Original Paper Landslides DOI 10.1007/s10346-015-0565-6 Received: 8 September 2014 Accepted: 12 February 2015 © Springer-Verlag Berlin Heidelberg 2015
Paraskevas Tsangaratos I Ioanna Ilia
Landslide susceptibility mapping using a modified decision tree classifier in the Xanthi Perfection, Greece
Abstract The objective of this study was to validate the outcomes of a modified decision tree classifier by comparing the produced landslide susceptibility map and the actual landslide occurrence, in an area of intensive landslide manifestation, in Xanthi Perfection, Greece. The values that concerned eight landslide conditioning factors for 163 landslides and 163 non-landslide locations were extracted by using advanced spatial GIS functions. Lithological units, elevation, slope angle, slope aspect, distance from tectonic features, distance from hydrographic network, distance from geological boundaries and distance from road network were among the eight landslide conditioning factors that were included in the landslide database used in the training phase. In the present study, landslide and non-landslide locations were randomly divided into two subsets: 80 % of the data (260 instances) were used for training and 20 % of the data (66 instances) for validating the developed classifier. The outcome of the decision tree classifier was a set of rules that expressed the relationship between landslide conditioning factors and the actual landslide occurrence. The landslide susceptibility belief values were obtained by applying a statistical method, the certainty factor method, and by measuring the belief in each rule that the decision tree classifier produced, transforming the discrete type of result into a continuous value that enabled the generation of a landslide susceptibility belief map. In total, four landslide susceptibility maps were produced using the certainty factor method, the Iterative Dichotomizer version 3 algorithm, the J48 algorithm and the modified Iterative Dichotomizer version 3 model in order to evaluate the performance of the developed classifier. The validation results showed that area under the ROC curves for the models varied from 0.7936 to 0.8397 for success rate curve and 0.7766 to 0.8035 for prediction rate curves, respectively. The success rate and prediction curves showed that the modified Iterative Dichotomizer version 3 model had a slightly higher performance with 0.8397 and 0.8035, respectively. From the outcomes of the study, it was induced that the developed modified decision tree classifier could be efficiently used for landslide susceptibility analysis and in general might be used for classification and estimation purposes in spatial predictive models. Keywords Landslide susceptibility . Decision tree . Certainty factor . Greece Introduction Landslides are considered as one of the most frequent and disastrous natural hazards worldwide (Schuster 1996; Glade et al. 2005). Already since the early 1990s, there was a keen interest in the international scientific community for the study of landslide phenomena, mainly because of the growing interest in the socioeconomic impact and the growing pressure in terms of development and urbanization of the environment (Aleotti and Chowdhury 1999). The proclamation of the decade 1990–2000 as the Decade for Disaster Reduction (International Decade for Natural Disaster
Reduction (IDNDR)) by the United Nations had a positive impact in encouraging the scientific community and all related communities to find solutions to the problem of natural disasters. The effort was focused on developing effective strategies for predicting and mitigating the effects of natural hazards. In the last two decades, the development of GIS data-processing techniques and the configuration of more advanced qualitative and quantitative techniques have allowed the production of numerous studies concerning landslide risk, hazards and susceptibility analysis (Van Westen et al. 2006; Fell et al. 2008). Assuming that landslides will occur in the future in areas that share the same conditions that produced them in the past, susceptibility assessments can be used to predict the geographical location of future landslides (Guzzetti et al. 1999, 2005, 2006). On this base, susceptibility zoning could be thought as a process that provides the spatial distribution and rating of the terrain units according to their propensity to produce landslides. Specifically, it refers to the process that provides highly valued knowledge that is influenced by topographical, geological-geotechnical, environmental and anthropogenic factors (Fell et al. 2008). Among the most used methods for the prediction of landslide susceptibility are those based on weighting the landslide-related factors using statistical and probabilistic techniques (Guzzetti et al. 1999; Lee and Min 2001; Lee and Pradhan 2007; Nandi and Shakoor 2010; Cervi et al. 2010; Pourghasemi et al. 2012a, b, c; Tien Bui et al. 2013; Sabatakakis et al. 2013; Tsangaratos et al. 2014; Pourghasemi et al. 2014). Specifically, numerous studies can be found that use bivariate statistical models (Thiery et al. 2007; Magliulo et al. 2008; Yilmaz et al. 2012), multivariate models that implement discriminant analysis (Lee et al. 2008) or linear and logistic regression (Dai and Lee 2003; Ayalew and Yamagishi 2005; Duman et al. 2006; Akgun 2012; Pourghasemi et al. 2013; Kavzoglu et al. 2014), frequency ratio (Lee and Sambath 2006; Lee and Pradhan 2006, 2007; Yilmaz 2010; Akinci et al. 2011), certainty factor approach (Binaghi et al. 1998; Lan et al. 2004; Sujatha et al. 2012; Devkota et al. 2013), Dempster-Shafer and weight of evidence models (Lee et al. 2004a; Tangestani 2009; Ilia et al. 2010; Park 2010; Neuhauser et al. 2012; Mohammady et al. 2012; Kouli et al. 2014). However, as stated extensively in the international scientific bibliography, the required spatial analyses during a landslide assessment deal with the manipulation of huge in volume geospatial databases where the traditional spatial analytical techniques, statistical and probabilistic methods cannot easily discover new and unexpected patterns, trends and relationships (Miller and Han 2001). An area of research that promises to overcome such difficulties is found in the domain of soft computing (SC). Specifically, SC has been applied for landslide susceptibility, hazard and risk evaluation. SC methods enable artificial neural networks (Lee et al. 2003; Ermini et al. 2005; Gomez and Kavzoglu 2005; Ferentinou and Sakellariou 2007; Caniani et al. 2008 ; Melchiore et al. 2008; Lee et al. 2004b; Marjanovic et al. 2009; Pradhan and Lee 2009, 2010b; Landslides
Original Paper Sezer et al. 2011; Tien Bui et al. 2012a; Zare et al. 2013; Tsangaratos and Benardos 2014), decision tree models (Flentje et al. 2007; Saito et al. 2009; Wan 2009; Nefeslioglu et al. 2010; Yeon et al. 2010; Tien Bui et al. 2012b; Tsangaratos 2012; Felicisimo et al. 2013; Pradhan 2013), fuzzy Logic approach (Juang et al. 1992; Binaghi et al. 1998; Ercanoglu and Gokceoglu 2002, 2004; Pradhan et al. 2009; Akgun et al. 2012; Pourghasemi et al. 2012a, b, c; Thiery et al. 2014), and neuro - fuzzy (Elias and Bandis 2000; Kanungo et al. 2006; Pradhan et al. 2010; Vahidnia et al. 2010; Oh and Pradhan 2011; Sezer et al. 2011; Tien Bui et al. 2012c; Pradhan 2013). Saito et al. (2009) utilized a decision tree (DT) model for landslide susceptibility mapping in the Akaishi Mountains, Japan, and concluded that the decision tree model produced results with appropriate accuracy for estimating the probabilities of future landslides. Yeon et al. (2010) applied a decision tree, using the Quinlan’s algorithm C4.5, to produce a landslide susceptibility map in Injae, Korea. After the tree construction process, leaf nodes were relatively evaluated by the m-branch smoothing method, a method utilized for representing susceptibility. The accuracy of a two-fold cross-validation was estimated to be 86.06 %, while the accuracy using all known data was estimated to be 89.26 %. Tien Bui et al. (2012b) investigated and compared the results of three data mining approaches, the support vector machines, decision tree and naive Bayes models for spatial prediction of landslide hazards in the Hoa Binh province, Vietnam. Although the DT was found to have the lowest prediction capability, it had three strong advantages: (a) easy to construct, (b) the resulting models could be easily interpreted and (c) the models provided clear information on the relative importance of the input factors. Pradhan (2013) also compared the prediction performances of three different approaches, decision tree, support vector machine and adaptive neuro-fuzzy inference system for landslide susceptibility mapping at Penang Hill area, Malaysia. For the decision tree model, the author selected the CHAID method for its accordance between its properties. According to the results, the DT model had a slightly higher prediction performance when the full ranges of factors were used. The main difference between the proposed methodology and the previously mentioned studies is that the modified DT grows in full extent, and to minimize the possibility of overfitting, a phenomenon that is responsible for poor prediction power, the certainty factor method, is implemented. The certainty factor method is a statistical method, for managing uncertainty in rule-based systems. In our implementation, the certainty factor value (CFv) for each class of each landslide-related variable is calculated. By combining the CFv pairwise, according to specific integration rules, the belief values of each decision rule that has been produced by the DT classifier are calculated. The final CFv expresses the landslide susceptibility belief value for each grid cell, and a landslide susceptibility belief map was produced with the use of GIS technology. To evaluate the performance of the developed methodology, the produced susceptibility map was compared with the outcomes of a DT model that follows the J48 algorithm. The computation process was carried out using WEKA ver.3.6.6 (Hall et al. 2009) for the J48 algorithm and the ID3 algorithm and Visual Basic ver.6.0 (Bradley and Millspaugh 2001) for the modified ID3 algorithm, while ArcGIS 9.3 (Ormsby et al. 2008) was used for compiling and analyzing the data and also for producing the landslide susceptibility maps. Landslides
The main objective of the present paper was to provide a methodological approach to predict the landslide susceptibility in an area of interest that is based on methods derived from the SC domain, such as those based on DT algorithms. The use of DT algorithms has received considerable attention in recent years in various geo-engineering applications, mainly due to their capability of solving problems and representing the solution in a rulebased format which can be easily understood and interpreted by humans. Study area and available data Study area The study area was the wider area of Perfection of Xanthi, between longitudes 560.000 and 600.000 and latitudes 4.584.650 and 4.557.250 using GGRS 1987 as the reference coordinate system, which covers approximately 800 km2. The area is bounded to the north by the Greek-Bulgarian borders and extended to the south up to the Neogene Thrace basin (Fig. 1). The area is characterized as highly mountainous, with elevation values ranging between 30 and 1.800 m. The geomorphological pattern includes gullies and small branches, a typical morphological pattern that is found in areas where impermeable rocks cover the surface. The mean annual rainfall of the area is approximately 1.100 mm, which mainly falls during the winter period (Ilias et al. 2000). The vegetation of the area is generally characterized as extensive, covering 60 % of land by broadleaf forests. The wider area exhibits moderate to low seismic activity. Data To extract the landslide parameters, a 1:50.000-scale topographic map and 1:25.000-scale engineering geological map were used. The ground conditions and the morphological settings of the area could be considered as the primary factors for numerous shallow and relatively small landslides triggered by physical (e.g. intense, short period rainfall) or man-made processes. The landslide conditioning factors involved a variety of input layers, some being directly digitized from the original thematic maps, while others were derived from spatial GIS calculations. All landslide conditioning factors were converted into a 20×20-m float-type raster file. These input-raster layers included: a lithological unit layer (LUL), a distance from geological boundaries layer (DGBL), a distance from tectonic characteristic layer (DTL), a distance from hydrographic network layer (DHNL), a distance from road network layer (DRNL), a slope angle layer (SANL), a slope aspect layer (SASL) and an elevation layer (EL). The most essential stage of the implementation is the process of dividing each input, raster layer into classes. Expert knowledge and statistical analysis could be useful means in defining the classes. Specifically, statistical measures in descriptive analysis that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. The mean, median, mode, the standard deviation, the range values of the variables, kurtosis and skewness were statistical measures that were estimated and helped to define the classes. The lithological data were obtained in the form of a digital vector map that had the same resolution and projection as those of the digital elevation model. The wider research area consisted of marbles and schists formations, magmatites, gneisses,
Fig. 1 The study area
amphibolites and ultra mafic rocks, of Palaeozoic age. Also, large areas are covered by tertiary mollasic and igneous formations (Liati and Seidel 1996). In the present study, the lithological unit layer was reclassified into five classes of different landslide susceptibility levels, namely, class A, formations of very low susceptible values (marbles, gneiss-leptinite), class B, formations of low susceptible values (tertiary conglomerate, schist-gneiss, dacite-andesite, gabbro-diorite, metagranodiorite), class C, formations of medium susceptible values (amphibolite, gneiss with intrusions of white coarse crystalline marble), class D, formations of highly susceptible values (granodiorite, ophiolite) and class E, formations of very high susceptible values (quaternary loose, flysch, migmatite and granite-gneiss) (Fig. 2a). The five landslide susceptibility levels were formed by combining our findings during the field survey and the geo-mechanical behaviour that has been described in previous studies contacted in the wider area (Ilias et al. 2000). As reported through the literature, the geological boundaries seem to have an influence on landslide occurrence (Kawabata and Bandibas 2009). It is believed that areas closer to geological boundaries have lower geo-mechanical values than the parent intact formation and as a consequence could be more susceptible to instability. In the present study, the Euclidean distance between each grid cell of the research area and the geological boundaries was calculated, and the areas were reclassified into three (3) classes A, B and C (Fig. 2b). The first class includes areas that are less than 200 m from geological boundaries, class B includes areas that have distance between 201 and 400 m, and finally class C, areas that are greater than 401 m. The range of boundaries for each class was based on the relative spatial distribution and the statistical indexes, like mean distance and standard deviation, of the landslide database. The tectonic characteristics, mainly faults, thrusts and overthrusts, were mapped based on field work and aerial photograph (Ilias et al. 2000). The research area was reclassified into three (3) categories, areas that cover zones that have distance less
than 250 m from tectonic features, areas that cover zones that have distance between 251 and 500 m and areas with distance greater than 501 m from tectonic characteristics (Fig. 2c). The range of boundaries for each class has also been based upon statistical analysis and the spatial distribution of the recorded landslides. It is common to appreciate that an area that is in proximity to hydrographic network is more likely to have higher water content than an area that is more distant from the network (Wan et al. 2010). This possibility may influence the stability of the area, since wet conditions affect the stability and the underground flow. In the present study, the values for each class were based upon expert knowledge and were attained by ArcGIS spatial module using the Euclidean distance between the sample grid cell and the nearest hydrographic network (Fig. 2d) producing four (4) classes (451 m). Road cuts are considered as sites of high instability induced by human intervention. According to Pradhan and Lee (2010a), a given road segment may act as a barrier, a net source, a net sink or a corridor for water flow, and it usually serves as a source of landslides. If a road is near a sample grid cell, the slope may present instability problems due to human disturbance (Fig. 2e). The layer was reclassified into four (4) classes, 601 m. The elevation of a surface is considered to be formed by the combined action of tectonic activity and weathering and erosion processes and is also related the action of the climatic conditions through a complex interactive influence (Dai et al. 2002). According to Pachauri and Pant (1992), altitude can be considered as a variable that indirectly contributes to the slope failure manifestation. In the present study, the elevation layer was classified into four (4) classes (801 m) based on expert knowledge and statistical analysis (Fig. 2f). The slope angle and the slope aspect were derived from DEM file using the second degree polynomial method of Zevenbergen and Thorne (1987) and were reclassified according to expert Landslides
Original Paper
Landslides
R Fig. 2
a Lithological units. b Distance from geological boundaries. c Distance from tectonic features. d Distance from hydrographic network. e Distance from road network. f Elevation. g Slope aspect. h Slope angle
knowledge and the local geological and geotechnical conditions. According to Rozos et al. (2006, 2008), in Greece, certain slope aspect is associated with increased snow concentration, with longer periods of freeze and thaw action and intensive erosion and weathering processes. For the purpose of the present study, the slope aspect layer was first classified into a 9 class layer (N-NE, NE-E, E-SE, SE-S, S-SW, SW-W, W-NW, NW-N and Flat) and then reclassified into four (4) classes with varying degree of landslide susceptibility (Fig. 2g). Class A 225°–270° (SW-W) low susceptibility, class B 45°–90° (NE-E) medium susceptibility, class C 90°–135° (E-SE), 270°–315° (W-NW) high susceptibility and class D 315°–45° (NW-N, N-NE) and 135°–225° (SE-S, S-SW). As for the slope angle layer, it was also reclassified into four (4) classes according to the local geological and geotechnical conditions (Fig. 2h). Class A (46°). The landslide inventory database was prepared in the form of a GIS geodatabase in which information about the location, features and abundance of 163 mapped landslides and 163 non-landslides locations were archived. The main landslide characteristics were described according to standard WP/WLI (1993) recommendations. Landslides in the research area were classified as rational (shallow) slide type and rapid earth—flows according to Cruden and Varnes Classification (1996) by analyzing airborne imagery, extensive field investigation and previous research studies (Ilias et al. 2000). The 163 non-landslide locations were identified though the use of a classifier that utilized a distance metric, the Mahalanobis distance, and provided areas of extremely low possibility of instability (Tsangaratos and Benardos 2014). From the contacted field survey, it was estimated that the largest landslide was approximately 3.200 m2 in size, while the smallest 285 m2 and that the average size of a typical landslide was about 1.950 m2. For the convenient of analysis, landslides are projected as areas that cover an area of 400 m2. In the case where the landslide is larger, more points were added in the inventory map. During the present study, it was also observed that slope instability phenomena are not only located in zones of previous landslide instability but also in zones where no activity has been reported. In most cases, the landslide activity affected urban and cultivated areas, linear infrastructures and civil engineering works. Decision tree and landslide susceptibility analysis A DT model appears with a hierarchical tree structure and is referred as a non-parametric method that is capable in identifying non-linear and non-additive relationships between input factors and targeting or predictive factors (Bell 1999; Jones et al. 2006). DT describes structural patterns in data, based on a set of rules (Witten and Frank 2005). The factors can be any type of factors from binary, nominal, ordinal and quantitative values, while the classes must be qualitative type (categorical or binary, or ordinal). For a given dataset of factors together with its classes, a DT produces a sequence of rules that can be used to recognize the class of unseen records (Murthy 1998). The structure or model and the possible consequence of decision tree can be explained in the form of a tree structure. The tree is composed of a root node, the top-most decision node which
corresponds to the best predictor variable, a set of internal nodes, decision nodes that have two or more branches and a set of terminal nodes, leaf nodes that represent a classification or a decision. Each node of the decision tree structure makes a binary decision that separates either one class or some of the classes from the remaining classes. The processing is carried out by moving down the tree until the terminal node is reached (Breiman et al. 1984). Several decision tree learning algorithms have been proposed, such as classification and regression trees (CART) (Breiman et al. 1984), Iterative Dichotomizer version 3 (ID3) (Quinlan 1986) and C4.5 (Quinlan 1993). They differ by the way they quantify the distinction and diversity criteria, but they all share a common hypothesis, that is, entities of the input dataset might be independent. The core algorithm for building a decision tree is called Interative Dichotomiser 3 (ID3) developed by Quinlan in the mid 1980s (Quinlan 1986). ID3 is a classical machine-learning algorithm for generating rules from decision tables, referred as an algorithm that employs a top-down procedure, and uses entropy and information gain as classification criteria in the search process (Quinlan 1986; Mitchell 1997). In information theory, a theory formulated by Shannon (1948), entropy is defined as a probability-based measure used to calculate the amount of uncertainty. If the impurity or randomness of a collection with respect to the target classifier is high, then the expected entropy is high, while if there is no randomness, complete uniformity-homogenous with respect to the target classifier then the entropy is zero. It is applied hierarchically at each level of the decision tree to aggregate the diversities exhibited by the supporting attributes at the top level of the hierarchy (Li and Claramunt 2006). Named after Boltzmann’s H-theorem, Shannon (1948) denoted the Entropy H as H ðDÞ ¼ −
n X
ð1Þ
Pi log2 Pi
i¼1
where n is the number of classes in the domain of the data set D; Pi the proportion of the number of class i elements over the total number of data set D. The information gain is used to measure the expected reduction in entropy at the immediate lower level of the hierarchy, where datasets are refined using another supporting attribute (Li and Claramunt 2006). Information gain can be written as GainðD; AÞ ¼ H ðDÞ−
X
jDv j H ðDv Þ jDj v∈ValuesðAÞ
ð2Þ
where values (A) provides the domain of supporting attribute (A); Dv denotes the subset of D where the corresponding value A is v for each record and |Dv| and |D| denote the cardinality of Dv and D, respectively. A typical tree generation process of ID3 algorithm is as follows: first, a condition attribute with minimal entropy of maximum information gain is chosen from a decision table. Then, this variable is used to divide the decision table into different classes. The above two steps are repeated until each record of the decision table only belongs to one of these classes. Once built, a decision tree can Landslides
Original Paper be used to classify data by starting at the root node of the tree and moving through it until a terminal node is encountered. Each terminal node provides a decision rule, or outcome, that allows us to make a predictive statement about the data. The next step is to choose variable with the highest information gain as the Bbest^ decision node. Best is defined by how well the variable splits the set into homogeneous subsets that have the same value of the target variable (Bin et al. 2004). In the past decade, DT was considered to be an unsuitable method to apply in spatial event prediction and landslide susceptibility analysis. This could be explained by the fact that DT models normally require a discrete type of output class, whereas when performing susceptibility analysis, we need the results to be represented as a continuous value (Yeon et al. 2010). Another characteristic that made the application of DT in landslide assessments problematic was the fact that when trying to estimate the ratio between landslide and non-landslide classes, the result showed the database to be highly imbalanced since landslides are represented in grid raster spatial data and are composed of a small numbers of pixels. Consequently, in this case, landslides were represented as a minority event class and were treated as noise, data with poor information (Yeon et al. 2010). A third point in which the implementation of DT could be proved to be inaccurate is the fact that the user has to confront a significant question about the optimal size of the final tree. A DT that is too large risks overfitting the training data and poorly generalizing to new testing samples. On the other hand, a small DT might not capture important structural information. However, it is hard to tell when a DT algorithm should stop training since it is not possible to evaluate if the addition of a single extra node will decrease the error of classification. On the other hand, DT models can incorporate both categorical and continuous factors without strict assumptions with respect to the distribution of the data (Bou Kheir et al. 2010). The outcome of applying a DT model is a set of rules that consists of an BAND^ combination of nodes from the root to the leaf. When a rule is interpreted, the use of all combinations of the node is needed, and so, the relationship among causal factors is implicitly included in the rule. More specifically, the implementation of a DT model made it possible to explain the relationship among the causal factors that contribute to the landslide phenomena, a process that other methods are not capable of doing (e.g. artificial neural networks). The objective of this study was to implement a method for landslide susceptibility analysis using a modified DT classifier, which followed the ID3 algorithm. A well-balanced landslide dataset with equal number of incidence that represented states of stability/instability was created and used to develop a full-grown decision tree. The leaf node ranking method for representing susceptibility values was achieved by applying a statistical method, the certainty factor (CF) method. The basic principles of the CF method were first introduced in MYCIN, an expert system for the diagnosis and therapy of blood infections and meningitis (Shortliffe and Buchanan 1975). Among the commonly used GIS analysis models for landslide hazard that follow the statistical approach, the CF model has been investigated by numerous researchers (Chung and Fabbri 1993, 1998; Binaghi et al. 1998; Luzi and Pergalani 1999; Lan et al. 2004; Gokceolu et al. 2005; Kanungo et al. 2011; Pourghasemi et al. 2012a, b, c). The CF method is one of the possible proposed favorability functions to Landslides
handle the problem of combination of different data layers and the heterogeneity and uncertainty of the input data (Lan et al. 2004). The CF, defined as a function of probability, was originally proposed by Shortliffe and Buchanan (1975) and later modified by Heckerman (1986) according to equation: 8 f i j −f > > > ; if f i j ≥ f > < f i j ð1−f Þ ð3Þ C Fi j ¼ f i j −f > > < f ; if f > i j > : f 1− f i j where CFij is the certainty factor that responds to a certain class i of variable j, fij, the landslide probability within the class i of the variable j, f, the landslide probability within the whole dataset. The probabilities are derived following a GIS procedure that overlays each landslide-related variable with the landslide inventory layer and calculates the landslide occurrence frequency. The positive outcome as mentioned above represents an increasing certainty in causality, while negative values correspond to the opposite, where the presence of the rule tends to disfavour the occurrence of a landslide. A value close to zero means that it is difficult to give any indication about the causality. Next, the CF values of the causative factor are pairwise combined using the CF combination rule. A combination of two CF values, x and y, from two different layers of information is a CF value z obtained as follows (Chung and Fabbri 1993; Binaghi et al. 1998; Luzi and Pergalani 1999): 8 x þ y−xy x; y ≥ 0 > > < xþy ; x; y opposite sign ð4Þ z ¼ 1−minðjxj; jyjÞ > > : x þ y þ xy x ; y 〈0 The final outcome measures the belief in the observed outcome. The belief of a rule ranged between a value of −1, which expressed decreasing certainty in landslide occurrence, and a value of +1 that expressed increasing certainty in landslide occurrence. The CF method calculated the certainty factor value (CFv) for each class of each landslide-related variable, and after combining the CFv pairwise according to specific integration rules, it measured the belief of each decision rule that was produced by the DT classifier. The final CFv expresses the landslide susceptibility belief value for each grid cell, and a landslide susceptibility belief map was produced with the use of GIS technology. Procedures and methods The developed framework could be separated into a five-phase procedure: (a) the data preparation phase, (b) the phase of estimating the CF method values, (c) the phase of constructing the rule database though the application of a DT classifier and estimating the belief values of each rule, (d) the phase of reclassifying and constructing the landslide susceptibility belief map and (e) the performance and validation phase (Fig. 3).
The preparation phase The first phase involves a series of actions that assist in preparing the available data for further analysis. It begins with gathering the
objective of many information processing domains, particularly when applied to the analysis of financial, economical, health, environmental and demographic phenomena where the data are potentially large, complex and not easily observable (Li and Claramunt 2006). In general, classification refers to finding rules to assign data items into pre-existing classes (Miller and Han 2001). In this phase, the user creates a relational database using the dbf file that was made in the preparation phase. The objective is to initialize the ID3 algorithm in order to create a set of rules that assist into classifying unknown areas into the two distinctive states of stability, stable or unstable. The outcome of this phase is a single txt file that contains a set of rules that have the following format: ½A; B; C1 ; C2 ; …; Cn ; D
Fig. 3 Flowchart of developed methodology
data and creating a geodatabase, the common data storage and management framework for ArcGIS. In the next step of the preparation phase, the user needs to reclassify the layers, according to expert knowledge into classes. This step involves the utilization of the geoprocessing tool BExtract values from points^, found in the Spatial Analyst Toolbox. The tool extracts the cell values of a raster based on a set of point features and records the values in the attribute table of an output feature class. The process is repeated for each layer, and finally, a singe shapefile has been created including for each landslide and non-landslide location the cell values for each layer. The preparation phase ends with the action of exporting the shapefile into a dbf format file and also exporting each reclassified layer into ASCII format files for further analysis. In landslide modelling, the landslide data are split into two parts, training and validation datasets. In the present study, the two datasets, landslide and non-landslide points were randomly divided into two subsets: 80 % of the data (260 instances) were used for training and 20 % of the data (66 instances) for validating the developed classifier. Estimating the certainty factor values The second phase involves the estimation of the CFv for each class of each layer, according to the CF method (Eq. 3). The values are stored in the geodatabase in order to assist in calculating the leaf node ranking that corresponds to the landslide susceptibility belief values. Constructing the rule database and estimating the belief values of the rule database The third phase involves techniques that could be found in classification and cluster analysis, where traditional classification problems present a set of data to be separated into two or more different groups. Classification of multi-attribute data is an
ð5Þ
where A = the id of rule, B = the number of the leaf, Ci = the number of the class (i=B) and D = (0,1) state of stability. The next step is to utilize the CF method combination rule (Eq. 4), in order to measure the belief of each rule that has been produced by the DT classifier. Table 1 shows the description and range of belief values that the produced rules may be assigned. The belief of a rule range between a value of −1, which expressed decreasing certainty in landslide occurrence, and a value of +1 that expressed increasing certainty in landslide occurrence. If the estimated belief value range between −0.05 and +0.05, then there is much quantity of uncertainty in the rule. Those rules that are characterized by uncertainty are excluded from the next phase. The classification and landslide susceptibility belief mapping phase The next phase was to combine all the weighted rules (Eq. 6) and produce the landslide susceptibility map. Each grid of the final landslide susceptibility belief map obtained a value that ranged between −1 and +1, whereas −1 corresponds to the most stable conditions and +1 corresponds to the most critical value of slope instability. 1X rule j n j¼1 n
LSBgrdi ¼
ð6Þ
where grdi the ith grid cell, rulej the jth rule. In order to proceed easily to the interpretation of the cartographic product, a zonation procedure was enabled by dividing the belief values into different susceptibility classes. The result of the Table 1 Certainty classes (Luzi and Pergalani 1999; Lan et al. 2004)
Description
Range values
Very low certainty–stable conditions
−1.0 to −0.5
Low certainty–moderate stable conditions
−0.5 to −0.05
Uncertain
−0.05 to +0.05
High certainty–moderate unstable conditions
+0.05 to +0.5
Very high certainty–highly unstable conditions
+0.5 to +1.0
Landslides
Original Paper reclassification procedure was to provide five classes of susceptibility, namely, very low, low, medium, high and very high susceptibility, using the Jenks natural breaks classification method (Jenks 1967; Ayalew and Yamagishi 2005; Akgun et al. 2012; Jaafari et al. 2014). The performance evaluation and validation phase The reliability of the developed model was evaluated by estimating the Cohen kappa index (k) (Cohen 1960; Hoehler 2000; Guzzetti et al. 2006; Tien Bui et al. 2012d). The Cohen kappa index was useful in order to estimate the model classification power compared to chance selection. In our case, a k value close to 0 indicates that no agreement exists between the landslide model and reality whereas a k value close to 1 indicates a perfect agreement (Landis and Koch 1977) (Table 2). k¼
Pc −Pexp ; 1−Pexp
ð7Þ
where Pc ¼
TP þ TN TP þ TN þ FP þ FN
Pexp ¼
ð8Þ
ððTP þ FN Þ*ðTP þ FPÞ þ ð FP þ TN Þ*ð FN þ TN ÞÞ sqrt ðTP þ TN þ FP þ FN Þ
ð9Þ
TP stands for true positive, when the outcome from a prediction is p and the actual value is also p. If the actual value is n, then it is said to be a false positive (FP). Conversely, a true negative (TN) has occurred when both the prediction outcome and the actual value are n, and false negative (FN) is when the prediction outcome is n while the actual value is p (Fawcett 2004). The sum of the four entries tp, tn, fp, fn equals the number of the test examples. The next procedure is to validate how well the modified DT classifier had classified the research area according to the susceptibility classes produced and the cumulative percentage of the observed landslide occurrence. An ideal landslide susceptibility map must have an increasing landslide density ratio when moving from low susceptible classes to high susceptible classes and satisfy two spatial effective rules (Can et al. 2005; Pradhan and Lee 2010b): the identified landslide areas should occupy areas of high susceptibility class and the high susceptibility class should cover small Table 2 Model classification power k values (Landis and Koch 1977)
k value
Agreement
0.8–1.0
Almost perfect agreement
0.6–0.8
Substantial agreement
0.4–0.6
Moderate agreement
0.2–0.4
Fair agreement
0.2–0.0
Slight agreement
Landslides
extent areas. The validation process was performed by comparing the produced landslide susceptibility map with the actual landslide locations using the success rate and the prediction rate methods (Chung and Fabbri 2003). The success rate curve assesses how many incidences, from the training dataset, are successfully captured by the susceptibility map and represents a measure for model efficiency. In order to estimate the predictive rate, the validation dataset is used. The prediction rate curve describes the percentage of correctly classified landslide incidence. It can be assessed how Bunknown^ landslide could be predicted. Analytical results—preparing the database and mapping the landslide susceptibility belief map Table 3 illustrates the estimated CF values for each class of each layer, according to the CF method (Eq. 3). Class D of the lithological unit layer, which corresponds to geological formations of highly susceptible values such as granodiorite and ophiolite, have the highest CF values (+0.4228). The next class with high value corresponds to the elevation layer and specifies the class with elevations between 401 and 600 m (+0.3418). According to the results, the slope aspect layer with classes that correspond to 45°–90°, 90°–135°, 270°–315°, 315°–45° and 135°–225° shows values near zero, indicating uncertainty in the prediction. The outcomes of the certainty factor method indicate that the class that corresponds with elevations greater that 801 m shows the most lowest CF value, −0.8745, followed by class A (marbles, gneiss-leptinite) with value equal to −0.7450 and the class that corresponds to distance from road network greater than 601 m (−0.6624). These three classes represent the most stable conditions. The next phase is to apply the ID3 algorithm in order to create the set of rules that assist into classifying unknown areas into two distinctive states of stability, stable or unstable. The constructed rule database was applied on training dataset and then validated into the testing dataset. The ID3 algorithm produced a total of fifty rules, twenty two of which indicated stable conditions and the remaining twenty eight indicated unstable conditions. The node rules were logical statements of the following form: Rule 1: If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS A THEN [STABLE]
As proposed by the methodology, the next step was to estimate the belief of each decision rule, by combing the CF values pairwise according to the specific integration rules (Eq. 4). The outcome of this calculation was each rule to be assigned by a certainty belief value that corresponded to the landslide susceptibility, ranging from −1 that expresses absolute certainty of stability to +1 that expresses absolute certainty of instability. The first decision (rule 1) indicates that when an area is located having an elevation less than 400 m and also when the slope aspect is between 225° and 270° and slope angle less 15°, then the area is characterized as stable. To evaluate the belief of this statement, we calculate the CF value for the first two classes found to be +0.010124. According to Table 1 classification scheme, the result is uncertain. As a result, the rule should be excluded from the analysis. Table 4 shows the produced set of rules which were applied along with the calculated CF values of each rule. Ranking the set of rules according to their CF values, rule 14 and rule 37 had the
Table 3 The CF values
Thematic layer Lithological units—LUL
Elevation— EL
Slope angle—SANL
Slope aspect—SASL
Distance from tectonic features—DTL
Distance from hydrographic network—DHNL
Distance from geological boundaries—DGBL
Distance from road network—DRNL
Class
Pixels in class
Landslides
CF
Class A
18584
1
−0.7450
Class B
265991
25
−0.5546
Class C
155050
44
+0.2563
Class D
24614
9
+0.4228
Class E
308186
84
+0.2257
801 m
226588
6
−0.8745
46°
132634
17
−0.3926
225°–270°
101361
15
−0.2987
45°–90°
94834
20
−0.0006
90°–135°, 270°–315°
166562
34
−0.0327
315°–45°, 135°–225°
409668
94
+0.0803
501 m
284084
42
−0.2994
451 m
399529
59
−0.3002
401 m
261831
37
−0.3303
601 m
112307
8
−0.6624
highest values. Rule 14 implies that areas having elevation ranging between 401 and 600 m with distance from road network less than 200 m, also with distance from tectonic features less than 250 m and covered by formations of very high susceptible values (quaternary loose, flysch, migmatite, granite-gneiss) are areas highly unstable. Rule 37 implies that areas located elevation ranging between 401 and 600 m with distance from road network less than 200 m and covered by formations of highly susceptible values (granodiorite, ophiolite) are also areas highly unstable. According to the proposed classification scheme of Table 1, ten (10) of the produced rules fall within the class Buncertain^ since the calculated values are in the range of −0.05 to +0.05.
The next phase was to combine all the weighted rules and produce the landslide susceptibility map, according to Eq. 6 (Fig. 4). The landslide susceptibility belief values were reclassified, using the Jenks natural break classification method into five classes of susceptibility, namely, very low, low, medium, high and very high susceptibility (VLS, LS, MS, HS and VHS, respectively). From the visual analysis of the final landslide susceptibility map, it illustrates a complex spatial pattern that does not follow the spatial distribution of any of the landslide conditioning variable. The estimated landslide susceptibility belief value is a product of the combined influence of each of the eight factors. Table 5 shows the relative landslide frequency as estimated for each Landslides
Original Paper Table 4 The produced set of rules and the calculated CF values
Rules id
Description
Calculated CF values
If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS A THEN [STABLE]
Uncertain
2
If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS B AND [LUL] is CLASS B THEN [STABLE]
Uncertain
3
If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS B AND [LUL] is CLASS E THEN [UNSTABLE]
Uncertain
4
If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS C THEN [STABLE]
Uncertain
5
If [EL] is CLASS A AND [SASL] is CLASS A AND [SANL] is CLASS D THEN [STABLE]
Uncertain
6
If [EL] is CLASS A AND [SASL] is CLASS B AND [LUL] is CLASS A THEN [STABLE]
−0.63289
7
If [EL] is CLASS A AND [SASL] is CLASS B AND [LUL] is CLASS C THEN [UNSTABLE]
+0.48340
8
If [EL] is CLASS A AND [SASL] is CLASS C THEN [UNSTABLE]
+0.28233
9
If [EL] is CLASS A AND [SASL] is CLASS D AND [SANL] is CLASS A THEN [UNSTABLE]
+0.48481
10
If [EL] is CLASS A AND [SASL] is CLASS D AND [SANL] is CLASS B THEN [UNSTABLE]
+0.43826
11
If [EL] is CLASS A AND [SASL] is CLASS D AND [SANL] is CLASS C THEN [UNSTABLE]
+0.34536
12
If [EL] is CLASS A AND [SASL] is CLASS D AND [SANL] is CLASS D THEN [STABLE]
Uncertain
13
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS A AND [LUL] is CLASS B THEN [STABLE]
−0.71199
14
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS A AND [LUL] is CLASS E THEN [UNSTABLE]
+0.65759
15
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS B THEN [UNSTABLE]
+0.58154
16
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS C AND [LUL] is CLASS B THEN [STABLE]
−0.38718
1
17
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS C AND [LUL] is CLASS C THEN [STABLE]
+0.45944
18
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS C AND [LUL] is CLASS D THEN [UNSTABLE]
−0.90179
19
If [EL] is CLASS B AND [DRNL] is CLASS A AND [DTL] is CLASS C AND [LUL] is CLASS D THEN [STABLE]
+0.43720
20
If [EL] is CLASS B AND [DRNL] is CLASS B AND [SANL] is CLASS B THEN [UNSTABLE]
+0.33578
21
If [EL] is CLASS B AND [DRNL] is CLASS B AND [SANL] is CLASS C THEN [UNSTABLE]
+0.23776
22
If [EL] is CLASS B AND [DRNL] is CLASS B AND [SANL] is CLASS D AND [LUL] is CLASS B THEN [STABLE]
−0.64159
23
If [EL] is CLASS B AND [DRNL] is CLASS B AND [SANL] is CLASS D AND [LUL] is CLASS E THEN [UNSTABLE]
Uncertain
24
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS A AND [LUL] is CLASS B THEN [STABLE]
−0.62862
25
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS A AND [LUL] is CLASS C THEN [UNSTABLE]
+0.10800
26
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS A AND [LUL] is CLASS E THEN [UNSTABLE]
+0.30766
27
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS B THEN [UNSTABLE]
+0.15829
28
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS C THEN [UNSTABLE]
+0.13039
29
If [EL] is CLASS B AND [DRNL] is CLASS C AND [SASL] is CLASS D THEN [UNSTABLE]
+0.22635
30
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS A AND [LUL] is CLASS B THEN [STABLE]
−0.83977
31
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS A AND [LUL] is CLASS C THEN [STABLE]
−0.5163
32
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS A AND [LUL] is CLASS E THEN [UNSTABLE]
−0.53541
33
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS B THEN [UNSTABLE]
Uncertain
34
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS C THEN [UNSTABLE]
Uncertain
35
If [EL] is CLASS B AND [DRNL] is CLASS D AND [SASL] is CLASS D THEN [UNSTABLE]
Uncertain
36
If [EL] is CLASS C AND [DRNL] is CLASS A AND [LUL] is CLASS B THEN [STABLE]
−0.33243
37
If [EL] is CLASS C AND [DRNL] is CLASS A AND [LUL] is CLASS D THEN [UNSTABLE]
+0.61484
38
If [EL] is CLASS C AND [DRNL] is CLASS B AND [LUL] is CLASS B THEN [STABLE]
−0.54966
39
If [EL] is CLASS C AND [DRNL] is CLASS B AND [LUL] is CLASS D THEN [UNSTABLE]
+0.42906
40
If [EL] is CLASS C AND [DRNL] is CLASS C AND [DGBL] is CLASS A THEN [UNSTABLE]
+0.11948
41
If [EL] is CLASS C AND [DRNL] is CLASS C AND [DGBL] is CLASS B THEN [STABLE]
−0.11081
42
If [EL] is CLASS C AND [DRNL] is CLASS C AND [DGBL] is CLASS A THEN [STABLE]
−0.39236
43
If [EL] is CLASS D AND [DRNL] is CLASS A THEN [STABLE]
−0.83779
44
If [EL] is CLASS D AND [DRNL] is CLASS B THEN [STABLE]
−0.89057
45
If [EL] is CLASS D AND [DRNL] is CLASS C THEN [STABLE]
−0.90179
46
If [EL] is CLASS D AND [DRNL] is CLASS D AND [DGBL] is CLASS A THEN [STABLE]
−0.94696
47
If [EL] is CLASS D AND [DRNL] is CLASS D AND [DGBL] is CLASS B THEN [STABLE]
−0.95848
48
If [EL] is CLASS D AND [DRNL] is CLASS D AND [DGBL] is CLASS C AND [DHNL] is CLASS A THEN [STABLE]
−0.95973
49
If [EL] is CLASS D AND [DRNL] is CLASS D AND [DGBL] is CLASS C AND [DHNL] is CLASS A THEN [STABLE]
−0.96262
50
If [EL] is CLASS D AND [DRNL] is CLASS D AND [DGBL] is CLASS C AND [DHNL] is CLASS D THEN [STABLE]
−0.98014
Landslides
Table 6 Comparing the accuracy and Cohen kappa index
Models
Fig. 4 The landslide susceptibility map of the modified ID3 DT
landslide susceptibility class were most of the landslides are located in the areas of high and very high susceptibility. The very high susceptibility class has the highest relative frequency 67.37 %, 93 landslide incidence. Validating the classifier and the produced landslide susceptibility map The efficiency of the modified ID3 DT model was estimated through the success rate curve using only the landslide data from the training database. The calculated value for the area under the curve (AUC) was estimated to be 0.8397 (Fig. 5). The predictive power of the model was estimated though the predictive rate curve using the landslide data from the validation database. The calculated value for the area under the curve (AUC) was estimated to be 0.8035 (Fig. 5). Finally, the reliability of the model was estimated by the Cohen kappa index (k) which was found to be equal to 0.9365 indicating an almost perfect agreement between the model and reality while the classified rate was estimated to be 96.82 % (Table 6). Comparing the performance of the modified ID3 model In order to compare the performance of the developed model with other techniques, we produced three landslide susceptibility maps utilizing the CF method, the J48 and the ID3 algorithm. The CF value of each class for all affecting factors has been already calculated during the second phase of the developed methodology (Eq. 3). The next steps involve combining pairwise each layer according to the integration rules, Eq. 4, and the calculation of Table 5 The relative landslide frequency
Description
Percentage of class (%)
Relative landslide frequency
Very low susceptibility
34.14
1.36 (5)
Low susceptibility
19.41
4.31 (9)
Medium susceptibility
12.81
5.08 (7)
High susceptibility
20.81
21.88 (49)
Very high susceptibility
12.83
67.37 (93)
tp
tn
fp
fn
accuracy
k
CF
22
29
9
3
0.8095
0.6190
ID3
32
27
1
3
0.9365
0.8730
J48
32
28
0
3
0.9523
0.9047
modified ID3
31
30
1
1
0.9682
0.9365
the landslide belief value for the whole set of the layers. As already mentioned, the belief ranged between a value of −1, which expressed decreasing certainty in landslide occurrence, and a value of +1 that expressed increasing certainty in landslide occurrence. The classified rate was estimated to be 80.36 % while the Cohen kappa index was estimated to be equal to 0.6073, characterizing the model as a model with substantial agreement. Concerning the initialization of J48 algorithm, the Java reimplementation of the C4.5 algorithm, the probability of belonging to the landslide or the non-landslide class for each observation was estimated using the Laplace smoothing. The selection of the most accurate model is achieved by determining the minimum number of instances per leaf and the confidence factor, two conditions necessary for the implementation of J48 algorithm. The highest classification accuracy 95.38 % was obtained with minimum instance per leaf of 9 and with confidence factor greater than 0.20. Using the same training and testing dataset, the decision tree was constructed. The size of the generated tree was seventeen including the root tree, with thirteen leafs. The Cohen kappa index was estimated to be equal to 0.9047, characterizing the model as a model with almost perfect agreement. Finally, the implementation of the ID3 algorithm estimated a classification rate equal to be to 93.65 % while the Cohen kappa index was estimated to be equal to 0.8730, characterizing the model as a model with almost perfect agreement. Comparing the four models, the modified ID3 DT model performed better than the J48, ID3 and CF model. It is also necessary to compare how well the modified DT classifier had classified the research area according to the landslide susceptibility classes produced and the cumulative percentage of the observed landslide occurrence, against the other three techniques. As in the case of the modified ID3 model, the validation process was performed by comparing the produced landslide susceptibility map with the actual landslide locations using the success rate and the prediction rate methods. Figure 6 shows the produced landslide susceptibility maps and Fig. 7 the success and prediction rate curve of the four models. The calculated value for each of the four models for the area under the curve (AUC) showed similar results. The efficiency of the modified ID3 was the highest among the models, followed by the J48 model (0.8220), the ID3 (0.8200) and the CF model (0.7936). Also, the predictive power of the modified ID3 was the highest among the models, followed again by the J48 model (0.8024), the ID3 (0.7983) and the CF model (0.7766). Discussion Soft computing methods take advantage of their highly accurate and learning ability and seem to be capable to extract patterns Landslides
Original Paper
Fig. 5 The success and prediction rate curve of the modified ID3 DT
from large amount of multi-thematic landslide data, making more precise predictions and providing a decision supporting tool for solving spatial problems. These advantages also affected the
Fig. 6 Certainty factor, J48 and ID3 landslide susceptibility map
Landslides
methods that were implemented in spatial analysis, allowing moving from a data-poor and computation-poor to a data-rich and computation-rich environment (Miller and Han 2001). In the case
Fig. 7 Comparing the four model success and prediction rate curve
of DT models, the applied algorithm makes no statistical assumptions for the frequency distributions of the data and can handle data that are represented on different measurement scales (Pal and Mather 2003). The main advantage is that a DT model represents the results that refer to estimating the order of importance for each explanatory variable in a tree structure format that is easily understood by humans (Witten and Frank 2005). The top-down induction of the decision, tree indicates that factors, in the higher order of the tree structure, are more important. In general, the DT model provides a visual interpretation and is thought to be a powerful predictive tool when compared with other approaches from the machine learning domain. Humans are able to understand more easily DT models. They require little data preparation, while DT can handle both numerical and categorical data. Landslide susceptibility analysis performed by DT algorithms has been proven to be a valuable tool. It is significant to point out that the quality of the available data and the expert’s judgment during the classification of the landslide conditioning factors are parameters that influence the degree of accuracy of any analysis. In our study, the outcome of the analysis performed by the ID3 algorithm was a set of rules that expressed the relationship between landslide conditioning factors and the actual landslide occurrence. This relationship was illustrated by a set of rules that assisted in classifying unknown areas into the two distinctive states of stability, stable or unstable. The top-most decision node which corresponded to the best predictor factor according to the developed DT model was the elevation layer. This was based on 326 input patterns; however, it is obvious that additional data may present a different factor as best predictor factor and also would certainly improve, in terms of predictive power, the outcome of the analysis. The advantage of the developed classifier is that it grows in full extent allowing the classifier to Blearn^ in depth from the available data. However, in order to minimize the possibility of overfitting, the belief values of each decision rule that has been produced by the DT classifier were calculated by using the CF method, allowing a mechanism analogous to pruning process.
The CF method is ideal for calculating the belief value since it sufficiently can handle the problem of combining different data layers and the heterogeneity and uncertainty of the input data. By this procedure, the discrete type of result was transformed into continuous values that express the landslide susceptibility belief value for each grid cell and enabled the generation of a landslide susceptibility belief map in GIS environment. It also made possible to exclude rules that, according to the CF method, have belief values that indicate uncertainty. Conclusion In the present study, a modified ID3 DT classifier was used to estimate the landslide susceptibility belief values of a certain research area, in Xanthi, Greece. A total of eight landslide conditioning factors were analyzed and included in the study, namely lithological units, elevation, slope angle, slope aspect, distance from tectonic features, distance from hydrographic network, distance from geological boundaries and distance from road network. The landslide inventory data were divided into two subsets, one for training (80 % of the total data) and one for estimating the prediction capabilities of the developed methodology. The overall accuracy of the developed classifier was calculated and reached 96 %, making the classifier a valuable tool that can be used efficiently in spatial prediction models. The qualitative interpretation of the produced landslide susceptibility maps provides strong evidence about how well the outcomes of the analysis agree with field evidence. When compared with the results obtained from the application of J48 algorithm on the same datasets, the prediction capabilities of the modified DT model were slightly better. The highest area under the success-rate curve is for the modified DT 0.8397 and for the J48 algorithm 0.8220. The highest area under the prediction-rate curve is for the modified DT 0.8035 and for the J48 algorithm 0.8024. The reliability of the developed technique was estimated through the Cohen kappa index (k) and was calculated to be equal to 0.9365. The value indicates an almost perfect agreement between the observed and the predicted values. Landslides
Original Paper The outcomes of the study indicated that the modified DT classifier could be appreciated as a useful tool for producing high accuracy landslide susceptibility maps and could provide valuable information to local authorities and government agencies that concern decision making and policy planning. Acknowledgments The authors would like to thank the Editorial Office of Landslides for editorial handling and also two anonymous reviewers for their helpful comments and suggestions that improved in quality the previous version of the manuscript.
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P. Tsangaratos ()) : I. Ilia School of Mining and Metallurgical Engineering, Department of Geological Studies, National Technical University of Athens, Zografou Campus: Heroon Polytechniou 9, 15780, Zografou, Greece e-mail:
[email protected] I. Ilia e-mail:
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