“Ensembled transfer learning approach for error reduction in landslide susceptibility mapping of the data scare region”

Table of Contents

Independence and Importance of LCFs

The independence of the LCFs is essential for effective model performance. Multicollinearity was checked by calculating the variance inflation factor (VIF) and tolerance for the LCFs. The results showed that the considered factors had no such issue of multicollinearity for both the source and target areas. In the source area, plane curvature obtained the highest VIF value of 1, in target areas 1 and 2, relief had the highest VIF value of 2.61, and the topographic wetness index had highest VIF value (2.96) (Table 1). However, the lower values of VIF suggested no such issue of multicollinearity between the dependent and independent variable.

Table 1 Multi-collinearity test for factor independence.

Machine learning and deep learning methods manifest the non-linearity between the variables; however, they are black boxes in nature and do not provide any insight related to the participation of individual factor in final prediction. Thus, feature importance of LCFs was calculated using the information gain ratio (Fig. 9). The IG value obtained for the source area (Mandi) demonstrated the higher contribution of factors such as distance to road (0.225), distance to lineament (0.116), aspect (0.115) and slope (0.097), depicting the occurrence of landslides along the road. Similarly, for distance to road, lineament aspect and slope were among the highest contributors in final prediction for target area 1. Contrastingly, in the case of target area 2, the topographic wetness index was highest contributor in landslides followed by other factors such as distance to road, distance to lineament and plane curvature (Fig. 9).

KL divergence

The Kullback–Leibler (KL) divergence measure was used to estimate the degree of entropy and similarity between the variables of the source and target areas. Although there is no upper bound to the value of KL divergence, it is important to note that a higher value of KL divergence corresponds to the least similarity between two distributions. In this study, KL divergence was calculated between the LCFs of the source and target areas (Table 2). Lithology showed the lowest KL value of 1, with the highest being 2.74 for distance to road, followed by relief (2.66), distance to stream (2.57), and distance to lineament (2.52) (Table 3). Thus, the results depicted the presence of similarity, if not exact, between the two areas in terms of topography, hydrology, and geology (Table 2).

Table 2 Table showing the KL divergence for LCFs for source and target area.

Table 3 Statistical details for LSM obtained using random forest and multi-layer perceptron method.

Random forest

The LSMs obtained using random forest (RF), were classified into five classes using the natural break classification method. The minimum, maximum, mean, and standard deviation are shown in the table (Table 3a). In LSM obtained for source area, 12% of the area covered in very high susceptibility, high susceptibility covered 16% area, while low and very low covered 51% area (Fig. 10a). In LSM of target area 1, trained from the data itself, very high susceptibility covered 10% area, high and medium susceptibility covered 28%, and 62% area was classified into very low and low susceptibility classes (Figs. 10a, 11a, 12a). Furthermore, when the source-trained model was applied on target area 1, very high susceptibility covered 16% of the area, 21% with high susceptibility, 22% with medium susceptibility and 40% area with very low and low susceptibility (Figs. 11b, 12ac). An increase of 3% area was observed in very high susceptibility, 4% in high susceptibility followed by a 2% increase in medium susceptibility. The increase in the areas of classes can be attributed to the scarcity of the landslide data in these areas which contrastingly present in the source trained model. Finally, when the landslide information from the source as well as target was used to prepare LSM of target area, 13% area was classified as very high, high 14%, 19% as medium and 52% as very low and low susceptibility (Figs. 11c, 12a). A significant decrease was observed when combined trained model were used, which was also concordant with the percentage values of LSM of the target area trained from the data itself. Furthermore, for target area 2, when random forest was trained, 5% of the area covered very high susceptibility, 15% area covered high susceptibility, 25% medium susceptibility (Figs. 12ba, 13ac). When random forest model was trained from the source area and applied to target area 2, very high susceptibility covered 7%, 18% in high susceptibility, 22% with medium susceptibility and very low and low susceptibility covered 51% of the total study (Figs. 12b and 13b). Finally, when the random forest model was trained using the data from the source as well as the target area , very high susceptibility covered 6% of the area, high and medium susceptibility covered 42% of the area while 49% area was classified as very low and low susceptibility (Figs. 12b, 13c). Notably, in source as well as the target area 1, the very high and high susceptibility were mainly concentrated in the proximity of roads as well as the rivers. Whereas in target area 2, high susceptibility was mainly concentrated along the river Mandakini, depicting the greater influence of river and topographic wetness index on landslide causation. Evidently, the very high and high susceptibility zones from the RF-TL and RF-Combined were nearly same as those obtained by LSM of target areas (Figs. 12b, 13c).

Multi-layer perceptron

Similarly, the LSMs obtained using the multi-layer perceptron (MLP) were classified into very less, less, medium, high and very high susceptibility classes based on natural break classification method (Table 3b). The LSM obtained for the source area, classified 17% area as very high, 13% into high and medium susceptibility, and 39% area as very low susceptibility (Figs. 10b, 12a). When the LSM was prepared for the target area 1 using the training data of itself, very high susceptibility covered 14% of the area while 9% area in high susceptibility, 11%, 16% and 48% area covered medium, high, and very high susceptibility (Figs. 11d, 12a). Further, LSM of target area 1 from the source-trained model, classified 29% area in very high and high susceptibility, while medium and very low and low susceptibility covered 14% and 46% of the target area respectively (Figs. 11e, 12a). Finally, the data from the source and target area were used to prepare the LSM of the target area, very high and high susceptibility constituted 21% of the area, medium covered 13%, low 18% and very low 47% of the target area (Figs. 11f, 12a). Additionally, in the case of target area 2, when LSM was prepared using the training data itself, 13% covered very high susceptibility, followed by 17% high susceptibility and 49% under very low and low susceptibility. When the source-trained model was applied in the area, 27% area classified as very high susceptibility, 15% were in high susceptibility, followed by 14% for medium susceptibility, and 16% and 26% for low and very low susceptible respectively. Also, when the LSM was prepared using the data trained from source and target area 2, 10%, 14%, and 12% area were classified into very high, high and medium susceptibility respectively, while 16% and 46% were classified as low and very low susceptibility. The results from the LSM indicated that when the source source-trained model was transferred in target area 2, the result tended to overestimate the very high and high susceptibility classes, while underestimating the low susceptibility regions (Figs. 12b, 13d–f).

Accuracy assessment and validation

The results from the LSM are utilized by planners and policymakers for future developmental strategies. For this reason, it is imperative to verify the results to ensure their reliability and credibility. Statistical tests, such as AUC-ROC, precision, recall, F-score, and accuracy, were employed to assess the performance of the LSM on unknown datasets during testing. The AUC value for the source area revealed an AUC value of 0.922 for RF and 0.917 for MLP, with precision, recall, F-score, and accuracy values of 0.856 each for RF (Fig. 14a), while MLP obtained a precision value of 0.832, recall of 0.856, F-score of 0.842, and accuracy of 0.844 (Fig. 14b). In the case of LSM prepared for target area 1 using the training data itself, obtained AUC values of 0.908 and 0.896 for RF and MLP, respectively. Precision values of 0.898 were obtained for both RF and MLP, with recall values of 0.851 for RF and 0.879 for MLP. F-score gave values of 0.874 for RF (Fig. 14a) and 0.888 for MLP, and accuracy values obtained were 0.87 and 0.844 for each model (Fig. 14b). Furthermore, when the source-trained model was applied to target area 1, results indicated an increase in the AUC value (0.942), precision (0.955), and F-score (0.876), was observed following up with a decrease in values such as recall (0.809) and accuracy (0.865). Lastly, for target area 1, when the knowledge from the source as well as the target, was used in LSM preparation, the AUC obtained was 0.959 for RF and 0.946 for MLP, whereas other statistical measures such as a precision value of 0.921 for RF and MLP, recall 0.82 and 0.901 for RF and MLP respectively (Fig. 14a, b). A slight decrease in the F-score was observed as 0.876 for RF, while an increase was observed for MLP as 0.911. Similarly, with in the case of accuracy as for RF accuracy was 0.859 and 0.91 for MLP (Tables 4a, b).Further to test the applicability of the proposed TL approach, the knowledge learned from the source were was used to in other areas. The target area 2 was Rudraprayag district located in the Uttarakhand Himalayas, with physiographic and geological conditions totally different form from that of the source area. The results depicted that when RF and MLP models were trained using the training data itself, RF obtained an AUC value of 0.95 (Fig. 14c)and 0.82 for MLP (Fig. 14d), while in the case of precision RF obtained 0.80 while MLP gave 0.84. Other statistical measures obtained recall values 0.75 and 0.84 for RF and MLP, F-score values 0.79 and 0.82, accuracy 0.82 each. Moving ahead when the source source-trained model was used in LSM preparation for target area 2, the AUC value was 0.80 for RF and 0.75 in the case of MLP., while the precision value for RF and MLP was 0.80 and 0.65, recall 0.89 and 0.71, F-score 0.76 and 0.68, and accuracy 0.72 and 0.66 for RF and MLP respectively (Fig. 14c, d). Moreover, when the knowledge from the source as well as the target area 2 was used, an increase in the AUC value was observed with 0.98 for RF and 0.84 in the case of MLP (Fig. 14c,d). Other statistical measure such as precision provided 0.88 and 0.81 for RF and MLP, whereas in the case of recall value for RF was 0.86 and 0.70 for MLP. While on the other hand, the F-score and accuracy value were 0.87 and 0.75 for RF and MLP each (Table 4a, b). The above result suggested that when the source trained was transferred and supplemented with the existing datasets, the model performance increases when compared with the LSM prepared from the training data itself. Contrastingly, when LSM was prepared for both the target area using the knowledge from the source-trained model, a decrease in the statistical measures was observed in both the case depicting differing geological, topographical, and physiographical conditions between the source and two target areas.

Table 4 Analysis results of statistical measures precision, recall, F-score and accuracy for models.

Additionally to validate the performance of the proposed TL we conducted field survey for landslides that were not considered in the model training and testing purposes for Mandi source domain (Fig. 15a and b), target area 1 (Kullu) (Fig. 15c–e) and target area 2 (Rudraprayag) (Fig. 15f–h).

Consistency assessment

Machine learning models being a data driven method are prone to data overestimation of susceptibility classes; thus, it is important to critically evaluate the results obtained from these models. Seed cell area index (SCAI) was used in this study to evaluate the consistency of the model. The SCAI value generated for the source area, the SCAI value ranged from 6.91 to 0.20, with very high covering 12% of the area and consisting of 60% landslides, while the SCAI value for target area 1, ranged from 34.27 to 0.14 (Fig. 16a). Further, when the source data was used, the SCAI value ranged from 15.61 to 0.20, a slight increase in the SCAI value for low susceptibility indicated slight overestimation in this class. However, the issue of overestimation was successfully removed when both the source data and the target were used to prepare the LSM, where the SCAI value ranged from infinite to 0.17 (Fig. 16b, c). An infinite SCAI value for the very low class in this case was attributed to zero landslide points falling the susceptibility class. Moreover, in the case of target area 2, the SCAI value decreased from very low susceptibility classes to very high susceptibility. Thus, the model gave a consistent result, classifying a greater percentage of low and very low susceptibility classes, and the least area in high and very high susceptibility classes, demonstrating the reliability of the LSM results.