Keywords

1 Introduction

Landslides frequently occur in hilly region of Viet Nam causing loss of life and damage to property every year [1,2,3]. Most of these landslides are triggered by heavy rains during monsoon (from May to October) [4]. It is well known that rainfall-induced landslides cannot be prevented but can be predicted in regional scale by identifying high susceptible areas using GIS technology to minimize damages caused by future landslides [5].

In recent decades, many algorithms have been developed and applied to predict landslides which can be grouped broadly into three categories namely qualitative, semi-quantitative, and quantitative methods [6, 7]. Qualitative methods, which are based on expert’s perspective, often use landside inventories to predict locations having identical geomorphological and geological characteristics [8]. Semi-quantitative methods use the expert’s perspective in conjunction with the idea of weighting and ranking for predicting potential landslides [9]. Quantitative methods are based on the numerical analysis of the spatial relationship between affecting factors and historical landslides [10]. Out of these, quantitative methods are more objective and popular for landslide susceptibility modeling [11].

In literature, Support Vector Machines [12], Artificial Neural Networks [13], Decision Trees [14] are some of the most popular quantitative methods for landslide susceptibility modeling. However, in recent years, the hybrid models, which are a combination of ensemble techniques and individual classifiers, are considered more efficient than single models such SVM [15]. Therefore, in this study, we have proposed a novel hybrid model namely RSS-REPT which is a combination of two machine learning methods of Random Subspace (RSS) ensemble and Reduced Error Pruning Trees (REPT) classifier for landslide susceptibility modeling at the Mu Cang Chai district, Yen Bai province (Viet Nam). Predictive capability of this hybrid model has been validated using the Receiver Operating Characteristic (ROC) curve and Statistical Indexes (SI) analysis and its performance has been compared with SVM.

2 Methods Used

2.1 Random Subspace

Random Subspace (RSS) was proposed by Ho [16] to generate multiple feature spaces for constructing multiple decision trees in classification. Main objective of the RSS is to sample a feature set from the original high dimensional feature space into low dimensional subspaces on which classifiers are then constructed for classifying the classes, and, finally, the final decision is obtained by applying a majority voting rule for combining the generated classifiers [17].

More specifically, let each training sample set \( X = \left( {X_{1} ,X_{2} , \ldots ,X_{m} } \right) \) is an n-dimensional vector \( X_{i} = \left( {x_{i1} ,x_{i2} , \ldots ,x_{in} } \right) \, \left( {i = 1,2, \ldots ,n} \right) \), described by \( n \) features (landslide affecting factors). In the RSS, we randomly select \( r < n \) features from the n-dimensional dataset of the original p-dimensional feature space \( X \) to obtain the r-dimensional random subspace. Thus, the modified training dataset \( X^{e} = \left( {X_{1}^{e} ,X_{2}^{e} , \ldots ,X_{m}^{e} } \right) \) includes r-dimensional training objects \( X_{i}^{e} = \left( {x_{i1}^{e} ,x_{i2}^{e} , \ldots ,x_{ir}^{e} } \right) \). Thereafter, the classifiers are constructed in the random subspace \( X^{e} \), and combined by applying simple majority voting in the final decision rule as following [18]:

$$ \alpha \left( x \right) = \mathop {\arg \,\hbox{max} }\limits_{{y \in \left\{ {0,1} \right\}}} \sum\limits_{a} {\delta_{\text{sgn}} } \left( {C^{a} \left( x \right)} \right),y $$
(1)

where \( y \in \left( {0,1} \right) \) is a decision of the classifier, \( \delta_{ij} \) is the Kronecker symbol, \( C^{a} \left( x \right) \) are the generated classifiers \( \left( {a = 1,2, \ldots ,A} \right) \) [18].

2.2 Reduced Error Pruning Trees

Reduced Error Pruning Trees (REPT) introduced by Quinlan [19] is a combination of Decision Trees (DT) method and Reduced Error Pruning (REP) technique. The DT is one of the most popular classification tree methods for solving a lot of real world problems including landslide prediction [20]. However, it has a problem of producing the outcome of a large decision tree in classification. The REP is an effective machine learning technique in reducing the size of decision trees so that it can reduce the complexity of the final classifier [21]. It can also improve the predictive accuracy of the classifier by reducing the over-fitting and removing the tree sections which might cause the noisy or erroneous data [21]. Thus, the hybrid REPT method can give the desirable outcomes for classification problems. In this study, the hybrid REPT method has been used as a base classifier in ensemble framework for landslide spatial prediction.

2.3 Evaluation and Comparison Methods

In this study, the Receiver Operating Characteristic (ROC) curve and several statistical indexes have been selected for validating the performance of the novel hybrid model. Out of these methods, the ROC curve is one of the most popular quantitative evaluation methods in landslide susceptibility modeling. It is based on the graph which is plotted using two statistical values (“sensitivity” and “100-specificity”) [11, 22]. To validate quantitatively the predictive capability of the model, the area under the ROC curve called AUC has been used. Model has better performance as the AUC values closer to “1” [10, 23]. Models with high AUC values are better than those with lower AUC values. In landslide modeling studies, statistical indexes namely positive and negative predictive values, sensitivity, specificity, accuracy, kappa, and root mean squared error have been widely used for validating the performance of models [24]. These statistical indexes are calculated on the basis of calculation of the probability of pixels (landslide pixels and non-landslide pixels) in the relation with variable classes (landslide and non-landslide). Models with higher values of positive and negative predictive values, sensitivity, specificity, accuracy, and kappa have better performance than those with lower values. In contrast, models with low root mean squared error values have better predictive capability than those with high values. Models are perfect when the root mean squared error values are equal to zero.

In addition, the SVM, which is known as a benchmark single landslide model [12], has been selected to compare with the proposed hybrid RSS-REPT model. The SVM is a binary classifier which is based on the statistical algorithm to separate two classes (landslide and non-landslide) by hyper-plane in the original space [25]. This method has already been applied widely and efficiently in many landslide studies [26, 27].

3 Description of the Study Area

The Mu Cang Chai district (long. 103o56′00″E to 104o23′00″E and lat. of 21o39′00″N to 21o50′00″N), the study area, is located in Yen Bai province in the northern part of Viet Nam (Fig. 1). It covers an area approximately 1196.47 km2. The study area falls into the humid subtropical climate region having annual average humidity of 81% and annual average temperature of 25°C. There are two separate seasons in a year namely dry season (November to April) and rainy season (May to October). Heavy rainfall usually happens in the rainy season generally during August and September. The total annual rainfall varies from 3700 mm to 5490 mm. Excessive rains is the main triggering factor causing many landslides in this area.

Fig. 1.
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Landslide inventory and location map of the study area

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Fig. 2.
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Slope map of the study area

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Topography of the study area is adulatory. The study area is occupied by high mountain ranges and deep intervening valleys. Elevation varies in this area from 280 m to 2820 m. About eighty percent of the ground slope in the area varies from 10 to 40 degrees. Some of the hills are having very steep slopes up to 88 degrees.

The study area is occupied mainly by extrusive volcanic rocks of Ngoi Thia and Tu Le complexes. The intrusive magmatic rocks of Tram Tau formation and Phu Sa Phin complex occupy the smaller part of the study area. Terrigenous sedimentary rocks and Quaternary sediments are also present in the area (Fig. 3). Tectonically, the area is disturbed and dissected by various faults namely Nghia Lo, Nam Co- Minh An, and Phong Tho- Van Yen.

Fig. 3.
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Lithology and structure map of the study area

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4 Preparation of GIS Database

4.1 Landslide Inventory Map

Landslide inventory map has been constructed with 248 historical landslide locations which have been identified using Remote Sensing techniques based on the interpretation of 1:30000 scale air photos (Year 2013) and Google Earth images. Field investigation has been carried out to check and validate these landslide locations under the national project of Viet Nam named “Survey, assessment and zoning of landslide warning in the mountainous region of Vietnam” at Vietnam Institute of Geosciences and Mineral Resources. In the study area, the largest size of landslides observed is of 100000 m3 volume at the Che Cu Na commune (2011).

4.2 Landslide Affecting Factors

In the study area, fifteen landslide affecting factors namely slope, aspect, profile curvature, curvature, plan curvature, elevation, distance to rivers, distance to faults, distance to roads, river density, fault density, road density, lithology, land use, and rainfall have been selected for landslide susceptibility modeling (Table 1). Thematic data has been obtained from the Vietnam Institute of Geosciences and Mineral Resources for the development of raster maps of 20 × 20 m size for the GIS analysis in conjunction with Digital Elevation Model (DEM).

Table 1. Landslide affecting geo-environmental factors and their classes
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Lithology and faults have been extracted from the available geological and mineral resources maps of the study area (1:50,000 scale) (Fig. 2). Distance to faults and fault density maps have been generated by using buffer and density functions in ArcGIS application. Similarly, distance to roads, road density, distance to rivers, and river density maps have been generated for the analysis.

Land use map (Fig. 4) has been generated from the interpretation of 1:30000 scale air photos (Year 2013) and updated from Google images. Rainfall data has been extracted from the Global Weather data for SWAT [28] of 30 years (1984 to 2014), and used to generated rainfall map of the study.

Fig. 4.
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Land use/ land cover map of the study area

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5 Landslide Susceptibility Assessment Using a Novel Hybrid RSS-REPT Model

Landslide susceptibility assessment at the Mu Cang Chai district using a novel hybrid model RSS-REPT has been carried out in four main steps: (1) generating training and testing datasets, (2) constructing landslide model, (3) validating landslide model, (4) constructing landslide susceptibility map.

  1. (1)

    Generating training and testing datasets: Data collected from the study area has been processed to generate the training dataset and testing dataset. Training data set has been used to construct landslide models, and the testing dataset for validating models. For generating the training dataset, 70% of landslide locations (174 locations) have been selected randomly and remaining 30% landslide locations (74 locations) have been used to generate the testing dataset. These landslide locations have also been used to sample with landslide affecting factors for generating the final datasets for machine learning models.

  2. (2)

    Constructing landslide model: In this step, the training dataset has been used. The RSS ensemble has been applied to divide the training datasets into different sub-training datasets in different ways with different iterations. Simultaneously, the REPT classifiers have been applied using the generated sub-training datasets for classification. Finally, the RSS ensemble has been used to combine all generated REPT classifiers to construct the RSS-REPT model. For constructing the hybrid model RSS-REPT, the parameters of algorithms have been set using trial-and-error process as follows: the number of iterations to be performed is 24; the amount of data used for pruning (folds) is 10; the minimum total weight of the instances in a leaf is 2; and tree pruning is applied.

  3. (3)

    Validating landslide model: In this step, the testing dataset has been used. Predictive capability of the proposed model RSS-REPT has been validated using different evaluation criteria such as the ROC curve and SI analysis. In addition, the performance of the RSS-REPT has been validated by comparing with another well-known landslide model namely SVM.

  4. (4)

    Constructing landslide susceptibility map: Landslide susceptibility map has been constructed by generating and classifying landslide susceptibility indexes using the results of proposed RSS-REPT model.

6 Results and Discussions

6.1 Training and Validating the RSS-REPT Model

Results of training of the proposed RSS-REPT model are shown in Table 2 and Fig. 5. The results show that the values of statistical indexes and the ROC curve analysis using training dataset are high. More specifically, the positive predictive value is 79.89% indicating that the probability of classification of pixels to landslide class is high; the negative predictive value is 75.86% indicating that probability of classification of pixels to non-landslide class is high; the sensitivity value is 76.80% indicating that the probability of classification of landside pixels to landside class is high; the specificity value is 79.04% indicating that the probability of classification of non-landside pixels to non-landside class is high; the accuracy value is 77.87% indicating that the classification accuracy of the model is high; the Kappa value is 0.558 indicating that the results of the proposed model is reliable; the RMSE value is 0.384 indicating that the error of training model is relative low; and the AUC value is 0.896 indicating that the general performance of the model is very good.

Table 2. Model performance using training dataset
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Fig. 5.
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The ROC curve analysis of landslide models using training dataset

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Results of validating the proposed RSS-REPT model are shown in Table 3 and Fig. 6. The results show that the values of statistical indexes and the ROC curve analysis using testing dataset are high. More specifically, the positive predictive value is 79.73% indicating that the probability of classification of pixels to landslide class is high; the negative predictive value is 72.97% indicating that probability of classification of pixels to non-landslide class is high; the sensitivity value is 74.68% indicating that the probability of classification of landside pixels to landside class is high; the specificity value is 78.26% indicating that the probability of classification of non-landside pixels to non-landside class is high; the accuracy value is 76.35% indicating that the classification accuracy of the model is high; the Kappa value is 0.527 indicating that the results of the proposed model is reliable; the RMSE value is 0.419 indicating that the error of training model is relative low; and the AUC value is 0.835 indicating that the general performance of the model is good.

Table 3. Model performance using testing dataset
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Fig. 6.
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The ROC curve analysis of landslide models using testing dataset

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Based on the analysis of the results, it is clearly observed that the proposed hybrid model RSS-REPT has a good performance for landslide susceptibility modeling in the present study, even better than the benchmark model SVM. Outperformance of good hybrid model in comparison to single model has also been observed by other workers [3]. In the present case, the hybrid RSS-REPT model takes advantages of both state of the art machine learning methods of the RSS and REPT. More specifically, the RSS ensemble used in the hybrid model RSS-REPT is known as one of the efficient ensemble techniques which can help in improving the performance of the single models [7, 29]. It has been observed that the RSS ensemble might get the benefits by using random subspaces for building and aggregating the classifiers, especially in the case of datasets with many redundant features [18]. Moreover, the classifiers combined by the RSS in random subspaces might be superior to a single classifier built in the original feature space [18]. In addition, the REPT classifier used in the hybrid model RSS-REPT also has many advantages, which can enhance the predictive capability of the hybrid model, such as (i) the REPT is also a hybrid tree model of the DT and REP which can be utilized efficiently for complex classification problems including landslide prediction, (ii) the sub-trees constructed in the REPT can be adapted to characteristics specific to different subsets of the data; and thus producing more accurate results [19, 30], and (iii) it uses the REP technique which can help in minimizing the error from the variance [31].

6.2 Cartographic Generation of Landslide Susceptibility Map

Landslide susceptibility map is a great tool for land use planners and decision makers in landslide hazard management [32, 33]. In the present study, the landslide susceptibility map has been constructed using the proposed hybrid model RSS-REPT through two main steps. Firstly, landslide susceptibility indexes have been generated for all pixels of the study area. Secondly, these susceptibility indexes have been classified to construct the landslide susceptibility map (Fig. 7) with different susceptibility classes (very low, low, moderate, high, and very high) using geometrical interval method [34, 35].

Fig. 7.
figure 7

Landslide susceptibility map of the study area using the RSS-REPT model

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To validate the reliability of the landslide susceptibility map produced in this study, the landslide density analysis has been carried out on the basis of the analysis of the distribution of historial landslide pixels on susceptibility classes of the map. The results of landslide density analysis are shown in Table 4. It can be observed that the highest density of landslide pixels is on the very high susceptibility class (4.08), followed by the high susceptibility class (0.98), the moderate susceptibility class (0.62), the low susceptibility class (0.17), and very low susceptibility class (0.07), respectively. These results indicate the reliability of the landslide susceptibility map.

Table 4. Landslide density analysis on landslide susceptibility map
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7 Concluding Remarks

Landslide susceptibility modeling has been done at the Mu Cang Chai district, Yen Bai province (Viet Nam) using a novel hybrid model namely RSS-REPT which is a combination of two state of the art machine learning methods of the RSS ensemble and the REPT classifier. For validation, the ROC curve and several statistical indexes have been used. In addition, performance of the proposed hybrid model has been compared with another benchmark single landslide model SVM.

Result analysis shows that the proposed hybrid model RSS-REPT performed well for landslide susceptibility modeling. Its predictive capability outperforms the well-known landslide model SVM. Therefore, it can be reasonably concluded that the proposed hybrid model RSS-REPT is a promising tool for landslide susceptibility modeling which can be considered as a better alternative method for landslide hazard management also in other landslide prone areas.