Science, Faculty of
Computer Science, Department of
DSpace
UBCV
Hajimoradlou, Ainaz
Master of Science - MSc
University of British Columbia
Landslides are movement of soil and rock under the influence of gravity. They are common phenomena that cause significant human and economic losses every year. To reduce the impact of landslides, experts have developed tools to identify areas that are more likely to generate landslides. We propose a novel statistical approach for predicting landslides using deep convolutional networks. Using a standardized dataset of georeferenced images consisting of slope, elevation, land cover, lithology, rock age, and rock family as inputs, we deliver a landslide susceptibility map as output. We call our model a Locally Aligned Convolutional Neural Network, LACNN, as it follows the ground surface at multiple scales to predict possible landslide occurrence for a single point. To validate our method, we compare it to several baselines, including linear regression, a neural network, and a convolutional network, using log-likelihood error and Receiver Operating Characteristic curves on the test set. We show that our model performs better than the other proposed baselines, suggesting that such deep convolutional models are effective in heterogenous datasets for improving landslide susceptibility maps, which has the potential to reduce the human and economic cost of these events.
Predicting Landslides Using Contour Aligning ConvolutionalNeural NetworksbyAinaz HajimoradlouB.Sc., Sharif University of Technology, 2017a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Scienceinthe faculty of graduate and postdoctoral studies(Computer Science)The University of British Columbia(Vancouver)November 2019© Ainaz Hajimoradlou, 2019The following individuals certify that they have read, and recommend to the Faculty of Grad-uate and Postdoctoral Studies for acceptance, the thesis entitled:Predicting Landslides Using Contour Aligning Convolutional Neural Net-workssubmitted by Ainaz Hajimoradlou in partial fulfillment of the requirements for the degree ofMaster of Science in Computer Science.Examining Committee:David Poole, Computer ScienceSupervisorJim Little, Computer ScienceAdditional ExamineriiAbstractLandslides are movement of soil and rock under the influence of gravity. They are commonphenomena that cause significant human and economic losses every year. To reduce the impactof landslides, experts have developed tools to identify areas that are more likely to generatelandslides. We propose a novel statistical approach for predicting landslides using deep con-volutional networks. Using a standardized dataset of georeferenced images consisting of slope,elevation, land cover, lithology, rock age, and rock family as inputs, we deliver a landslide sus-ceptibility map as output. We call our model a Locally Aligned Convolutional Neural Network,LACNN, as it follows the ground surface at multiple scales to predict possible landslide occur-rence for a single point. To validate our method, we compare it to several baselines, includinglinear regression, a neural network, and a convolutional network, using log-likelihood error andReceiver Operating Characteristic curves on the test set. We show that our model performsbetter than the other proposed baselines, suggesting that such deep convolutional models areeffective in heterogenous datasets for improving landslide susceptibility maps, which has thepotential to reduce the human and economic cost of these events.iiiLay SummaryLandslides, the downslope movement of Earth materials under the influence of gravity, are com-mon and destructive phenomena. We propose a novel statistical approach to predict landslidesusceptibility using deep convolutional networks. Our model follows contour lines and alignsitself to the up-hill direction to predict possible landslide occurrence for every point on theimage. We show that our model achieves the best results among several standard and novelmodels, suggesting that such models are effective in improving landslide susceptibility maps,which has the potential to reduce the environmental and economic costs of these events.ivPrefaceThis thesis explores how we can apply machine learning models to predict landslides usinggeo-referenced maps. It contains both under-review and unpublished work done by myself withadditional inputs from my supervisor David Poole.A briefer version of Chapter 4 and Chapter 5 is available on arXiv as Ainaz Hajimoradlou,Gioachino Roberti, and David Poole. A Probabilistic Approach for Predicting Landslides byLearning a Self-Aligned Deep Convolutional Model. The coding and the majority of writing aredone by myself. Gioachino Roberti advised on landslides and helped in writing the introduction.David Poole, my supervisor, advised on AI and edited the paper.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background and Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Fully Convolutional Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Geographic Information System Mapping . . . . . . . . . . . . . . . . . . . . . . 42.3 INSPIRE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Standardizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Veneto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Memory Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Locally-Aligned Deep Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2.1 Balancing the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18vi4.2.2 Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3 Baselines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1.1 Receiver Operating Characteristic Curves . . . . . . . . . . . . . . . . . . 245.1.2 Negative Log-Likelihood Error . . . . . . . . . . . . . . . . . . . . . . . . 256 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31viiList of TablesTable 2.1 INSPIRE terminology for Landcover. . . . . . . . . . . . . . . . . . . . . . . . 5Table 2.2 INSPIRE terminology for Rock Family. . . . . . . . . . . . . . . . . . . . . . . 5Table 2.3 INSPIRE terminology for lithology. . . . . . . . . . . . . . . . . . . . . . . . . 6Table 2.4 INSPIRE terminology for rock ages. . . . . . . . . . . . . . . . . . . . . . . . . 7Table 4.1 Top twenty-three features used for aligning the filters in Locally-Aligned CNNmodel. FEATURE NUM is the number of feature used in the dataset. . . . . 16Table 4.2 Training Hyper-Parameters. LR and BS represent the learning rate and thebatch size respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Table 5.1 Negative Log Likelihood Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 25viiiList of FiguresFigure 3.1 A one-hot encoding of categorical rock ages: olocene and pleistocene. . . . . . 11Figure 3.2 Continuous feature maps consisting of slope and digital elevation model. Thefeature maps are displayed after standardization. . . . . . . . . . . . . . . . . 12Figure 3.3 A subset of categorical feature maps consisting of land cover, lithology, androck family in the dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 4.1 The process of finding aligned features at multiple scales. The red pointshows the point of interest where we want to find the up-hill directions. Eachblue circle shows a set of neighboring points at a specific range. The greenpoint in each circle is the detected point with the highest elevation at thatdistance, from which the aligned features will be extracted. . . . . . . . . . . 15Figure 4.2 The locally-aligned convolutional neural network (CNN) architecture usedfor predicting landslides. Each conv2d uses a kernel of size 3 with stride 1and each MaxPool unit uses a kernel of size 2. Upsample units interpolatethe image with scale factor of 2 by bi-linear interpolation. . . . . . . . . . . . 15Figure 4.3 The probability map of Veneto produced by CNN architecture with batch-norm between layers. The resolution of the image is 21005x19500. . . . . . . 17Figure 4.4 Comparing optimization using a weighted and unweighted version of the neg-ative log-likelihood loss on a Convolutional model. We used the same hyper-parameters in both cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 4.5 This image shows the data partitioning used for the whole region of Veneto.Light purple, blue, and green colors are used to represent train, validation,and test sets respectively. The white background shows no-data points. . . . 21Figure 4.6 The neural network architecture used for predicting landslides. Each conv2d1x1uses a kernel of size 1 with stride 1, acting as a fully connected layer. Thisarchitecture is used in both neural network (NN) and locally-aligned neuralnetwork (LANN) baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22ixFigure 5.1 locally-aligned convolutional neural network (LACNN) probability map of21005x19500 resolution for Veneto and its corresponding ground truth. Redregions correspond to higher probabilities and blue regions are areas withprobabilities close to zero. The yellow rectangle in 5.1a shows the chosenarea in Figure 5.2 to compare various models with each other. Red polygonsrepresent observed landslides in the Veneto region in 5.1b. . . . . . . . . . . . 25Figure 5.2 The acquired probability maps for a small region in Veneto and its corre-sponding ground truth. The resolution of the images are 2500x2500 pixels. . 26Figure 5.3 Data Partitioning for the provided area in Figure 5.2. Light purple, blue,and green colors show training, validation, and the test sets respectively. . . . 27Figure 5.4 receiver operating characteristic (ROC) curves from all models on the test set. 27Figure 5.5 Negative log-likelihood error of all models on the validation set in the first10 epochs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28xGlossaryAUC area under the curveCNN convolutional neural networkDEM digital elevation modelFCN fully convolutional networkGIS geographic information systemINSPIRE infrastructure for spatial information in EuropeLLR linear logistic regressionLACNN locally-aligned convolutional neural networkLANN locally-aligned neural networkNN neural networkROC receiver operating characteristicSVM support vector machinexiAcknowledgmentsI would like to express my gratitude to those that have helped me throughout this journey.My supervisor, David Poole, who has guided me at every step of the way and the MinervaIntelligence company, specially Gioachino Roberti, for advising me throughout this project. Iwould like to thank my amazing partner, Farzad Abdolhosseini, for his love and support, andmy dear family, who have supported and encouraged me all my life. I am forever grateful foryour love and support.xiiChapter 1IntroductionLandslides, the downslope movement of Earth materials under the influence of gravity, arecommon and destructive phenomena. Although there have been many studies focusing onlandslide mapping [15] and landslide spatial and temporal probability prediction [4, 36], thesestudies are not applied to real-world problems at a large scale [33]. There are two types of factorsinvolved in causing landslides: conditional and triggering factors. The conditional factors areinternal properties of the slope, such as lithology1 or land cover, while triggering factors areexternal properties of the slope, such as temperature or rainfall, that cause the slope to fail.There are three different approaches to landslide susceptibility mapping that have beenused: expert-based, physical-based, and statistical approaches. Expert-based methods relyon the qualitative judgment of domain experts, while physical-based approaches model thestability of the slope given physical parameters such as geotechnical rock and soil properties,and calculate the equilibrium between destabilizing factors and slope strength, but often requiremore information than is available at scale. Statistical models rely on the statistical analysisof large landslide databases and their relation with landscape attributes. Landscape attributesused in statistical analysis typically include internal (e.g. slope angle, lithology, etc.) andexternal (e.g. rainfall) properties of the slope. These data are then used to map the spatialand/or temporal probability of slope failure [4]. The spatial probability of landslide occurrence isusually referred to as the susceptibility map. When the magnitude and the temporal component(e.g. frequency and triggers) are also considered, it is referred to as a hazard map [4].Statistical approaches for predicting landslides have significantly increased in recent years.However, they mostly apply models such as linear logistic regression, support vector machine(SVM), or neural networks [36]. In this study, we propose a novel convolutional model whichwe call a locally-aligned convolutional neural network (LACNN) for producing susceptibilitymaps. Convolutional neural networks form a category of neural network models with tiedparameters [19]. Convolutional neural networks with pooling layers can capture both local andglobal features of an image which has been proven extremely useful in many vision tasks such1The lithology of a rock unit is a description of its physical characteristics such as texture, color, and compo-sition, visible at outcrop, in hand or core samples, or with low magnification microscopy.1as object recognition, image classification, and object detection.To produce good susceptibility maps for landslides, we hypothesize that learning filters thatcan follow the ground surface and extract features towards the up-hill direction will performbetter than our baselines. For this to work, we need the convolutional neural network (CNN)model to preserve orientation information of landslides to each other. In traditional techniques,filters are rotation invariant and use all directions; they align themselves up, down, left, andright, which corresponds to north, south, east, and west.In our proposal method, we add a pre-processing stage to our CNN model to find thebest directions for each pixel at multiple scales and then learn hidden features according tothose directions. We call this model LACNN as the model first aligns itself to a specific set oforientations locally and then learns a classifier. This can also be considered local hard attentionto finding important features to predict landslides.It is important to note that we could have augmented data by multiple rotations and thenlearned a rotation-invariant model for finding the up-hill direction. However, this is much hardercompared to our proposed method since we need to learn up-hill implicitly. Our proposedmethod uses a strong prior on the up-hill direction to learn the weights and is a simpler model.Learning up-hill can be an extension of the current work.The contributions of this thesis are:• We provide an open-source dataset with a standard set of features. The dataset consistsof several input features such as the slope, elevation, lithology with age and family, andland cover, along with the ground truth in the shape of landslide polygons which can beused in both a supervised and unsupervised learning framework. This dataset is collatedfrom public data.• We propose a novel statistical approach for predicting landslides using deep convolutionalnetworks. We develop a model that can capture each pixel’s orientation at three differentranges to classify a landslide. We use ranges of 30, 100, and 300 meters in our model.These scales can be optimized using cross-validation.• We define several baseline models for comparison. We provide five different baselinesincluding a Random model, a linear logistic regression (LLR), a neural network (NN), aCNN, and a locally-aligned neural network (LANN) model without any convolutions, tocompare our model’s performance against them.• We provide a way to use CNNmodels with heterogeneous datasets for predicting landslidesrather than only using images in our convolutional models.2Chapter 2Background and Related Work2.1 Fully Convolutional NetworksConvolutional networks used in classification usually consist of multiple layers of convolutionsfollowed by some number of fully connected layers, which give the classifier of the network.A fully convolutional network (FCN) is a convolutional network without any fully connectedlayers. Instead, it contains one or more convolution layers. It lets us predict properties ofindividual points as opposed to global properties (such as ”there is a cat in the image”). Thistype of architecture captures both local and global features of the image; convolution layersfind local features specific to each pixel, and pooling layers capture a more global structure ofthe image.This type of network does not have any constraints on the size of the input data since it doesnot contain any fully connected layers and we can train the network on multiple resolutions.The reason is that we need to specify the size of the input and output vectors when we definea fully connected layer while convolutions do not have such constraints and work on any size ofdata.The intuition behind using FCNs is that we are interested in predicting a probability foreach pixel in the image instead of assigning an output probability for the whole image as inclassification tasks. Thus, the layers that replace the classifier of the network should be ableto up-sample the obtained features from the convolutional layers such that we can map a low-resolution image to a higher-resolution image. Convolution transpose or deconvolution layersare usually used for up-sampling in such networks.Images get smaller after applying convolutions unless we pad them as convolutions are notsupported at borders (e.g. applying convolution with a 3x3 kernel on a 5x5 input results in a3x3 output). Convolution transpose layers first pad the images and then apply convolutionssuch that the final images have larger sizes compared to the inputs. Convolution transposeallows us to scale up the image while learning local spatial features that are specific to eachpixel. If the receptive field of view of the network is large enough, we can construct an output3image that is the same size as the input image, which makes this network a great candidate forvision tasks such as image segmentation, and landslide prediction.There are currently several variations of fully convolutional networks: we can constructnetworks with skip connections between layers to reduce training time, use interpolation layersinstead of convolution transpose layers to reduce the number of parameters, or use un-poolinglayers to approximately inverse max-pooling operations by recording the positions where welocated the biggest value.2.2 Geographic Information System MappingA geographic information system (GIS) is a system to store, manipulate, manage, and analyzespatial data on the Earth [9, 24]. A GIS integrates several types of data such as images, features,and base maps, linked to spreadsheets and tables using spatial location. It visualizes data usingmaps that are geographic containers for data layers. GIS can also visualize data using 3Dscenes. A GIS provides the user with spatial and also statistical tools to analyze, estimate, andevaluate different types of data, offering new perspectives for decision-making.Geographic information systems are a well-developed framework for visualization and anal-ysis. Many organization such as health, education, transportation, natural resources, retail,government, and sustainability apply it for visualization and decision-making. There are manyavailable GIS software from which Quantum GIS software (QGIS) [14] is used in this thesis fordata processing.QGIS is an open-source and cross-platform desktop GIS application that supports editing,viewing, and analyzing spatial information. QGIS supports both vector and raster data formats.Vector data is stored in points, lines, or polygons, and raster data include several formats suchas ArcInfo Binary Grid, ArcInfo ASCII Grid, GeoTIFF, and many more. QGIS is also used togeoreference data.Most databases in a GIS framework are georeferenced, meaning that they contain spatiallocation information (i.e. geographical coordinates). Using this information, we can integratemultiple layers of data on top of each other while knowing their location on the Earth. In thisthesis, we are mainly interested in using QGIS software for processing data that is relevant tolandslides (e.g. slope or land cover). We applied this software for georeferencing the maps,identifying no-data points, vector to raster conversion, and sampling.2.3 INSPIREinfrastructure for spatial information in Europe (INSPIRE)1, is an infrastructure for standard-izing spatial information between European countries, aiming at creating a union for environ-mental policies or policies that have an impact on the environment. INSPIRE facilitates datasharing between public organizations and further policy-making by defining standards that are1https://inspire.ec.europa.eu4Table 2.1: INSPIRE terminology for Landcover.NAME INSPIRE CODEagricultural areas 1artificial surfaces 2forest and semi-natural areas 3water bodies 4wetlands 5Table 2.2: INSPIRE terminology for Rock Family.NAME INSPIRE CODEmetamorphic 1sedimentary 2plutonian 3volcanic 4null or no value 5acceptable across Europe.Since we are also interested in providing a standard set of features for producing susceptibil-ity maps, we use the same standards as INSPIRE in our experiments. We apply the INSPIREstandards to lithology, land cover, rock age, and rock family, resulting in 44 types of rock, 5types of land cover, 5 different types of rock family, and 38 kinds of ages for various rocks.Tables 2.3, 2.1, 2.2, and 2.4 show a more detailed summary of these metrics. Each table showsthe name of the features with their corresponding INSPIRE code.2.4 Related WorkWe apply modern convolutional neural network tools to susceptibility mapping. Our model canalign itself to contour lines and learn features using filters that point to the up-hill direction. Weknow of no other work that does this. Producing susceptibility maps by statistical approachesis not new in the landslide community. Many people have been using models such as logisticregression, SVMs, and random forests.Catani et al. [7] used random forests to generate susceptibility maps, emphasizing sensitivityand scaling issues. Micheletti et al. [26] and Youssef et al. [44] used random forest models inpredicting landslides for Switzerland and Wadi Tayyah Basin in Saudi Arabia. Some havedeveloped software packages using random forests for susceptibility mapping [6]. Michelettiet al. [27] generate several susceptibility mappings using SVMs, random forests, and Adaboost.Atkinson and Massari [2], Ayalew and Yamagishi [3], and Davis et al. [10] focus on linearregression for predicting landslides due to its simplicity and easy training procedure. Lom-bardo and Mai [21] proposed standardization of binary logistic regression analysis for landslidesusceptibility using rescaling coefficients and experimenting with different cut-off probability5Table 2.3: INSPIRE terminology for lithology.NAME INSPIRE CODEgneiss 1mica schist 2lakes and glaciers 3serpentinite 4impure limestone 5debris 6phyllite 7dolomite 8tonalite 9glacial 10clay 11granite 12limestone 13siltstone 14claystone 15quartz diorite 16conglomerate 17sandstone 18clastic sediment 19basalt 20rhyolitoid 21dacite 22granulite 23chlorite actinolite epidote metamorphic rock 24sand 25migmatite 26monzonite 27diorite 28gabbro 29peridotite 30foidite 31phonolite 32gypsum or anhydrite 33lacustrine 34travertine 35eolian 36quartz monzonite 37syenite 38trachyte 39andesite 40clastic sedimentary material 41evaporite 42sedimentary material 43fluvial 446Table 2.4: INSPIRE terminology for rock ages.NAME INSPIRE CODEcambrian 1carboniferous 2paleozoic cycle 3alpine cycle 4cretaceous-jurassic cycle 5average triassic cycle 6myocene cycle-paleogenetics 7neogenic-quaternary cycle 8permo-carboniferous cycle 9triassic cycle 10lower cretaceous 11upper cretaceous 12cretaceous 13upper cretaceous-Jurassic 14devonian 15jurassic 16high grade prealpine metamorphites* 17low-grade prealpine metamorphites* 18medium grade prealpine metamorphites* 19prealpine metamorphites of various degrees* 20middle-lower miocene 21upper miocene 22ophiolites and green stones 23holocene 24holocene, pleistocene pro-part 25paleogene 26Upper paleogene-cretaceous 27lower Permian and Carboniferous 28permian 29pleistocene and pliocene 30pleistocene, sometimes holocene 31pleistocene 32pliocene 33silurian 34lower triassic 35average triassic 36upper triassic 37upper-middle triassic 38* All these ages correspond to unknown periods in time but we rep-resent them with different codes because of the domain expert’sopinion.7choices. Mousavi et al. [29] used linear logistic regression for spatial prediction of landslidesmainly focusing on road networks as their input features. Lee [20] trained a logistic regressionmodel for susceptibility mapping on aerial photographs and satellite images and showed that itcan perform better in prediction than their probabilistic baseline.There is a volume of approaches that formulates the problem in a probabilistic frameworksuch as Bayesian networks [16, 22]. Neural networks and convolutional models are among morerecent approaches for susceptibility mapping. Luo X [23] used neural networks to assess minelandslide susceptibility mapping in Shangli County, China. Tien Bui et al. [41] introduces aframework for training and validation of shallow landslide susceptibility models by statisticalmethods such as radial basis function neural networks (RBF neural networks) and SVMs. Ortizand Martinez-Grana [32] applied a neural network to produce a susceptibility map in Columbia.Pradhan and Lee [34] used a neural network model for landslide hazard and risk analysis usingremote sensing data while Pradhan and Lee [34] focused on different training strategies andvarious training sites using neural networks.Ghorbanzadeh et al. [13] used a CNN model for detecting and observing landslides fromsatellite images using neighboring features at different scales. It is important to note that theirmodel cannot predict landslides while predicting landslides is our main goal. Wang et al. [42] dida comparative study on CNNs for landslide susceptibility mapping in China but their approachdoes not incorporate any orientational information or aligning filters either. Xiao L [43] used aCNN to learn features from high-resolution remote sensing images which were further fed intoan LSTM cell along with other features to predict landslide susceptibility.Most of these models used in landslide susceptibility mapping are quite simple and do nottake into account any orientations. The existing convolutional models are not usually deepand do not use any pooling layers to consider multiple resolutions for feature extraction [43].Additionally, their networks do not contain filters that can rotate or capture orientation betweenlandslides.We are interested in predicting the landslide probability for each point on the ground. Theoutput of our model is a probability map with the same resolution as the input features. Weuse a fully convolutional model [39] for this purpose. These models have been widely usedfor image segmentation [30, 37] and usually consist of down-sampling and up-sampling stages.One of the popular models in this category is UNet [37], which our architecture is based on.The down-sampling stage consists of convolutions with pooling layers and tries to create aset of compact features capturing both local and global properties of the input features. Theup-sampling stage typically consists of convolution transpose layers. These layers do the sameoperation as convolution layers, but convolution layers reduce the size of the image unless wepad it because convolution is not supported at borders, while convolution transpose layers padthe image such that applying the convolution afterward results in a larger image.Using convolution transpose for up-sampling tends to produce checkboard artifacts, espe-cially in two dimensions [31]. Roughly speaking, convolution transpose layers allow the model8to use every point in the low-resolution image to ”paint” a square in the high-resolution imagewhen up-sampling. These painted squares in the larger image overlap with each other and arelikely to have uneven overlaps when the kernel size is not divisible by the stride (e.g. kernel ofsize three and stride of size two), putting more of the metaphorical paint in the same places[1, 12]. Stride is how far the kernel/filter moves in every step along one direction. Neural net-work architectures usually consist of multiple layers of convolution transpose, gradually buildinga higher-resolution image. Although these layers may cancel out each other’s artifacts, theyoften compound and create artifacts at multiple scales.Convolution transpose layers with stride one are effective in dampening such artifacts, butthey cannot completely avoid them. We could also enforce the model to learn weights foruneven overlaps, but it sacrifices model capacity and restricts the range of possible filters tolearn. Our model also produces checkboard artifacts when we use convolution transpose layers inour architecture. Thus, we use bilinear interpolation followed by convolutions for up-samplinginstead of convolution transpose. There are also other methods of handling these types ofartifacts such as subpixel convolution [40], but they introduce unnecessary complications to themodel and the training procedure.It has been demonstrated that adding skip connections to a fully convolutional model im-proves its performance [11, 25]. Adding skip connections to a network implies skipping some ofthe layers int the network and feeding the output of one layer to another directly. The intuitionbehind using skip connections in a network is that some of the information from the top layersget lost or become too abstract for the deeper layers. Adding skip connections enable us to feedthis information explicitly to the deeper layers, which are useful for image reconstruction. Ad-ditionally, skip connections facilitate the flow of gradients throughout the network and preventvanishing gradients. In deep networks, the gradients become smaller after each layer and mightbecome too small to affect the weights in the upper layers. We only apply long connections toour model, as short skip connections have been shown to work only in very deep networks.9Chapter 3DatasetThe dataset used for predicting landslides is from Italian open-source databases: the landcover is based on the CORINE land cover inventory1, the bedrock geology and the landslidelabels are based on Italian National Geoportal website2, and the slope and elevation maps arecollated from the National Institute of Geophysics and Volcanology3. The dataset containsboth continuous and categorical features in the shape of rasters and vector files respectively.Continuous features include slope and digital elevation model (DEM) and categorical featuresconsist of lithology, land cover, rock age, and rock family.Slope values should be between 0 and 90 degrees. Any negative or above 90 degrees valueis considered an outlier. The original slope map contained outliers that we identified andreplaced with an arbitrary number that is not in the range of the data, which we treat specially.Categorical features also included no-data points. We identified those data points and replacedthem with the same value that we used for identifying out of range slope values. The sameprocedure is applied to cleaning the landslide labels from no-data points. We then make surethat each sample of the data does not correspond to a no-data label and only back-propagate[18] through the valid data points excluding out of range or no-data features.Since our proposed model is a convolutional neural network and we are interested in usingthe relative spatial information in the maps, we converted each categorical data in vector formatto multiple binary rasters using a one-hot encoding. This resulted in a new dataset of rasterswith identified no-data and out of range values. Figures 3.1, 3.2, and 3.3 show a subset of theinput features used in this dataset.3.1 StandardizingAs we wanted to propose a baseline framework for this type of problem, we needed to come upwith a standard set of features for our categorical data. Using the INSPIRE terminology andbased on the domain expert’s knowledge, we chose forty-four different lithology, five types of1https://land.copernicus.eu/pan-european/corine-land-cover2http://www.pcn.minambiente.it/mattm/en/wfs-service/3http://tinitaly.pi.ingv.it/10(a) Holocene: code 24. (b) Pleistocene: code 32.Figure 3.1: A one-hot encoding of categorical rock ages: olocene and pleistocene.rock family, and thirty-eight kinds of ages for various rocks. Land cover terminologies consistof multiple layers of abstraction. We only used the first layer, including five general types ofland cover to have fewer features and avoid collinear features. It is possible to use more typesof land cover to investigate how much detail is important for predicting landslides in futureexperiments.Using the INSPIRE terminology, we ended up with ninety-four standard input features thatconsisted of two continuous features, (slope and DEM) along with ninety-two binary features(refer to Tables 2.1, 2.2, 2.3, and 2.4 for a complete list of binary features), which we obtainedby using a one-hot encoding on categorical data. Both our model and our prepared dataset canbe used in any other framework that uses INSPIRE.3.2 VenetoWe chose the region Veneto in Italy that stretches from Venice on the coast into the mountains.We think Veneto is one of the best regions in Italy to be used for landslide susceptibilitymapping. Landslides usually occur in areas with high slope and we rarely have any landslideoccurrence in flat areas. Since Veneto extends over both mountains and flat zones close tothe sea, it is a good candidate for us to train our models on. Each pixel in the DEM mapand the slope have ten meters resolution. We chose ten meters resolution since it is the finestresolution that is open-source and free. Using this resolution, we end up with rasters that areall 21005x19500 pixels, resulting in an area with approximately 210 (km) width and 195 (km)height.11(a) Digital Elevation Model. (b) Slope.Figure 3.2: Continuous feature maps consisting of slope and digital elevation model. Thefeature maps are displayed after standardization.3.2.1 ChallengesThe ratio of landslides in Veneto is below 1% which makes the dataset extremely imbalanced.The landslides in Veneto occur in both mountainous and less steep areas, which is good sincewe can train our model on less frequent landslides as well. There are many different types oflandslides (e.g. rock falls, debris flow, etc.), but the landslides in Veneto are not categorizedbased on their type and contain various types of landslides. Moreover, training a separate modelfor each type of landslide needs more training data as some of the landslide types are very rare.Therefore, we decided to train one model for all types of landslides. It is also important to notethat the landslides in Veneto do not contain any information about the date of occurrence. Allof these characteristics make this dataset challenging from the machine learning point of view.But it is typical of a real-world dataset in this domain.3.3 Memory ConsiderationsAll of the rasters in the dataset are too large to fit into memory when training. We useda Titan XP GPU with 12 GB memory for most of our experiments but also had access tocomputecanada clusters. We divide each raster into smaller images of size 500x500, which wecall patches. We further feed mini-batches of these patches into our model for training. Since wewant to produce a coherent probability map for the whole region, we use patches that overlapeach other. For this purpose, we pad each patch with 64 pixels on each side resulting in 628x628images. This padding number was chosen to ensure that the overlap between patches is biggerthan the receptive field of view of our networks. We then partitioned these patches into training,testing, and validation sets. More details about partitioning are provided in section 4.2.2.12(a) Rock family: code 1, metamorfico. (b) Rock family: code 2, sedimentario.(c) Land cover: code 3, forest and semi-natural ar-eas. (d) Land cover: code 2, artificial surfaces.(e) lithology: code 5, impure limestone. (f) lithology: code 6, debris.Figure 3.3: A subset of categorical feature maps consisting of land cover, lithology, androck family in the dataset.13Chapter 4Locally-Aligned Deep NetworkThe slope is considered one of the main conditioning factors in causing landslides. Almost allavailable literature on landslide susceptibility mapping, use slope as one of their main inputfeatures [21, 29, 32, 34–36] regardless of where that mapping is done, and the domain expertsagree on this matter. We also confirmed this by learning a LLR baseline for susceptibilitymapping, where the slope’s weight is among the top five learned weights.Traditional CNN filters are either oriented vertically in an image or treated as rotationallysymmetric, but the important orientation is up-hill and down-hill for landslides. Based on this,we propose a Locally-Aligned CNN model with filters that align themselves according to theup-hill direction and extract features alongside that direction. As illustrated in Figure 4.1, foreach pixel in the image, we find the highest elevation value at three different looking distancesand extract relevant features at those located points. Table 4.1 shows the list of these selectedfeatures for aligning the filters.Because space is at a premium for batch size, we selected a subset of twenty-three featuresfor this purpose. These features are chosen based on our trained LLR baseline. If we definethe LLR’s weight vector by 𝑤, each feature is chosen such that |𝑤𝑖| >= 0.2. We used thisthreshold arbitrarily, but it is possible to experiment with different thresholds. Almost half ofthe weights are very close to zero (|𝑤𝑖| <= 0.05). It would be interesting to experiment withvarious thresholds and see how the number of selected features for alignment affects the model’sperformance, but we anticipate that such small weights will not change the final accuracy muchsince they play less significant roles in the prediction due to their small weights. Moreover,a larger input size will take more time to train, and would mean we need smaller patchesto put into a fixed size memory. The source code of the project can be found under https://github.com/ainazHjm/Landslide.4.1 ArchitectureOur LACNN architecture consists of a preprocessing module and four layers of down-samplingand up-sampling, as in Figure 4.2. The preprocessing module takes the elevation map along14Figure 4.1: The process of finding aligned features at multiple scales. The red pointshows the point of interest where we want to find the up-hill directions. Each bluecircle shows a set of neighboring points at a specific range. The green point in eachcircle is the detected point with the highest elevation at that distance, from whichthe aligned features will be extracted.PreProcess1616I32 32I/264 64I/4128 128I/8128 128I/16Bottleneck128 128I/864 64I/432 32I/216 16 16IConv2dReluMaxPool2dUpsampleConcatenationSigmoidFigure 4.2: The locally-aligned CNN architecture used for predicting landslides. Eachconv2d uses a kernel of size 3 with stride 1 and each MaxPool unit uses a kernelof size 2. Upsample units interpolate the image with scale factor of 2 by bi-linearinterpolation.15Table 4.1: Top twenty-three features used for aligning the filters in Locally-Aligned CNNmodel. FEATURE NUM is the number of feature used in the dataset.NAME INSPIRECATEGORY CODESlope Slope -Micha Schist Rock Type 2Lakes and Glaciers Rock Type 3Impure Limestone Rock Type 5Debris Rock Type 6Dolomite Rock Type 8Clay Rock Type 11Granite Rock Type 12Claystone Rock Type 15Clastic Sediment Rock Type 19Basalt Rock Type 20Sand Rock Type 25Travertine Rock Type 35Agricultural Areas Land Cover 1Artificial Surfaces Land Cover 2Forest and Semi-Natural Areas Land Cover 3Sedimentary Rock Family 2Jurassic Rock Age 16Holocene Rock Age 24Pleistocene Rock Age 32Upper Triassic Rock Age 37Upper-Middle Triassic Rock Age 38DEM Elevation -with other input features from the dataset as inputs and outputs twenty-three features thatwere extracted based on the up-hill direction for each distance. We use thirty, one hundred,and three hundred meters as distances (or ranges) in our experiments, but the number ofranges and distance values can also be considered hyper-parameters and be optimized usingcross-validation. The preprocessing module outputs sixty-nine up-hill features in total that wefurther feed into the convolutional network along with the original ninety-four features.The fully convolutional network in LACNN consists of down-sampling and up-samplinglayers. We down-sample the image by pooling layers and up-sample by interpolating featuresfollowed by convolution layers at four different scales. We also apply long skip connectionsbetween each sampling layer to reduce training time and improve model performance. Weuse the same architecture as UNET for our convolutional network in Figure 4.2. The onlydifference between our network and UNet is that our network uses fewer parameters due tosmaller training data and does not include batch-norm layers after convolutions (see [17] for a16Figure 4.3: The probability map of Veneto produced by CNN architecture with batch-norm between layers. The resolution of the image is 21005x19500.description of batch-norm layers).The intuition behind using skip connections in a network is that some of the information fromthe top layers get lost or become too abstract for the deeper layers. Adding skip connectionsenable us to feed this information explicitly to the deeper layers, which are useful for imagereconstruction. Additionally, skip connections facilitate the flow of gradients throughout thenetwork and prevent vanishing gradients. In deep networks, the gradients become smaller aftereach layer and might become too small to affect the weights in the upper layers.Each down-sampling layer consists of two convolution layers. We use ReLU as non-linearityand a max-pooling layer after each convolution. Every up-sampling layer includes an up-sampling module to interpolate the data. We use bilinear interpolation for up-sampling. Afterinterpolating the features, we concatenate the obtained features from the previous layer withthe features from the skip connection and apply a convolution layer with ReLU afterward. Inthe end, we apply a Sigmoid function to the output of the model to obtain probabilities.Batch normalization [17] is an operation to fix the mean and variance of each input layer.We can normalize data at each layer of a neural network to have a mean of zero and variance ofone or learn the distribution (i.e. mean and variance) of each layer separately. However, we donot apply this operation between layers in our architecture since it introduces artifacts in theoutput image. Each sample in the dataset, which is a patch, is not independent of the othersamples, and using batch normalization enforces each patch to have a separate distribution.This is undesirable since we are interested in producing a coherent probability map as theoutput which has a unique distribution. Figure 4.3 shows the effect of batch-normalization forVeneto. We did not use it in any subsequent experiments due to the artifacts produced.174.2 Training4.2.1 Balancing the DataIt is important to balance the data in machine learning especially when we care about predictinga minority class [8]. Balancing the data is a well-known approach in deep learning applicationsand is done frequently in practice [5]. Since the majority class has a significantly higher prob-ability, the model tends to classify new observations to the majority class [28]. Moreover, themodel will be biased toward learning the majority class well since it has the most data andmight perform poorly on the minority class [38]. Using a log likelihood loss can be useful insuch datasets but cannot fully solve the issues related to imablanced datasets.Our training set is very imbalanced. Since we care about predicting the minority class,which is the landslide, we need to balance the ratio of positive to negative samples/patchesin our dataset. This ratio is about 0.7% in the whole dataset before applying any balancingmethods. However, we want to change the distribution of the data as little as possible so thatthe model does not become overconfident when predicting landslides, as they are pretty rareevents. There are many methods to balance imbalanced datasets, including under-sampling themajority class, oversampling the minority class, and optimizing a weighted loss that assignsmore penalty to wrong predictions for the minority class. There are also hybrid methods thatcombine oversampling and under-sampling.Under-sampling is not a good approach for our dataset since we need to throw away mostof the data because of the small ratio of positive to negative samples. We tried a weighted lossfunction, but the model did not converge to a good solution in most of the cases, and we endedup with noisier loss function, which is very hard to optimize.A reasonable explanation for this behavior is that the optimizer tends to overshoot becauseof the assigned weight to the positive class. In the gradient descent algorithm, if we define theloss function and the learning rate to be 𝑓((𝑥1,𝑥2, ...,𝑥𝑛),𝑦) and 𝛼 respectively, we iterate overthe following optimization step for every feature 𝑥𝑖 at each iteration of the gradient descentalgorithm:𝑥𝑛𝑒𝑤𝑖 = 𝑥𝑐𝑢𝑟𝑟𝑖 −𝛼∗𝜕𝑓𝜕𝑥𝑖(𝑥𝑐𝑢𝑟𝑟𝑖 ,𝑦). (4.1)The weighted loss function (𝑓𝑤) will have a bigger partial derivative in our case comparedto a non-weighted loss function since the weight is bigger than one. If we define the positiveweight to be 𝑤𝑝𝑜𝑠 >> 1 and the loss function to be the negative log-likelihood function (i.e.BCEwithLogitsLoss in Pytorch), we have:18𝜕𝑓𝑤𝑥𝑖>> 𝜕𝑓𝑥𝑖(4.2)𝜕 [𝑤𝑝𝑜𝑠.𝑦. log𝜎(𝑥)+(1−𝑦). log(1−𝜎(𝑥))]𝜕𝑥𝑖>> 𝜕 [𝑦. log𝜎(𝑥)+(1−𝑦). log(1−𝜎(𝑥))]𝜕𝑥𝑖(4.3)𝑤𝑝𝑜𝑠(𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖)+ 𝜕 [(1−𝑦) log(1−𝜎(𝑥))]𝜕𝑥𝑖>> 𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖+ 𝜕 [(1−𝑦) log(1−𝜎(𝑥))]𝜕𝑥𝑖,(4.4)where 𝜕[(1−𝑦) log(1−𝜎(𝑥))]𝜕𝑥𝑖 has the same value in both sides of the inequality. Therefore:𝑤𝑝𝑜𝑠(𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖)+𝜕 [(1−𝑦) log(1−𝜎(𝑥))]𝜕𝑥𝑖>> 𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖+𝜕 [(1−𝑦) log(1−𝜎(𝑥))]𝜕𝑥𝑖(4.5)(𝑤𝑝𝑜𝑠−1)(𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖)>> 0 (4.6)𝜕 [𝑦 log𝜎(𝑥)]𝜕𝑥𝑖≠ 0⟶𝑤𝑝𝑜𝑠 >> 1. (4.7)Based on equation 4.7, using a positive weight that is much bigger than one will result in amuch bigger derivative for the weighted loss function if we assume that the derivative cannotbe zero. Therefore, the weighted loss function will have drastic changes in 𝑥 values and willovershoot according to equation 4.1 unless we pick a very small learning rate that cancels outthe overshooting effect. However, picking a small learning rate (e.g. 10−5) makes the trainingprocess extremely slow. We can confirm the slow training by looking at the plots in Figure 4.4:it takes 100 times more iterations for the weighted loss function than the non-weighted one toconverge. We use oversampling to balance the data for the non-weighted function in Figure 4.4.The weighted loss function in figure 4.4b has larger loss values and higher variance com-pared to its non-weighted function that uses oversampling. We use Pytorch for optimizingover the weighted loss function as in equation 4.3. Pytorch does not normalize the loss func-tion after applying the weight and therefore outputs likelihood values that are bigger thanone. Implementing a normalized version is not straightforward, so we decided to stick with theunnormalized version for comparison.Instead, we use oversampling to balance the data. Since our dataset consists of patches,as explained in Chapter 3, and we want to preserve the spatial relation between pixels in eachpatch, we do not oversample the landslide pixels but patches that have at least one landslidepixel. After oversampling, the distribution of landslides will be equal to 1.3% in the trainingdata. Even after oversampling, the data is still imbalanced but we were able to improve theratio and also provide more training data for our models. Better ways of balancing the datashould be considered one of the future directions of this work.190 1000 2000 3000 4000iteration0.050.100.150.200.250.30negative log-likelihood lossUnweighted(a) Unweighted negative log-likelihood loss.0 10000 20000 30000 40000iteration1.001.051.101.151.201.251.301.35negative log-likelihood lossWeighted(b) Weighted negative log likelihood loss.Figure 4.4: Comparing optimization using a weighted and unweighted version of thenegative log-likelihood loss on a Convolutional model. We used the same hyper-parameters in both cases.It is important to note that we do not want to balance the data such that we end up with50% landslides since this will change the distribution of landslides by great extent and thetraining data will not be a representation of the test data; our trained models on such datawill predict probabilities for the test data that are 50 times more likely than they are in reality.This type of sampling can also be seen as data augmentation, providing more training data.We used an oversampling ratio of 5 in our experiments which was chosen arbitrarily.4.2.2 PartitioningWe partition image patches after shuffling such that 80% of the data is used for training, 10%for testing, and the other 10% for validation. Although we care about the accuracy on thetest set, we pay more attention to predicting and identifying landslides that are the minorityclass. Thus, it is better to evaluate our model on a balanced validation set so that we canmake sure that the model learns how to predict landslides well. However, we cannot choose abalanced validation set since our dataset consists of patches that may or may not have landslideoccurrences and landslide’s distribution is relatively low on all patches. We chose the validationset such that all patches have at least one landslide occurrence. This way, we ended up with avalidation set that had a distribution of 2.3% landslides. Figure 4.5 shows the partitioning onthe whole dataset.4.2.3 ValidationWe train the model by optimizing the negative log-likelihood loss. We use the validation setto prevent overfitting by monitoring the train and validation losses at each epoch. The modelstarts overfitting when validation error keeps increasing for some number of epochs. This can200 2500 5000 7500 1000012500150001750002500500075001000012500150001750020000Figure 4.5: This image shows the data partitioning used for the whole region of Veneto.Light purple, blue, and green colors are used to represent train, validation, and testsets respectively. The white background shows no-data points.be avoided by lowering the learning rate. Therefore, if the validation error keeps increasing fortwo consecutive epochs, we will reduce the learning rate by 0.5.The number of epochs to wait before reducing the learning rate and how much to reduce itdepend on the user and are considered hyper-parameters of the model that can be optimizedusing cross-validation. We used 2 and 0.5 respectively for each of these hyper-parameters inour experiments. We terminate the training process once training for more epochs does notdecrease the validation loss anymore.We also use 5-fold cross-validation for one epoch to optimize the learning rate and theoptimizer for different models. For cross-validation, we combine training and validation patcheswith each other and partition them into five folds after shuffling. We use one fold for validationand the rest for training. This process is repeated until each fold is chosen once to be thevalidation set. Since we are not training the models completely and only for one epoch, it canbe considered partial optimization of the hyper-parameters. Optimizing all hyper-parametersis an exhaustive task and takes a very long time.4.3 BaselinesWe propose a baseline model called Naive that predicts 0.013 (ratio of landslides in trainingset) everywhere in the image. We define 𝑝𝑛 to be the ratio of negative/zero labels and 𝑝𝑝 tobe the ratio of positive/one labels in the training set. For our dataset, these numbers are 0.987and 0.013 respectively. Given 𝑝𝑛 and 𝑝𝑝, we can calculate the expected negative log-likelihood2132I4I1I IConv2d1x1ReluSigmoidFigure 4.6: The neural network architecture used for predicting landslides. Eachconv2d1x1 uses a kernel of size 1 with stride 1, acting as a fully connected layer.This architecture is used in both NN and LANN baselines.Table 4.2: Training Hyper-Parameters. LR and BS represent the learning rate and thebatch size respectively.MODEL OPTIMIZER LR EPOCHS BS DECAY PATIENCELLR Adam 0.125 10 15 0.001 2NN Adam 0.125 10 13 0.001 2LANN Adam 0.0156 15 10 0.001 2CNN SGD 0.125 20 12 0.001 2LACNN Adam 0.001 30 9 0.001 2error of the Naive baseline on train and test sets:𝑓𝑙𝑜𝑠𝑠(𝑥,𝑦) = 𝑦. log𝜎(𝑥)+(1−𝑦). log(1−𝜎(𝑥))𝔼[𝑓𝑙𝑜𝑠𝑠(𝑥,𝑦)] = 𝑝𝑝. log(0.013)+𝑝𝑛. log(1−0.0.013)= 0.013 log0.013+0.987 log0.987≈ 0.069,We can find the expected error with the same calculations on the test set as well. On the testset, 𝑝𝑝 is equal to 0.012 and 𝑝𝑛 is equal to 0.988, resulting in an error which is approximately220.065. We compare the test and training errors of our other baselines with the Naive model tomake sure that the learned models perform better than Naive.We also propose several other baselines to compare our model against them including linearlogistic regression (LLR), NN, CNN, and a Locally-Aligned Neural Network (LANN). The LLR,NN, and LANN baselines do not use any convolutions and consist of fully connected layers thatare applied to each pixel in the image. It is important to note that each pixel is treated as anindependent sample without considering its neighbors when we use a fully connected layer.A convolution layer with 1x1 kernel, C1 input channels, and C2 output channels, act as afully connected layer with C1xC2 weight matrix. In other words, for each pixel, the propertiesof one layer are connected to the properties of the pixel at the next layer. Thus a pixel does notdepend on the properties of its neighbors. It is as though each pixel is a separate example. Weuse 1x1 convolutions in our models instead of fully connected layers. Using 1x1 convolutionsenables us to feed images to the network without dealing with reshaping input tensors.The LLR model is only one fully connected layer that is followed by a sigmoid function.Figure 4.6 shows the NN architecture that consists of three fully connected layers. Adding thepreprocessing unit to the NN architecture for aligning filters makes the LANN model. Thedifference between LANN and LACNN is in convolution layers. LANN does not learn weightson neighboring pixels to predict a probability for a single pixel while LACNN is a convolutionalnetwork and learns weights on neighboring pixels at multiple scales. The CNN baseline usesthe convolutional architecture in Figure 4.2 without the preprocessing unit and does not applyany alignment to the filters.Table 4.2 shows the hyper-parameters used for training each of the models. We optimizedthe learning rate and the optimizer with 5-fold cross-validation for one epoch. We choose thebatch size such that we can fit the maximum number of samples in memory. We train eachmodel until it gets saturated and training for more epochs does not decrease the errors. If thevalidation error keeps increasing for some number of epochs, we reduce the learning rate. Thenumber of epochs to wait before changing the learning rate is shown by PATIENCE in thetable.23Chapter 5ResultsWe show the final susceptibility map of our main model, LACNN, with the correspondingground truth in Figure 5.1. This susceptibility map is for the whole region of Veneto. Theproduced probability map contains many details and can identify areas with high susceptibilityaround the landslides. Since time scale is not provided for landslides, the output probabilitiesare for an undefined period, and therefore should only be interpreted as relative scales.We show the results of all models for a smaller region of Veneto so that we can compare theoutput of various models against each other with more details since the original susceptibilitymap is too large. This region includes both landslide polygons and non-landslide areas and hasa variety of terrain. Figure 5.2 shows that the susceptibility map becomes more detailed asthe number of parameters increases and the model gets more complicated. The range of thepredicted probabilities is also different between models. More complicated models have a largervariance between their predictions. The data partitioning for this area is shown in Figure 5.3.5.1 EvaluationWe evaluate our models by two different metrics: the receiver operating characteristic (ROC)curve and the negative log-likelihood error. ROC curve plots the true-positive rate, which isalso called sensitivity, and false-positive rate or specificity at different cut-off thresholds. They axis shows sensitivity and the x axis is the specificity. This is a good way of showing howdifferent thresholds affect the accuracy of the predictions. The area under the curve (AUC) isa measure of how well the model can distinguish between distinct classes.5.1.1 Receiver Operating Characteristic CurvesWe evaluate our model, LACNN, against other baselines using the ROC curve on the test setand show that it can achieve the best results among all models, as shown in Figure 5.4. It isimportant to note that the LANN model achieves the same AUC as the CNN model. This isinteresting since this model does not use any convolutions for predictions and only looks at theup-hill direction at 30, 100, and 300 meters, suggesting that alignment plays a significant rule24(a) Probability Map.0 2500 5000 7500 10000125001500017500025005000750010000125001500017500200000.00.20.40.60.81.0(b) Ground Truth.Figure 5.1: LACNN probability map of 21005x19500 resolution for Veneto and its cor-responding ground truth. Red regions correspond to higher probabilities and blueregions are areas with probabilities close to zero. The yellow rectangle in 5.1ashows the chosen area in Figure 5.2 to compare various models with each other.Red polygons represent observed landslides in the Veneto region in 5.1b.Table 5.1: Negative Log Likelihood LossMETHOD TEST ERR TRAIN ERR AUCRandom 0.065 0.069 0.50LLR 0.055 0.057 0.80NN 0.052 0.055 0.83LANN 0.048 0.052 0.85CNN 0.047 0.051 0.85LACNN 0.046 0.050 0.87in predicting landslides.5.1.2 Negative Log-Likelihood ErrorWe further assess our model by getting the negative log-likelihood error on both the trainingand the test set. Table 5.1 illustrates the final results of all the baselines. The LACNN modelobtains the lowest errors on both train and test sets.We then plot the validation errors of all models for the first 10 epochs in Figure 5.5. Thisplot shows that all models can obtain lower errors than the Naive model. Using the samecalculations from Section 4.3, we can obtain the error on the validation set with 𝑝𝑝 = 0.023and 𝑝𝑛 = 0.977. We can also see that the models do not overfit as the validation error does25(a) Linear Logistic Regression with 94 parameters. (b) Neural Network with 3140 parameters.(c) Locally-Aligned NN with 5348 parameters. (d) CNN with 849904 parameters.(e) Locally-Aligned CNN with 859840 parameters. (f) Ground truth.Figure 5.2: The acquired probability maps for a small region in Veneto and its corre-sponding ground truth. The resolution of the images are 2500x2500 pixels.260 500 1000 1500 20000500100015002000Figure 5.3: Data Partitioning for the provided area in Figure 5.2. Light purple, blue,and green colors show training, validation, and the test sets respectively.0.0 0.2 0.4 0.6 0.8 1.0False Positive Rate0.00.20.40.60.81.0True Positive RateLACNN with AUC = 0.87CNN with AUC = 0.85LANN with AUC = 0.85NN with AUC = 0.83LLR with AUC = 0.80Figure 5.4: ROC curves from all models on the test set.270 2 4 6 8 10epoch0.00.10.20.30.40.50.60.7negative log-likelihood lossLACNNCNNLANNNNLLRNaiveFigure 5.5: Negative log-likelihood error of all models on the validation set in the first 10epochs.not keep increasing. The reason is that we decrease the learning rate if the validation errorkeeps increasing for two epochs to prevent overfitting. You can see that the validation errorcorresponding to LACNN starts to increase at 6th and 7th epoch but decreases at epoch 8thafter reducing the learning rate. All of these metrics show that the locally-aligned CNN modelperforms better than the other baselines in predicting landslides.28Chapter 6Conclusion and Future Work6.1 ConclusionLandslides are the movement of ground under the force of gravity. They are common phenom-ena that can cause significant casualties and damages to properties. There have been manyapproaches to produce susceptibility maps to reduce the impact of landslides including expert-based, physics-based, and statistical methods. All of these methods have their flaws and lack astandard set of features.We provide a standardized open-source dataset using the INSPIRE terminology so thatanyone who uses the INSPIRE terminology can compare their results to our proposed baselines.We also propose a novel statistical approach for predicting landslides using machine learning.We introduce a deep convolutional model, called LACNN, that can follow the ground surfaceand align itself with the ground contour lines to extract relevant features.We evaluate our model by ROC curves and negative log-likelihood error and show that it canachieve the best results on both the training and test sets among all the baselines. Our resultssuggest that this type of statistical approach is effective for generating susceptibility maps whichin turn has the potential to alleviate human and financial losses caused by landslides.6.2 Future WorkThere are many possible ways to improve our current model. It would be interesting to train arotation-invariant model by data-augmentation and compare LACNN’s performance against it.We can optimize over various distances to see which of them are good for extracting featuresor even formulate the problem using soft attention for aligning the filters instead of hard at-tention on a fixed set of distances. Some of the other possible extensions can be finding betterapproaches to balance the data, proposing better metrics to compare different susceptibilitymaps with each other, applying different models such as auto-encoders for landslide suscepti-bility mapping, and using the ground truth as positive and unlabeled data instead of positiveand negative labels. Another interesting direction to extend this work is learning the up-hill29direction without programming it as a strong prior in the model.30Bibliography[1] A. P. Aitken, C. Ledig, L. Theis, J. Caballero, Z. Wang, and W. Shi. 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Thesis/Dissertation
eng
Computer Science
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Predicting landslides using contour aligning convolutional neural networks
Text