Landslide susceptibility maps are important tools forterritorial planning. However, there are many openissues in their construction due to the complexity ofnatural processes in connection with their conditioningfactors and with the difficulties for the cartographicgeneralization of such variables. The need for predictingthe location of future landslides at basin scale requiresa quantitative methodology to model these complex
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phenomena from past events using data gathered in thefield or in laboratory. In this paper we propose aquantitative methodology to map the landslide suscep-tibility level given information from past mass move-ments and conditioning factors focusing on an automaticprocedure to choose the dataset. The procedure, whichinvolves the use of Artificial Neural Networks (ANNs)and Cluster Analysis (CA), demonstrates that an ac-curate sampling strategy improves the model results andincreases the landslide occurrence prediction.
ANNs have been widely used for landslide suscep-tibility zonation (Lee et al., 2003a,b; Lu and Rosen-baum, 2003; Lee et al., 2004; Ermini et al., 2005;Gomez and Kavzoglu, 2005). In fact, in indirect hazardmapping the landslide prediction should be based oncomplex, unknown, and non-linear relationships be-tween mass movement distribution and conditioningfactors. ANNs are data-driven models and universalnon-linear function approximators. The ability to learnnon-linear functions from the data is an important
Fig. 1. Schematic representation of an artificial neuron
feature in the problem of classifying landslide-proneareas. Moreover, a neural network does not requireassumptions about the input variable distribution orabsence of correlations between such variables. The useof the ANNs can be a valid alternative in the indirecthazard mapping, when the conditioning factors are notapproximable by a normal distribution and are stronglycorrelated.
Spatial data can have inherent uncertainty. Identifi-cation and mapping of landslides are subjective: suchan uncertainty is proved by large mismatches amonginventory maps produced by different research teams(Ardizzone et al., 2001). Other digital maps containerrors caused by measurement and interpolation errors(e.g., slope and aspect maps) (Heuvelink, 1993). ANNsare able to give a good prediction even though trainedwith noisy and uncertain data.
However, ANNs and other statistical methods needtwo kinds of samples to estimate the probability oflandslide: the first one must be representative of sliding
(a) and of a simple feed-forward topology (b).
Fig. 2. Location of the study area.
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conditions (presence of landslides), the second one mustbe representative of stability conditions (absence oflandslides). Whereas the dataset representative ofsliding conditions is known (landslide inventory map),the non-landslide set is usually obtained by randomsampling from the unlabeled data (pixels withoutlandslides).
In the present work we propose a strategy to samplefrom the unlabeled data by using an unsupervisedtechnique (CA), introduced in data pre-processing toanalyse the data structure before sampling the non-landslide cases. A domain-specific distance is intro-duced to improve clustering and to introduce expertknowledge in non-landslide selection.
2. State of the art
In recent years, the development of GeographicInformation Systems (GISs) and spatial analysis techni-ques has increased and improved indirect hazardmapping. The main reasons for such a widespread useof GIS technology are the efficiency in collection, manip-ulation, and analysis of data given by these software. Evenif there are many open questions in landslide hazardmapping, as widely discussed by Carrara et al. (1999), themodels obtained by means of spatial analysis show en-couraging outcomes.
The common idea of the statistical models used insusceptibility mapping is to estimate:
P Luajcf 1 uað Þ; cf 2 uað Þ; N N ; cfm uað Þð Þ ð1Þ
the probability that the unit analysis ua (i.e, pixel, unitcondition area) will be affected by landslide given the mvalues, one for each conditioning factor (cf). An area isclassified as susceptible when its terrain conditions arecomparable to landslide areas. Several frameworks havebeen introduced in order to analyse these terrain var-iables in relation to the mass movement distribution.Joint conditional probability function (Chung andFabbri, 1999), certainty factor function (Binaghi et al.,1998) and weights of evidence (Bonham-Carter, 1994)have been used to estimate the probability P in Eq. (1).Carrara (1983), and Carrara et al. (2003) presentedmultivariate statistical techniques to classify study areasaccording to conditioning factors.
In recent years, after the developing and the spread-ing of soft computing, fuzzy set theory, ANNs andgenetic algorithm were applied in different regressionand classification problems with GIS data, mainly fortheir capability of analysing heterogeneous and uncer-tain data (Lee et al., 1998).
Focusing on landslide hazard zonation, due to theircapability of being universal approximators, ANNswere used to study mass movements and to maplandslide hazard. In the work of Lu and Rosenbaum(2003), ANNs were introduced as a tool for the analysisand the prediction of future ground movements based ongeotechnical properties. The networks were implemen-ted as a tool to predict the Factor of Safety (FS) and thestate of stability (failed or stable); the capability of thenetworks to predict the FS as well as the stability of theslope was demonstrated. Lee et al. (2003b) developedlandslide susceptibility analysis techniques using amulti-layered perception (MLP) network. The resultswere verified by ranking the susceptibility index inclasses of equal area and showed satisfactory agreementbetween the susceptibility map and the landslidelocation data. Lee et al. (2003a) obtained landslidesusceptibility by using neural network models andcompared neural models with probabilistic and statisti-cal ones. Lee et al., (2004) developed a method tointegrate ANNs in calculating the Landslide Suscepti-bility Index (LSI). The network was built and trained inorder to find the weights of the relative importance ofdifferent factors for landslide occurrence. Such weightswere used successively for calculating the LSI. Erminiet al. (2005) used ANNs to classify terrain units con-sidering hillslope factors and applying two neural
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architectures: a PNN (Probabilistic Neural Network) anda MLP (Multi-Layered Perceptron) network. A goodprediction was achieved by the use of neural modelswith a slight preference for the MLP network. Finally,Gomez and Kavzoglu (2005) described an approach forassessing landslide risk by using parameters derivedfrom Digital Elevation Models (DEM), remote sensingimagery, and documentary data in a MLP.
Fig. 3. Geological map of the Brembilla Municipality with bedrock units showa 1:2500 scale (Azzoni and Agliardi, 2004).
3. Methodology
Traditional classification problems present a set ofdata to be separated into two or more different groups(i.e., the classes) through the use of a discriminative rule(i.e., the classifier) and a training algorithm used to learnthis rule. In the literature, different approaches to clas-sification have been proposed ranging from the early
n. This map was obtained through an original filed survey carried out at
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Decision Trees presented by Quinlan (1986) to recentdevelopments in support vector machines (Burges,1998) and artificial neural networks (Bishop, 1995).However, all these methods require the use of a set oflabelled data for each class.
With binary problems, in particular, we distinguishbetween positive and negative data, i.e., whether theybelong to the interest class, or not. When we have only aset of positive data and a set of unlabelled data (data we
Fig. 4. As is Fig. 3, but just showing th
can not yet classify as positive or negative), traditionalalgorithms cannot be used to effectively classify thedata. In fact, the lack of negative examples makes itmore difficult to build a classifier to partition theunlabelled examples into positive and not-positive caseswithout having a clear idea of the latter. Landslidesusceptibility zonation is one of the typical exampleshaving this type of problem. In fact, it is rather easy toidentify positive examples (i.e., areas where landslides
e Quaternary deposits of the area.
Table 1Frequency of active, stabilized, dormant, and inactive landslides in theBrembilla Municipality
Typology n° Area (m2) % Brembilla area
Active slide depletion areas 42 28,321 0.13Active slide accumulation areas 42 145,316 0.68Stabilised slide depletion areas 14 9606 0.05Stabilised slideaccumulation areas
15 47,548 0.22
Dormant slide depletion areas 51 16,941 0.08Dormant slideaccumulation areas
41 72,511 0.34
Inactive slide depletion areas 42 252,380 1.19Inactive slideaccumulation areas
26 610,118 2.87
Total 1,182,742 5.57Total areaBrembilla Municipality
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have already occurred), but difficult to identify statis-tically meaningful examples of stable areas.
In the past, several techniques were proposed to solvethis problem. The most common technique tries toidentify a set of negative examples by random samplingof the unlabelled data (i.e., areas where landslides havenot yet occurred), based on the assumption that theunlabelled data set contains a small number of positiveexamples and a large number of negative examples. Thedrawback of this technique is that false non-landslidecases could be selected worsening the discriminationcapabilities of the trained classifier. The main idea of thisresearch is to use an unsupervised technique to find outpattern distribution in the dataset, in order to captureaspects (presence/absence of landslides) in the datastructure and devise a sampling procedure able to improvethe performance of the final classifier.
3.1. Cluster analysis: the k-means algorithm
Clustering can be considered as the most importantunsupervised learning technique. As for any otherproblem in unsupervised learning, it deals with findingan unknown structure in a collection of unlabelled data. Aloose definition of clustering could be “the process ofcollecting objects into groups whose members are similarin some way” (Kaufman and Rousseeuw, 1990). The goalof clustering is thus to determine the intrinsic grouping ina set of unlabelled data and our intent is to exploit thisresult in order to reduce the number of erroneous samplesintroduced in the training set.
k-means (MacQueen, 1967; Hartigan and Wong,1978) is one of the simplest unsupervised learningalgorithms to solve a clustering problem. This procedurefollows a simple and easy way of classifying a givendata set through a certain number k of clusters (i.e.,prototypical samples) fixed a priori. Starting from arandom initialization the algorithm iterates two simplephases: takes each point belonging to a given data setand associates it with the nearest centroid and then,when no point is pending, recomputes the k newcentroids as the barycenters of groups resulting from theprevious step. After we have these k new centroids, newassociation phases are performed iteratively between thesame data set points and the nearest new centroid. As aresult of this loop we may notice that the k centroidschange their location step by step until no more changesoccur, i.e., the centroids do not move anymore.
This simple procedure can be viewed as a greedyalgorithm for partitioning the dataset into k clusters so asto maximize the similarity between objects in a clusterand its prototype, while minimizing the similarity
between cluster barycenters. In most cases, the similaritycriterion is distance, but how to decide what constitutes agood distance metric is not trivial. It can be shown thatthere is no absolute “best” metric which would beindependent of the final aim of the clustering (Romes-burg, 1984). Consequently, it is the final user who mustsupply this criterion, in such a way that the result of theclustering will suit the needs.
If the components of the data instance vectors are allin the same physical units then simple Euclidean dis-tance is sufficient to successfully group similar datainstances. However, in landslide susceptibility zonationthe variables used in classification are not immediatelycomparable. In this case, domain knowledge must beused to formulate an appropriate similarity measure. Inthe Section 4.3 we describe the metric used for the studyarea.
3.2. Artificial neural networks
ANNs are generic non-linear function approximatorsextensively used for pattern recognition and classifica-tion (Bishop, 1995; Haykin, 1999). A neural network is acollection of basic units, called neurons, computing anon-linear function of their input. Every input has anassigned weight that determines the impact this input hason the overall output of the node. In Fig. 1 (a) it ispossible to see a schematic representation of such anartificial neuron, where wji is the weight of the con-nection from neuron i to neuron j, and sj is the activation
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or output of neuron j. Unit j output is obtained by ideallyfollowing a two step-procedure. First the total weightedinput zj is computed using the formula zj=∑i wji siwheresi is the activity level of the i-th unit in the previous layerand wji is the weight of the connection between the i-thand the j-th unit. Then, the neuron output is obtained as anon-linear function (e.g., sigmoid or hyperbolic tangent)of the total weighted input zj minus a bias term.
Fig. 5. Landslide map overlaid on the hillshade DTM obtained from the 1:5landslides used in the analysis.
By interconnecting a proper number of nodes in asuitable way and by setting the weights to appropriatevalues, a neural network can approximate any non-linearfunction with arbitrary precision (Hornik et al., 1989).This structure of nodes and connections, known as net-work topology, together with the weights of the connec-tions, determines the final behaviour of the network.Fig. 1b describes a simple feed-forward topology (i.e., no
000 topographic map. The map shows active and dormant rotational
Table 2Erosion/weathering rating and permeability rating assigned to thegeological classes
Zu Limestone 0.40 Slope deposits 0.35Dolomie Zonate 0.30 Breccias slope
deposits0.35
Dolomia a Conchodon 0.20 Alluvialdeposits
0.25
Dolomia Principale 0.20 Coarse grainedslope deposits
0.25
(a) (b)
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loops are present)with a single hidden layer (i.e., a layer ofneurons neither connected to the input nor the output).Given a neural network topology and a training set, it ispossible to optimise the values of the weights in order tominimise an error function by means of any back-propagation algorithm (Rumelhart et al., 1986), standardoptimisation techniques (Press et al., 1992), or randomisedalgorithms (Montana and Davis, 1989).
The topology of a neural network plays a critical rolein whether or not the network can be trained to learn aparticular data set. A simple topology will result in anetwork that cannot learn to approximate a complexfunction, whereas a complex topology is likely to resultin a network losing its generalisation capability. Thisloss of generalisation is the result of overfitting thetraining data, i.e., instead of approximating a functionpresent in the data, the neural network memorises thetraining set resulting in inaccurate predictions on futuresamples. In this paper to improve generalisation we usethe early stopping technique (Caruana et al., 2000),consisting of using a validation set to stop the trainingalgorithm before the network starts learning noise in thedata as part of the model. The error on the validation setcan be used also as an estimate of generalisation errorand thus can be used to select a proper number of hiddenneurons.
4. Case study
4.1. Area description
The Municipality (Fig. 2) extends for about 20 km2
across the lower part of the Brembilla valley, which is partof the Brembo river catchment. The area, along thesouthern foothills of the Alps (Prealpi Orobiche), wasrecently stricken by heavy rainfalls (November, 2002),triggering several unexpected landslides. The middle-agevillage of Ca' Morone was partially destroyed during thisevent and the only main road was interrupted by alandslide for one month. Other landslides occurred allover the study area, which has been recently built up andindustrialized. Considering the morphological and geo-logical conditions of the Brembilla Valley, it is evidentthat slope stability processes are the most relevant prob-lem for public safety and land use.
4.2. Geological setting
The study area belongs to the frontal sector of theSouthern Alps, a Late Cretaceous to Miocene south-vergent fold and thrust belt (Forcella and Jadoul, 2000).The Brembilla valley consists of a thick carbonate and
shaly succession, ranging in age from Late Triassic toEarly Jurassic, forming an open NW-SE trendingsyncline. The lowermost unit, named Dolomia Princi-pale, consists of thick massive carbonates (100 m). It iscovered by well bedded dark limestones of the ZorzinoLimestone, about 100 m thick. Most of the study areaconsists of the Riva di Solto Shale (RRS). Its lowermember, 150 m thick, shows black shales with minorintercalations of marly limestones which grade intoshales, marly limestones, and calcilutites forming the250 m thick upper member (Jadoul et al., 1994). TheRRS passes upward to the Zu Limestone with 500 m ofmarls, bioclastic limestones and thick massive
Table 3Rating assigned to the land-use classes
Landuse Rating
Urban 1.00Bedrock 1.00Grass-pasture 0.75Uncultivate land 0.75Natural vegetation 0.75Orchard 0.60Newly reafforested land 0.60Forest 0.40Riverbed 0.00Lakes 0.00
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boundstones. Jurassic units form the highest part of theexposed succession and consist of the massive ooliticlimestones of the Dolomia a Conchodon (100 m)covered by well bedded cherty marly limestones of theSedrina Limestone.
The oldest units outcrop along the uppermost part ofthe eastern side of the Brembilla valley forming thenorthern limb of the fold with dips up to 45°, whereasthe western side and the central part of the valley showsthe youngest units. Vertical N-S and NNE-SSW strike-slip and normal faults cross the fold and bound itlaterally. The Jurassic units are exposed to the east.
The structural setting strongly controls landslideoccurrence. Most of the observed phenomena developedwithin the RRS, which is one of the most landslide-prone units in the region. This is due to the associationof intensively cleaved shales and marly limestones with
Fig. 6. MSE for the validation set of several neural arc
low geomechanical properties and the structural settingwhich favours the formation of bed-parallel slip causingrotational and complex slides especially along theeastern limb of the syncline. Earth-flow slides are alsofrequent due to deep weathering of this unit. It is worthnoting that the major slide of the area, the “Ca' Morone”slide, which caused major economic damages to thewhole valley developed in close association with theNE-SW normal and strike-slip fault which separates theRRS from the Zu Limestone. Rock falls are lesscommon and are related to the large rock walls formedby the massive carbonates which surround the valley.
4.3. Available data and conditioning factors
The cartographic database used in the analysis includesseveral maps (topographic, land use, geological andlandslides inventory maps) stored in a GIS and elaboratedto obtain input and output variables suitable to perform thesusceptibility analysis by means of ANNs. Six differentdata layers consisting of erosion/weathering rating, per-meability rating, landuse rating, cosine aspect, slope andcontributing area were obtained from the original dataand used as input variables. The presence/absence oflandslides layer was derived from the landslide inventorymap and used as the output variable.
The geological map was obtained through fieldsurvey (Azzoni and Agliardi, 2004) and was used toindividuate geological and geomorphological featuresrelevant to slope stability problems. Field mapping wascarried out at a 1:2500 scale. The geological units were
hitectures with different number of hidden units.
Table 4aWeights used to perform the cluster analysis
Aspect Contributing area Erosion/weathering rating Permeability rating Slope Land use rating
Weight 0.2 1 0.3 0.3 0.5 0.1
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classified according to their lithology, composition andorigin, on which their geomechanical and hydrogeolo-gical properties depend. The bedrock (Fig. 3) has beenmapped according to its litostratigraphic subdivisions,ranging from strong limestones and dolomites, to veryweak shales. Single rock outcrops have been distin-guished from partially covered discontinuous outcrops(maximum: 0.5 m soil cover thickness). Quaternarydeposits (Fig. 4), which are mainly related to slopeprocesses, cover most of the area. Due to the medium-high slope angle (28°) of the Brembilla valley,superficial deposits are usually quite thin; the thickestaccumulations occur at the bottom of the slopes, wherethey are generally rich in clay.
The landslide inventory map has been obtained fromfield survey combined with aerial photo interpretation(1:25,000 scale) and includes phenomena which aredistinguished according to their degree of activity andtypology. Active slides include all the areas where slopeinstabilities occurred in recent decades and are stillactive at present. The most important slides mainlycorrespond to rotational slides and earth flows. In mostcases they affect the soil cover and the uppermostweathered part of the shaly bedrock. They have beenalso observed in unweathered shale and limestone. Themajor slides are located around Cà Morone (rotationalearth slump), Val Porno, at Grumello village. Minorslides have been also recognised along the Brembillariver banks, in Valcava valley. Most of the major activeslides have been artificially stabilised in the last fiveyears. The most important ones are located near Laxolo(rotational earth slump), along the Valcava valley, nearLera (rotational earth slump), and near Garateno village(rotational earth slump and earth flow).
Table 4bExample of subdivision of the study area in 7 clusters and example of the v
Cluster 1 Cluster 2 Cluster 3 Cluster 4
Number of landslide pixels 239 0 321 495Number of absencelandslide pixels
63,123 78,065 144,424 153,311
Number of pixels 63,362 78,065 144,745 153,806Sampling condition (pc/pt) 0.04 0.00 0.05 0.08Verified sampling condition Yes Yes Yes Yes
Dormant slides include all the areas where slopeinstability phenomena have been clearly identified, butwithout any particular evidence of recent activity, suchas slope deformation, cracks in houses and roads, etc.No dormant slide showed any relevant movementduring the last major meteorological events (Autumn2000, November 2002).
Inactive slides show overall good stability condi-tions, with vegetation usually covering old slidefeatures. No reactivation is known from past historicalrecords. All these slides evolved within the Riva di SoltoShale outcrop area, except for the Passo del Canto rockslide, which evolved in the Zu Limestone and produceda wide accumulation of limestone blocks and can beclassified as a rock avalanche. Table 1 shows the fre-quency of active, stabilised, dormant, and inactivelandslides in the study area.
The 1:5000 topographic map (contour interval of 5 m)has been digitized in order to prepare a DTM of the area.The 1:10,000 scale land-use map (Regione Lombardia,1991) identifies areas with presence or absence ofvegetation. The areas covered by vegetation are distin-guished according to dominant species and naturalness ofvegetation. Before elaborating the landslide inventorymap to derive the output layer (presence/absence of massmovements), it was necessary to consider the type oflandslides. Since we decided to test the susceptibilityanalysis on a homogeneous data population, we haveselected only the rotational landslides that have occurredin the recent past from the landslide inventory map,including active and dormant slides (Fig. 5). This isjustified by the fact that the rotational landslides are themost common phenomena in the study area and that theinactive landslides may not be representative of the
erified sampling condition
Cluster 5 Cluster 6 Cluster 7 Total in theseven clusters
114,141 113,813 177,999 845,931 847,2810.00 0.28 0.55Yes No No
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present-day sliding conditions. The rotational landslidesanalysed are 118: their medium slope angle is 24° andtheir medium size is 440 m2. Most of the landslides aresmaller than 200m2. In order to givemore emphasis to thefailure conditions, we considered the highest part (50%)of each landslide unit (accumulation and depletion area).The output layer was obtained by assigning value 1 to thehighest part of the landslide part and value 0 to areas withabsence of mass movement.
Fig. 7. An example of subdivision of the study area in 7 clusters. Th
Slope, aspect and contributing area layers have beencalculated from the DTM. We chose the d-infinitivealgorithm to calculate contributing area (Tarboton,1997). We scaled the raw continuous data (slope, aspectand contributing area) into a range of 0–1. The aspectdata were scaled by means of the coseno operator, sinceits value distribution range is between 0° and 360° andvalues close to minimum of the range (0°) have the samephysical meaning as values close to the maximum of the
e landslides in the test set were excluded from the clustering.
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range (360°). Taking into consideration the landslidedistribution, the coseno operator is enough to discrim-inate between north-facing and south-facing slopes.
Categorical variables (i.e., geology, land-use) havebeen converted into numerical values by assigning a ratingto each class between 0 and 1. We chose this approach toreduce network complexity and improve classificationperformance.
Geological classes have been used to define land-slides susceptibility with their erosion/weatheringattitude and permeability using two different ratings,according to the approach suggested by Anbalagan(1992a,b). This author presents a methodology based onan empirical approach which combines past experiencesof the conditioning factors and their impact on landslideoccurrence in a study area. The main idea of that ratingscheme is to assign index values to each conditioning
Fig. 8. The two sampling procedures compared. (a) describes the classical ranthis contribution. Coloured boxes highlight the differences in the two algori
factors taking into consideration its influence on massmovements. We have converted the categorical vari-ables into erosion-weathering rating and permeabilityrating by following that numerical scheme.
The erosion-weathering rating was derived by con-sidering the response of rocks and deposits to theseprocesses. As several units with similar composition(limestones,marlstones, slates) form the substratum of thearea, the rating was based on their composition.Limestone is generally hard and massive, whereas theterrigenous rocks, as the RSS, are weak and often deeplyweathered and rotational landslides more easily occur inthat kind of rock. A rough estimate of the spacing of thebeds has also been taken into account, as a wide range ofconditions occur, from massive bedded (Dolomia Princi-pale, Dolomia a Conchodon) to finely stratified units(RRS). Loose deposits have been rated based on the
dom sampling procedure, whereas (b) shows the algorithm proposed inthms.
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relative abundance in fine-grained sediments (silt–clay/versus sand–gravel) and according to their consolidation.The maximum erosion-weathering rating was assigned tothe weakest degradable terrains (RSS-shaly and colluvi-um on shaly bedrock), as shown in Table 2a. The per-meability was scored by attributing the greatest rating toterrains prone to the development of high pore pressureconditions (RRS formation-shaly) and the lowest rating toporous and coarse-grained deposits (Table 2b).
The land-use rating layer was finally obtained fromthe land-use map again by using the method ofAnbalagan (1992a,b), which considers the type andstructure of vegetation, its stability or its absence. Sinceground cover affects erosion, weathering, fluctuation inthe water table, etc., and thus the stability of the slope,we assigned the maximum rating to areas devoid ofvegetation (Table 3). The minimum value was given toareas where landslides do not occur (i.e., lake andriverbed) and 0.4 value to forested areas with shade-treevegetation ensuring the maximum protection withrespect to superficial erosional processes. Intermediatevalues have been given to other classes.
5. Analysis and results
The ANN was trained with six network inputs(erosion/weathering rating, permeability rating, land-userating, coseno aspect, slope, and contributing area)scaled in the range 0–1 and the network output was alsodefined in the range 0–1 by setting the output value to 1for landslide presence and to 0 for landslide absence.
The analysis was performed using an MLP networkwith the Levenberg–Marquardt training algorithm (Mar-quardt, 1963; Hagan and Menhaj, 1994). We used theearly stopping technique (Caruana et al., 2000) to improvethe generalization of the network. Several structures with
different numbers of hidden units have been tested to findthe best one. Results are shown in Fig. 6. In the left part ofthe plot, the Mean Square Error (MSE) for the validationset decreases if the number of hidden units increases, i.e.,the higher the network complexity, the better theperformance on the validation set. In the right part ofthe plot the error increases, since the network is toocomplex and overfits the training data. The curve in Fig. 6has two minimums, the first one at 14 hidden units, thesecond one at 16. The structure with 14 hidden units hasbeen chosen, as it ensures the best generalization withoutexcessively increasing the network complexity.
Landslides from the output layer were subdivided intothree subsets: training, validation, and test set. By meansof random permutation, 100 different subdivisions of thelandslide dataset were found. Although the analysis wasperformed on a pixel-by-pixel basis, each landslide wasconsidered as a unit during the dataset subdivision.
To find clusters meaningful for the instability analysis,a measure based on variable domains and the importanceof each factor to landslide occurrence was used in thecluster formation. In order to identify similar objects, thedifferent variables have been differently weighted. Inparticular, a weighted sum of the absolute value of thedifference has been used as a distance measure:
D ¼X
kjxik � xjkjwk
where D is the distance between the two objects i and j,and k is the number of factors (variables). The weights(Table 4a) have been chosen considering the distributionof each variable in its domain with the aim of avoiding theformation of clusters over-influenced by the distributionof a single variable. In this particular case, weight valueshave been assigned in order to identify clusters showingthe separation of classes based on presence and absence of
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landslides. Landslides in the test sets have been excludedfrom the dataset and from the CA. They have been used tovalidate both the trained neural models and the effective-ness of the sampling procedure.
Wewant to underline that the weights are not assignedto the input of the model, so they do not represent theimportance (i.e., weight) of each factor for landslideoccurrence.Weights are considered only in the clusteringprocedure to define a proper similarity criterion.
Fig. 9. Plot of the mean values of the trained networks against the freq
Introducing a proper metric into CA allows us toidentify clusters in which the presence of landslidepixels is dominant. In fact, two of the seven clustersfound after performing CA contain the most of thelandslide pixels, as shown in Table 4b. Those clustershave to be excluded from the selection cases, since theyare representative of instability conditions. An exampleof the subdivision of the study area into the 7 clusters isshown in Fig. 7.
uency after random sampling (a) and after cluster sampling (b).
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For each of the 100 different landslide subdivisions,the procedures for random sampling and cluster samplingwere carried out as follows. In the random sampling, thenegative cases (stable pixels) were sampled from un-labelled data (pixels without landslides) by randomlyselecting 16,000 pixels and dividing those pixels intothree subsets (training, validation, and test set). In thecluster sampling, after excluding the landslide test setfrom the dataset, the k-means clustering was performed
Fig. 10. Output of the network classified into 3 ranges for the model afte
and the 16,000 negative cases were uniformly sampledonly from clusters in which the following ratio wasverified:
pcpt
b0:1 ð2Þ
where pc is the number of unstable pixels in the clusterand pt is the number of total unstable pixels in the trainingand validation sets.
r random sampling (a) and for the model after cluster sampling (b).
Fig. 10 (continued ).
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In order to compare classification results on manydatasets, we found two non-landslide sample sets for eachof the 100 subdivisions of all landslides: the first one wasobtained by random sampling, the second one by clustersampling (Fig. 8). The performance of the models afterrandom and cluster sampling was evaluated through thesensitivity, because the main aim of the proposedapproach is to improve landslide-prone area classification.Thismeans that sensitivity, i.e., the percentage of correctly
classified landslide cases, is the most useful measure tocompare random and cluster sampling strategies. Thesensitivity Sen (i.e., true positive rate) is defined as:
Sen ¼ TP
TPþ FN� 100 ð3Þ
in which TP represents the number of true positives(pixels with the presence of landslides classified as
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unstable) and FN represents the number of false negatives(pixelswith the presence of landslides classified as stable).
The single network outputwas used to separate the twoclasses. The first classification was obtained using 0.5 asthreshold. Output values in the range 0.5–1 represent thelandslide class and the values in the range 0–0.5 the non-landslide class. Table 5 illustrates the difference inperformance measures after random or cluster sampling.
Fig. 11. Susceptibility maps after random sampling (a) and after cluster sampli10% more susceptible area. There are some differences between the two mapsand the final response of the model.
A Student's t-Test shows that there is a significantdifference between the averages of the means of the twosamples with a p-level b0.0001. The minimum and themaximum in sensitivity show that the network is able toseparate stable and unstable classes only if it is trainedafter pre-processing data with CA. The mean value of thesensitivity after the random sampling is 35%. Randomsampling does not allow us to classify unstable pixels,
ng (b). The area more susceptible is the 0–0.1 class, which represent the: the different sampling strategy influence the behaviour of the network
Fig. 11 (continued ).
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since the network is not able to extract the features ofslope instability from the data. However, CA assists in theselection of non-landslide data and allows the ANNs tounderstand hidden data structures, which improves theclassification of unstable areas (Table 6).
One could think that after cluster sampling, thesensitivity increases since the ANN classifies all thesamples in the unstable area class. In order to disprovethat, performance measures were also calculated afterchoosing different cut-off points. In this case we also
kept in consideration also the specificity Spe (truenegative rate) defined as:
Spe ¼ TNTNþ FP
� 100 ð4Þ
The value (1−Spe) is the rate of false positives.Table 6 shows the performance measures, calculated
using different cut-off points. The mean sensitivity of the
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cluster sampling-ANN model does not significantlychange with the cut-off point. On the contrary, the meansensitivity of the random sampling-ANNmodel is strictlyrelated to the threshold chosen, demonstrating therobustness of the classifier trained after cluster sampling.
The trained networks were simulated for the wholestudy area. We have obtained two mean values for each
Fig. 12. The relationship between the output of the network and the susceptibrandom sampling — ANNs model some of the susceptibility classes are def
pixel in the study area, one by averaging the 100 networkstrained after the random sampling and one by averagingthe 100 networks trained after the cluster sampling. Themean value against the frequency after random sampling(Fig. 9a) shows that the output of the networks is close tolow values (stable areas) or close to 0.4. The value regionaround 0.5 is an uncertain region for the classifier. Fig. 9a
ility classes after random sampling (a) and after cluster sampling. In theined in the uncertain region of the classifier.
398 C. Melchiorre et al. / Geomorphology 94 (2008) 379–400
underlines oncemore that the neural classifier trained afterrandom sampling, is able to distinguish only the stableareas. In contrast, the frequency after cluster sampling(Fig. 9b) shows values close to 0 or 1 and the uncertainregions contain only a few pixels. A preliminary classi-fication of the twomean outputs in three classes,where theclass 0.4–0.6 represents the uncertain region of theclassifier, shows that the difference in the uncertain areasize between the random sampling (Fig. 10a) and thecluster sampling map (Fig. 10b) is evident. Looking at themap in Fig. 10, one could think that the neural classifiertrained after cluster sampling, only shifts the output tohigher values. In order to verify the shifting of the outputvalues, we have chosen two networks (one trained aftercluster sampling, one after random sampling) andwe haveanalysed the simulation (output values) of these networksfor the study area. Two susceptibilitymapswere produced,first ordering the output values in increasing order andthen ranking the values in classes with the same number ofpixels. The 0–0.1 class includes the 10% of the pixelswithhighest mean output value. The 0.1–0.2 class includes thefollowing 10% more susceptible, and so on. We obtainedtwo susceptibility maps, one for the random sampling-ANN model, shown in Fig. 11a, the second one for thecluster sampling-ANNmodel, shown in Fig. 11b. At eachpixel, we have two values: the output of the network andthe class value. Fig. 12 shows the scatter plot of thesepairs, each point represents one pixel in the study area. Thecurves in Fig. 12 express the relationship between theoriginal output values and the defined classes for therandom sampling-ANN model (a) and for the clustersampling-ANN model (b). The differences in thesusceptibility classes of the two maps (Fig. 11) provethat the neural classifier does not shift the output to highervalues, but it weighs the input variables in a different way.Since the sensitivity is highly increased (Table 5), it ispossible to conclude that the cluster sampling-ANNmodelis better to distinguish and classify landslide-prone areas.
6. Conclusions and discussions
Considering the satisfactory results achieved withMLP networks, we introduced an integrated use ofsupervised and unsupervised techniques to improve theresults of neural classifiers. Moreover, the use of adomain-specific distance introduces expert knowledge tothe black-box neural models which would allow exten-sion of the methodology to different study areas withdifferent conditions of mass movements. In this contri-bution particular attention was given to the choice of thesamples to use in a landslide susceptibility model. Weapplied a cluster sampling method before performing the
analysis by means of ANNs. However, it is important tounderline that such a method can be used for otherstatistical techniques (e.g., discriminate analysis, logisticregression, etc.), which need two sample groups toseparate and to classify cases into landslide and non-landslide groups. We have described a possible way tosample from unlabelled data that would be applicable inother case studies: the proposedmethod requires an expertknowledge of sliding conditions and a preliminaryanalysis of the domains of each conditioning factor.
We have demonstrated that an accurate samplingstrategy outperforms random sampling, when training alandslide classifier. In fact, sensitivity of classificationwithout cluster sampling was not sufficient for solvingthe stable area classification problem and the sensitivityhas been clearly increased after performing CA.
Moreover, the CA and the possibility to choose thedistance measure make it possible to introduce expertknowledge to a black-boxmodel such as the neural one. Infact, the user can condition and strongly control theselection of the data by the use of cluster sampling. Evenwithout looking inside the black-box model, it is thuspossible to achieve a better definition of the landslideconditions by weighting the relative importance of eachconditioning factor.
Finally, the most robust susceptibility map wasobtained after the cluster sampling, since the clustersampling-ANNmodel is able to distinguish and separatethe unstable areas and thus to identify more reliablesusceptibility classes. Although the results are encour-aging, the model output and the discrimination ofunstable areas can be improved. In the analysis somevariables (e.g, bedding dip domain, distance fromdrainage lines, geomechanical properties, etc) have notyet been considered. The introduction into the dataset ofthese variables could improve the classification ofunstable areas, since the cluster formation and then thenegative case selection would be influenced. In fact, anincreased number of conditioning factors would influ-ence the discrimination and the selection of clustermeaningfully for the instability classification problem.
Learning with only positive labelled data is a quitesensible issue in machine learning and quantitativeapproaches to modelling in general. This issue has beenalready faced in the literature especially in the textclassification field. Techniques generally used in thatfield have been extensively tested in the case of textdocument classification (Nigam et al., 1998; Li and Liu,2003; Liu et al., 2003). The main idea behind thosetechniques is to identify (guess) a set of reliable negativesamples from the unlabelled dataset, based on thesupposition that the unlabelled set contains a small
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number of positive examples and a large number ofnegative examples (i.e., as in the case of landslide-susceptibility zonation). After an initial guess has beenmade, the classifier is built by iteratively applying aclassification algorithm to the positive and reliablenegatives and then refining this partitioning once apreliminary model has been defined. This approach, toour knowledge, has never been applied in contextsdifferent from text classification. It is quite differentfrom the approach we proposed in this paper since theset of positive and negative examples change during thelearning process and vary both in size and composition.This refining procedure of selected data should be afuture direction of investigation to obtain better resultsin landslide-susceptibility zonation.
Acknowledgements
This work was realized in the framework of theDottorato di Ricerca in Scienze Ambientali with an ItalianPhd scholarship. Fieldwork was supported with MIUR40% grants. The authors thank the Local Authority ofBrembilla Municipality for its kindness in making the dataavailable. D. Alexander, G.B. Crosta, and P. Frattini arealso thanked for their reviews.We are indebted to the editorin chief of the volume, A. Harvey, for his final suggestions.
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