prior research and the significance of environmental consistency (Zhao et al. 2023b), we initially devised the environmental similarity criterion (ESC) to discern valuable landslide samples within the source domain. The identified samples within the source area are considered a new source for further analysis. Its purpose is to minimize the difference between the source and target domains and further prevent negative transfer. Specifically, an ESC method measures transferability by considering the environmental consistency between the source and target domains. We assumed two landslide collections among the source and target areas, C_S ={L₁ ($F_1^s$, $F_2^s$, … $F_i^s$), L₂ ($F_1^s$, $F_2^s$, … $F_i^s$), … L_n ($F_1^s$, $F_2^s$, … $F_i^s$)} and C_t ={L₁ ($F_1^t$, $F_2^t$, … $F_i^t$), L₂ ($F_1^t$, $F_2^t$, … $F_i^t$), … L_m ($F_1^t$, $F_2^t$, … $F_i^t$)}. L_n ($F_1^s$, $F_2^s$, … $F_i^s$) is the environmental factor collection of the n^th landslide. n and m are the numbers of landslides for the C_s and C_t collections, respectively. The equations for ESC are as follows:

(3) $S_i=1-\frac{|F_i^t-F_i^s|}{\mathit{max}(F_{\mathit{max}}-F_i^t,F_i^t)}$(3)

(4) $\mathit{S}=\frac{1}{i}\sum _{\mathit{k}=1}^i{W}_i\cdot S_i$(4)

(5) $\mathit{NC}=\left\{\begin{array}{c}{L}_n\in \mathit{NC},\mathit{ifS}\ge \mathit{\sigma }\\ L_n\notin \mathit{NC},\mathit{ifS}<\mathit{\sigma }\end{array}\right.$(5)

where S_i denotes the similarity coefficient of the i^th landslide-related environmental factor of a landslide between source domain s and target domain t. $F_i^s$and $F_i^t$ denote the i^th landslide-related environmental factor corresponding to the landslide collections (s and t). F_max is the maximal value of i^th landslide-related environmental factor in the target domain t. W_i denotes the weight of the i^th landslide-related environmental factor. S and i are the sum of S_i and the number of landslide-related environmental factors, respectively. Finally, we filter a new subset with more similar environments according to a user-defined threshold $\mathit{\sigma }$. Thus, a new collection (NC) is generated by filtering the original source domain (s) based on Eq. (5)(5) $\mathit{NC}=\left\{\begin{array}{c}{L}_n\in \mathit{NC},\mathit{ifS}\ge \mathit{\sigma }\\ L_n\notin \mathit{NC},\mathit{ifS}<\mathit{\sigma }\end{array}\right.$(5) . A landslide in the source domain belongs to the NC when S is greater than the threshold. In this study, we set multiple thresholds for repeated experiments and set 0.98 as the optimal threshold $\mathit{\sigma }$ according to the best performance of the model.

3.3.3. Instance-based transfer learning

The third step employs an instance-based transfer learning method to formulate LSP results based on the new source domain established in Step 2. Typically, a transfer learning method is initially trained on a substantial volume of labeled data to acquire general features, knowledge, relationships, or weights. Subsequently, this acquired general knowledge is transferred from data-abundant regions to data-limited areas to address specific tasks (Pan and Yang 2010). Transfer learning methods can be categorized into four main types: instance-based transfer learning, feature representation-based transfer learning, parameter-based transfer learning, and relational knowledge-based transfer learning. A fundamental assumption of instance-transfer learning is that the mechanism of landslide occurrence (e.g. landslide distribution characteristics) in some source domains is similar to that in the target domain, and knowledge transfer is realized by adjusting the weights of the samples between the source domain and the target domain. Conversely, the other three transfer methods realize knowledge transfer according to the feature distribution, parameter sharing and relational understanding. Consequently, in this study, we selected the TrAdaBoost algorithm based on instance-transfer learning to carry and transfer knowledge from the source domain, and then combined it with a random forest as a base classifier to train a robust LSP model in the target domain (Dai et al. 2007). A more detailed flowchart of the TrAdaBoost algorithm is shown in Table 2 (Dai et al. 2007).

Table 2. TrAdaBoost algorithm.

Algorithm 1. TrAdaBoost method for landslide susceptibility mapping

Input: Source dataset Ta, target dataset Tb. The base algorithm: Learner. Iterations: N.

Output: Final classifier Fi.

Initialization: 1. Initialize the weights of the vectors $w_i=\left\{\begin{array}{c}\frac{1}{n}\mathit{\hspace{0.17em}}\mathit{if}\mathit{\hspace{0.17em}}\mathit{i}=1,\dots ,\mathit{n}(\mathit{source}\mathit{\hspace{0.17em}}\mathit{domain})\mathit{\hspace{0.17em}}\\ \frac{1}{m}\mathit{\hspace{0.17em}}\mathit{if}\mathit{\hspace{0.17em}}\mathit{i}=\mathit{n}+1,\dots ,\mathit{n}+\mathit{m}(\mathit{target}\mathit{\hspace{0.17em}}\mathit{domain})\end{array}\right.$ 2. Define the initial value $\mathit{\beta }=1/(1+\sqrt{ln\mathit{n}/\mathit{N}})$

For t=1,…,N

1. Normalize weights of all samples and develop a base learner to produce an LSP model $P^t=\frac{{\omega }^t}{\sum _{\mathit{i}=1}^{\mathit{n}+\mathit{m}}{\omega }_i^t}$

2. Calculate the error rate in the target domain${\epsilon }_t=\sum _{\mathit{i}=\mathit{n}+1}^{\mathit{n}+\mathit{m}}\frac{P_i^t|h_t(x^t-y^t)|}{{\sum }_{i=n+1}^{n+m}{P}_i^t}$

3. Update the value $\mathit{\beta }={\epsilon }_t/(1-{\epsilon }_t)$

4. Update weights of all samples${\omega }_i^1=\left\{\begin{array}{c}{\omega }_i^t{\beta }^{|h_t(x^t-y^t)|}\mathit{\hspace{0.17em}}\mathit{if}\mathit{\hspace{0.17em}}\mathit{i}=1,\dots ,\mathit{n}\mathit{\hspace{0.17em}}\\ {\omega }_i^t{\beta }^{-|h_t(x^t-y^t)|}\mathit{\hspace{0.17em}}\mathit{if}\mathit{\hspace{0.17em}}\mathit{i}=\mathit{n}+1,\dots ,\mathit{n}+\mathit{m}\end{array}\right.$

3.4. Model evaluation

In this study, we propose a heterogeneous transfer learning method considering feature representation and environmental consistency to improve the robustness and transferability of LSPs. To validate the robustness of the proposed method and explore the influence of feature representation on similarity calculations, we developed three models for comparison: The TrAdaBoost-RF, SAE-RF, and RF models. The TrAdaBoost-RF model is trained by traditional TrAdaBoost without considering feature representation and environmental consistency. The SAE-RF model is developed by combining a stacked autoencoder with a random forest as a base classifier. RF is generated by a random forest method. For LSP model training, the experimental dataset was divided 7:3 by using stratified random sampling, of which 70% was used for model training and 30% was used for model validation (Zhao et al. 2023b). Finally, we used the area under the receiver operating characteristic curve (AUC) and statistical indicators to assess the performance of the proposed method based on 10-fold cross-validation.

4. Results

4.1. Quantification analysis of the landslide-related environmental factors

The collinearity analysis of landslide-related environmental factors for the three study areas is illustrated in Figure 6. The quantification analysis of factors serves to mitigate noise and indicates that all factors demonstrate sufficient independence. It is evident that no linear correlation exists among the 10 landslide-related environmental factors in both the source and target areas, as evidenced by the variance inflation factor (VIF) values of all factors being less than 10. This suggests that all predisposing factors can be effectively incorporated into the development of the LSP model.

Figure 6. Collinearity analysis of the landslide-related environmental factors in the three study areas.

The mechanism of landslide occurrence may be different for different study areas. In Table 3, the FR values and classification schemes for each predisposing factor are presented. The different classifications of each landslide-related environmental factor exhibit varying effects on landslide occurrence, as indicated by their distinct FR values in both the source and target areas. Notably, in Wenchuan County, a greater frequency of landslides is inclined to occur in the middle altitude range (900–2500 m), while fewer landslides occur in low altitude areas. Similar trends are observed in Lushan County and Luding County. Conversely, the slope analysis reveals a greater likelihood of landslide occurrence between 80° and 90° in Wenchuan County, 0° and 24° in Lushan County, and between 26° and 49° in Luding County. These results underscore the utility of FR analysis in addressing issues of feature dissimilarities.

Table 3. Frs of landslide-related environmental factors.

Landslide-related environmental factor	Source area (Wenchuan)		Target area (Lushan)		Target area (Luding)
	Value	FR	Value	FR	Value	FR
Elevation	>2900	0.330	>1557	0.022	>4637	0.034
	2500–2900	1.093	1357–1557	0.531	2992–4637	0.034
	2100–2500	1.414	1157–1357	2.185	3372–3992	0.142
	1700–2100	1.961	957–1157	2.809	2776–3372	0.508
	1300–1700	2.818	757–957	3.022	2231–2776	1.628
	900–1300	2.448	557–757	2.776	1635–2231	6.431
	781–900	0.787			817–1635	7.160
Slope	80–90	1.236	>42	0.000	49–74	0.000
	70–80	0.451	36–42	0.121	42–49	1.542
	60–70	0.435	30–36	0.351	37–42	2.088
	50–60	0.588	24–30	0.422	32–37	1.789
	40–50	0.460	18–24	1.336	26–32	1.067
	30–40	0.210	12–18	2.076	20–26	0.749
	20–30	0.549	6–12	2.429	12–20	0.649
	10–20	0.758	0–6	2.337	0–12	0.340
	0–10	0.000
Aspect	Northwest	1.146	Northwest	0.813	Northwest	0.431
	West	0.909	West	1.223	West	0.359
	Southwest	0.784	Southwest	1.236	Southwest	0.504
	South	0.822	South	0.818	South	0.793
	Southeast	1.113	Southeast	0.890	Southeast	0.688
	East	1.199	East	1.136	East	1.251
	Northeast	1.014	Northeast	1.109	Northeast	1.668
	North	0.908	North	0.670	North	1.447
	Flat	1.008	Flat	0.540	Flat	0.803
Distance to a road	>3200	0.754	>3000	0.099	>17688	0.114
	2800–3200	0.957	2700–3000	0.182	14525–17588	0.434
	2400–2800	0.931	2400–2700	0.333	12075–14525	0.735
	2000–2400	0.935	2100–2400	0.451	9975–12075	0.378
	1600–2000	0.929	1800–2100	0.470	8050–9975	0.598
	1200–1600	0.960	1500–1800	0.776	6300–8050	0.999
	800–1200	1.144	1200–1500	1.523	4637–6300	1.658
	400–800	1.524	900–1200	1.902	2975–4637	2.598
	0–400	1.711	600–900	2.259	1312–2975	3.928
			300–600	4.947	0–1312	4.247
			0–300	0.036
Distance to a river	>2700	0.612	>1000	0.185	>7251	0.045
	2400–2700	1.118	900–1000	0.458	5786–7251	0.134
	2100–2400	1.087	800–900	0.118	4706–5786	0.284
	1800–2100	1.169	700–800	0.518	3857–4706	0.173
	1500–1800	1.307	600–700	0.694	3124–3857	0.200
	1200–1500	1.390	500–600	0.579	2468–3124	0.406
	900–1200	1.665	400–500	0.763	1851–2468	0.585
	600–900	2.076	300–400	0.946	1234–1851	0.953
	300–600	2.752	200–300	1.192	578–1234	1.933
	0–300	3.063	100–200	1.511	0–578	2.880
			0–100	0.000
Distance to a fault	>4000	0.690	>9000	1.956	>22291	0.344
	3500–4000	1.735	8000–9000	2.502	19166–22291	1.189
	3000–3500	1.508	7000–8000	2.083	16145–19166	1.163
	2500–3000	1.486	6000–7000	1.261	13229–16145	1.131
	2000–2500	1.397	5000–6000	0.861	10520–13229	1.044
	1500–2000	1.151	4000–5000	0.621	8124–10520	1.329
	1000–1500	1.261	3000–4000	0.426	5937–8124	2.110
	500–1000	1.326	2000–3000	1.093	3749–5937	2.079
	0–500	1.090	1000–2000	0.877	1666–3749	2.386
			0–1000	2.081	0–1666	3.307
Distance to an earthquake	>38000	0.005	>9000	0.264	>52680	1.120
	32702–38000	0.025	8000–9000	1.471	46775–52680	1.049
	28461–32702	0.141	7000–8000	0.348	41106–46775	0.849
	24397–28461	0.378	6000–7000	0.880	35201–41106	1.466
	20333–24397	0.923	5000– 6000	0.945	29060–35201	0.876
	16622–20333	1.268	4000–5000	1.441	23155–29060	0.690
	13265–16622	1.599	3000–4000	1.904	17959–23155	0.234
	9731–13265	1.525	2000–3000	1.726	12998–17959	0.391
	5800–9731	1.101	1000–2000	1.714	7802–12998	0.524
	0–5800	0.816	0–1000	0.384	0–7802	0.035
Land use	Water body	0.000	Woodland	0.877	Woodland	0.000
	Barren	0.026
	Ice and snow	0.000	Road	4.251	Road	0.007
	Cropland	0.206	Construction land	2.749	Construction land	0.003
	Wetland	0.120	Ice and snow	0.000	Ice and snow	0.175
	Grassland	0.553	Barren	1.354	Barren	0.149
	Savanna	1.403	Farmland	3.023	Farmland	1.898
	Woody Savanna	2.263	Water body	1.635	Water body	1.166
	Others	1.872	Others	0.000	Others	2.668
Lithology	Magmatic rock	2.272	Magmatic rock	4.311	Magmatic rock	3.253
	Granite	0.467	Granite	2.507	Granite	1.757
	Sand and soil	0.454	Sand and soil	1.167	Sand and soil	3.410
	Carbonate rock	0.089	Carbonate rock	0.944	Carbonate rock	3.960
	Phyltite	0.605	Phyltite	0.048	Phyltite	0.687
	Sandstone	0.020	Sandstone	1.697	Sandstone	0.592
	Others	0.000	Others	0.000	Others	0.809
PGA	0.45–0.49	1.009	0.20–0.15	1.312	0.30–0.40	0.176
	0.40–0.45	1.083	0.10–0.20	0.000	0.20–0.30	2.210
	0.33–0.40	0.522	0–0.10	1.232	0–0.20	0.579
	0.18–0.33	0.000

A similar feature distribution between the source and target areas contributed to developing a better LSP result to avoid a negative transfer. Table 4 presents the Kullback-Leibler (KL) divergence values for each landslide-related environmental factor. The results indicate that the feature distributions across the source and target areas are not entirely consistent. In particular, the probability distributions of distance to a road, distance to a river, and distance to a fault exhibit significantly higher KL values, suggesting notable differences in their distributions. Consequently, the presence of feature dissimilarities, especially in these variables, may lead to negative transfer when directly applying them to transfer learning methods.

Table 4. KL values of landslide-related environmental factors.

Landslide-related environmental factor	KL values (Landslides)		KL values (Samples)		KL values (Study areas)
	Case1	Case2	Case1	Case2	Case1	Case2
Elevation	0.180	0.162	0.154	0.240	0.119	0.134
Slope	0.107	0.040	0.114	0.048	0.099	0.055
Aspect	0.321	0.289	0.319	0.303	0.301	0.311
Distance to a road	0.421	0.583	0.523	0.502	0.571	0.328
Distance to a river	0.368	0.486	0.308	0.463	0.280	0.315
Distance to a fault	0.460	0.482	0.377	0.404	0.357	0.309
Distance to an earthquake	0.260	0.125	0.434	0.178	0.466	0.208
Land use	0.074	0.067	0.087	0.144	0.101	0.189
Lithology	0.185	0.059	0.264	0.187	0.301	0.279
PGA	0.102	0.057	0.094	0.080	0.100	0.100

Note: Case 1 shows the KL values between Wenchuan County and Lushan County. Case 2 indicated that the KL value differed between Wenchuan County and Luding County.

4.2. Landslide susceptibility mapping

Table 5 summarizes the 12 LSP models used to evaluate the performance of the proposed transfer learning method. These models are compared based on their ability to predict landslide susceptibility indices (LSIs), which are classified into five categories using the natural break method: very low (0–0.13), low (0.13–0.37), moderate (0.37–0.60), high (0.60–0.82), and very high (0.82–1.0). Obviously, all the landslide susceptibility maps (LSMs) have similar spatial patterns. Specifically, the very high and high susceptibility levels are mainly distributed along rivers and roads.

Table 5. Performance comparison among the 12 methods.

Dataset	Model	AUC	F1	Kappa	Precision	Recall
Dataset 1	^1Proposed method	0.920	0.850	0.682	0.821	0.886
Dataset 2	^2Proposed method	0.972	0.924	0.845	0.904	0.947
Dataset 1	^1TrAdaBoost-RF	0.909	0.821	0.624	0.782	0.864
Dataset 2	^2TrAdaBoost-RF	0.969	0.916	0.828	0.896	0.936
Dataset 1	^1SAE-RF	0.851	0.790	0.562	0.758	0.826
Dataset 2	^2SAE-RF	0.900	0.833	0.652	0.847	0.866
Dataset 3	^3SAE-RF	0.790	0.734	0.441	0.700	0.771
Dataset 4	^4SAE-RF	0.937	0.875	0.742	0.847	0.906
Dataset 1	^1RF	0.890	0.823	0.628	0.786	0.863
Dataset 2	^2RF	0.935	0.871	0.732	0.836	0.910
Dataset 3	^3RF	0.915	0.844	0.676	0.813	0.878
Dataset 4	^4RF	0.966	0.922	0.837	0.887	0.959

Note: Dataset 1 denotes a combination dataset of Lushan County and Wenchuan County; Dataset 2 denotes a combination dataset of Luding County and Wenchuan County; Dataset 3 denotes the Lushan County; and Dataset 4 denotes the Luding County.

Figure 7(a,b,e) shows a slight difference for the susceptibility levels. In addition, it must be emphasized that a large number of high-susceptibility areas in Figure 7(f) are clumps in the southern part of the study area, which is greater than that in other methods. This suggests that a direct combination of all the datasets does not necessarily improve the accuracy of the model.

Figure 7. Landslide susceptibility maps of the six models for Lushan County. (a) Proposed method; (b) TrAdaBoost-RF method; (c) SAE-RF method-based Lushan dataset; (d) SAE-RF method-based Lushan dataset and wenchuan dataset; (e) RF method-based Lushan dataset; and (f) RF method-based Lushan dataset and wenchuan dataset.

Furthermore, the LSM (Figure 7(c,d)) predicted by the SAE-RF method displays a chaotic spatial pattern in which features overlap several landslide-related environmental factors. Similarly, the LSM results in Luding County also show the same spatial distribution pattern (Figure 8).

Figure 8. Landslide susceptibility maps of the six models for luding county. (a) Proposed method; (b) TrAdaBoost-RF method; (c) SAE-RF method-based luding dataset; (d) SAE-RF method-based luding dataset and wenchuan dataset; (e) RF method-based luding dataset; and (f) RF method-based luding dataset and wenchuan dataset.

Accordingly, this suggests that an unsupervised SAE method can not only effectively extract local characteristics among predisposing factors, but can also reduce dimensionality in the selection of predisposing factors.

4.3. Model comparison and validation

In Figure 9, the training loss and validation loss of the SAE model are plotted against the number of iterations. The SAE model demonstrates high learning ability, as evidenced by the sharp decrease in both training and validation loss values, which stabilize at approximately 3 and 6, respectively, after 2000 iterations, while the training accuracy continues to increase. For all the statistical indices, the proposed method consistently achieves the highest values, with AUC, F1, kappa, precision, and recall values of 0.920, 0.850, 0.682, 0.821, and 0.886, respectively, for Lushan County and 0.972, 0.924, 0.845, 0.904, and 0.947, respectively, for Luding County. These results indicate that the proposed method outperforms other methods in terms of predictive accuracy and robustness. Furthermore, the AUC of the¹TrAdaBoost-RF (0.909)-based transfer learning method is lower than that of the³RF method (0.915), which explains why valuable landslide samples should be screened in the source domain. In addition, although the number of the¹RF and²RF datasets is larger than that of the³RF and⁴RF datasets, the AUC values of the¹RF (0.890) and²RF (0.935) datasets are lower than those of the³RF (0.915) and⁴RF (0.966) datasets.

Figure 9. Loss values of the SAE model training process.

5. Discussion

5.1. Importance of feature representation

Effective feature representation among environmental factors is beneficial for exploring latent information in complex and heterogeneous environments (Huang et al. 2022a, 2022b; Wang et al. 2020; Zhao and Chen 2023; Zhao et al. 2021). In this study, we first calculated FRs and KL values for the three study areas, which show the obvious effect of each environmental factor on landslide occurrence (Tables 3 and 4) and contribute to solving the problem of feature dissimilarity. The differences in FR values hinder the process of transfer learning between source and target areas. The enhancement of knowledge representation among environmental factors can be achieved with the optimal discretization method and knowledge extraction (Huang et al. 2020a, 2024; Zhao and Chen 2023). Therefore, we introduced the SAE algorithm, which can effectively explore the linear and nonlinear correlations among input variables and extract natural and deep features from unlabeled data to avoid incorrect label assignment and reduce bias (Huang et al. 2020b; Zhang, Isola, and Efros 2017). For instance, a study investigated the performance of combining a sparse autoencoder and support vector machine, which provided better feature descriptions than the original data (Huang et al. 2020b). In contrast to previous studies, we only regard the output features of the SAE model as the input variables of environmental consistency rather than the final features (Huang et al. 2020b; Nam and Wang 2020). The results also show that the SAE-RF model can extract multidimensional characteristics of the environmental factors (Figures 7(c,d) and 8(c,d)) and that the proposed method obtains the best AUC values (0.920 and 0.972) compared with traditional¹TrAdaBoost-RF and² TrAdaBoost-RF. Therefore, well-characterized features learned from original data can be used and provide insights into environmental similarity constraints. This can explain why the feature representation is considered in this study.

5.2. Importance of environmental consistency

The essential contribution of this study is that we propose a methodology for exploring feature representations and filtering similar data based on environmental consistency constraints. In this study, we successfully achieved knowledge transfer and extracted 2,130 and 120 useful samples from the Wenchuan dataset. The experimental results show that the AUC values of¹RF and² RF (0.890 and 0.935, respectively) are not improved by directly combining samples from the two study areas; instead, the proposed method has better performance than other methods. Thus, it is necessary to eliminate interfering samples by considering environmental consistency before knowledge sharing for different target areas. This is why we considered the SAE model and added environment-related similarity indices to the ESC to improve the interpretability of the proposed method. Although many studies have considered various unsupervised methods in LSP (Huang et al. 2020b; Nam and Wang 2020), a mathematical procedure based on ESC for filtering effective samples in the source domain has not been considered. Previous studies have developed only environmental similarity calculations that derive the best performance susceptibility results (Wang, Goetz, and Brenning 2022; Zhao et al. 2021, 2023b; Zhu et al. 2020). This study proposes filtering useful landslide samples in the source domain, which explains when, where and how knowledge in the source area transfers to the target area with limited data. In addition, environmental consistency or dissimilarity is a critical factor for model transferability (Wang, Goetz, and Brenning 2022; Zeng et al. 2022). The introduction of ESC may be able to handle negative transfer via overall environmental similarity calculations, suggesting the suitability of samples adopted in different study areas (Yates et al. 2018).

5.3. Future research

There are some potential improvements that can be considered in future work regarding transfer learning analysis.

First, more feature-related or process-related indices can be considered in the selection of similarity samples. The essential attributes among landslide-predisposing factors cannot describe complex and heterogeneous geographic environments (Masrur et al. 2022; Wang et al. 2020; Zhao et al. 2023b), and we recommend the extraction of more spatial features to help differentiate useful samples.

Second, we assumed that all landslide-related environmental factors in the source and target domains were identical. However, the physical processes of landslides in different areas are different, and we cannot guarantee that the same factor has a uniform effect on the spatial prediction of landslides. Accordingly, a suitable landslide-related environmental factor should be implemented in model transfer rather than all variables considered for use in the transfer process (Liang, Qin, and Zhu 2021). In other words, a more likely transferable approach should focus on the selection of features, as well as individual variables.

Third, relationship-based transfer, which is a type of physical landslide process, can be considered in the LSP. Therefore, landslide spatial prediction utilizing multiple landslide inventories is promising.

6. Conclusions

This study proposes and assesses a heterogeneous transfer learning method considering feature representation and environmental consistency to improve the robustness and transferability of spatial landslide predictions. The proposed method trains a stacked autoencoder to extract more representation features in an unsupervised manner, and then an environmental similarity criterion is implemented to filter valuable landslide inventories in the source area. Previous studies have not differentiated transferable landslide data and have directly adopted all data in the process of transfer learning. An extensive case study shows that the proposed method has better robustness and transferability than the other three methods. First, a stacked autoencoder can effectively extract latent knowledge from the source domain. Second, the introduction of the environmental similarity criterion filters the useful landslide samples in the source domain to avoid negative transfer learning. As a result, the proposed method can not only be applied to emergency rescue and disaster prevention but can also provide a promising way to improve landslide predictions of models in incomplete landslide inventories. Future work can be dedicated to advancing this transferring approach by considering more suitable relationship-related transfer learning methods and covering more transferable landslide datasets for different areas.

Data and code availability statement

The experimental data and the software source codes can be obtained at https://github.com/millet5818/TL_LSM.

Highlights

1. A heterogeneous transfer learning method considering feature representation and environmental consistency is proposed.

2. A stacked autoencoder can effectively extract latent knowledge from the source domain.

3. The environmental similarity criterion filters the valuable samples to avoid negative transfer learning.

4. The proposed transfer learning contributes to improving the performance of landslide spatial prediction.

Acknowledgments

We thank the Lushan Natural Resources and Planning Bureau, Lushan Public Security Bureau, Lushan Transportation Bureau, Ya’an Public Meteorological Service Center, Sichuan Institute of Geological Survey, China Earthquake Network Center, Geospatial Data Cloud Website, United States Geological Survey, and European Space Agency for providing the data needed for the experiments. In addition, we thank Mr. Yulong Qin for his warm support during the experiments. This study was supported by the Project of Sichuan Science and Technology Program [Grant No. 2019YFG0187]. The authors are grateful to the editor of the journal and the anonymous reviewers for their valuable comments and recommendations.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Project of Sichuan Science and Technology Program [2019YFG0187].