Predicting landslides for risk analysis — Spatial models tested by a cross-validation technique

A landslide-hazard map is intended to show the location of future slope instability. Most spatial models of the hazard lack reliability tests of the procedures and predictions for estimating the probabilities of future landslides, thus precluding use of the maps for probabilistic risk analysis. To correct this deficiency we propose a systematic procedure comprising two analytical steps: “relative-hazard mapping” and “empirical probability estimation”. A mathematical model first generates a prediction map by dividing an area into “prediction” classes according to the relative likelihood of occurrence of future landslides, conditional by local geomorphic and topographic characteristics. The second stage estimates empirically the probability of landslide occurrence in each prediction class, by applying a cross-validation technique. Cross-validation, a “blind test” here using non-overlapping spatial or temporal subsets of mapped landslides, evaluates accuracy of the prediction and from the resulting statistics estimates occurrence probabilities of future landslides. This quantitative approach, exemplified by several experiments in an area near Lisbon, Portugal, can accommodate any subsequent analysis of landslide risk.     

Novel evaluation metrics for sparse spatio-temporal point process hotspot predictions - a crime case study

Many physical and sociological processes are represented as discrete events in time and space. These spatio-temporal point processes are often sparse, meaning that they cannot be aggregated and treated with conventional regression models. Models based on the point process framework may be employed instead for prediction purposes. Evaluating the predictive performance of these models poses a unique challenge, as the same sparseness prevents the use of popular measures such as the root mean squared error. Statistical likelihood is a valid alternative, but this does not measure absolute performance and is therefore difficult for practitioners and researchers to interpret. Motivated by this limitation, we develop a practical toolkit of evaluation metrics for spatio-temporal point process predictions. The metrics are based around the concept of hotspots, which represent areas of high point density. In addition to measuring predictive accuracy, our evaluation toolkit considers broader aspects of predictive performance, including a characterisation of the spatial and temporal distributions of predicted hotspots and a comparison of the complementarity of different prediction methods. We demonstrate the application of our evaluation metrics using a case study of crime prediction, comparing four varied prediction methods using crime data from two different locations and multiple crime types. The results highlight a previously unseen interplay between predictive accuracy and spatio-temporal dispersion of predicted hotspots. The new evaluation framework may be applied to compare multiple prediction methods in a variety of scenarios, yielding valuable new insight into the predictive performance of point process-based prediction.     

Predictive modelling of gold potential with the integration of multisource information based on random forest: a case study on the Rodalquilar area,Southern Spain

Mineral exploration activities require robust predictive models that result in accurate mapping of the probability that mineral deposits can be found at a certain location. Random forest (RF) is a powerful machine data-driven predictive method that is unknown in mineral potential mapping. In this paper, performance of RF regression for the likelihood of gold deposits in the Rodalquilar mining district is explored. The RF model was developed using a comprehensive exploration GIS database composed of: gravimetric and magnetic survey, a lithogeochemical survey of 59 elements, lithology and fracture maps, a Landsat 5 Thematic Mapper image and gold occurrence locations. The results of this study indicate that the use of RF for the integration of large multisource data sets used in mineral exploration and for prediction of mineral deposit occurrences offers several advantages over existing methods. Key advantages of RF include: (1) the simplicity of parameter setting; (2) an internal unbiased estimate of the prediction error; (3) the ability to handle complex data of different statistical distributions, responding to nonlinear relationships between variables; (4) the capability to use categorical predictors; and (5) the capability to determine variable importance. Additionally, variables that RF identified as most important coincide with well-known geologic expectations. To validate and assess the effectiveness of the RF method, gold prospectivity maps are also prepared using the logistic regression (LR) method. Statistical measures of map quality indicate that the RF method performs better than LR, with mean square errors equal to 0.12 and 0.19, respectively. The efficiency of RF is also better, achieving an optimum success rate when half of the area predicted by LR is considered.     

The representation of geoscience information for data integration

In mineral exploration, resource assessment, or natural hazard assessment, many layers of geoscience maps such as lithology, structure, geophysics, geochemistry, hydrology, slope stability, mineral deposits, and preprocessed remotely sensed data can be used as evidence to delineate potential areas for further investigation. Today's PC-based data base management systems, statistical packages, spreadsheets, image processing systems, and geographical information systems provide almost unlimited capabilities of manipulating data. Generally such manipulations make a strategic separation of spatial and nonspatial attributes, which are conveniently linked in relational data bases. The first step in integration procedures usually consists of studying the individual charateristics of map features and interrelationships, and then representing them in numerical form (statistics) for finding the areas of high potential (or impact).Data representation is a transformation of our experience of the real world into a computational domain. As such, it must comply with models and rules to provide us with useful information. Quantitative representation of spatially distributed map patterns or phenomena plays a pivotal role in integration because it also determines the types of combination rules applied to them.Three representation methods—probability measures, Dempster-Shafer belief functions, and membership functions in fuzzy sets—and their corresponding estimation procedures are presented here with analyses of the implications and of the assumptions that are required in each approach to thematic mapping. Difficulties associated with the construction of probability measures, belief functions, and membership functions are also discussed; alternative procedures to overcome these difficulties are proposed. These proposed techniques are illustrated by using a simple, artificially constructed data set.     

Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space

Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.

     

Mineral Potential Mapping Using a Conjugate Gradient Logistic Regression Model

Mineral potential prediction is a process of establishing a statistical model that describes the relationship between evidence variables and mineral occurrences. In this study, evidence variables were constructed from geological, remote sensing, and geochemical data collected from the Lalingzaohuo district, Qinghai Province, China. Based on these evidence variables, a conjugate gradient logistic regression (CG-LR) model was established to predict exploration targets in the study area. The receiver operating characteristic (ROC) and prediction–area (P-A) curves were used to evaluate the effectiveness of the CG-LR model in mineral potential mapping. The difference between the vertical and horizontal coordinates of each point on the ROC curve was used to determine the optimal threshold for classifying the exploration targets. The optimal threshold corresponds to the point on the ROC curve where the difference between the vertical coordinate and the horizontal coordinate is the largest. In exploration target prediction in the study area, the CG algorithm was used to optimize iteratively the LR coefficients, and the prediction effectiveness was tested for different epochs. With increasing iterations, the prediction performance of the model becomes increasingly better. After 60 iterations, the LR model becomes stable and has the best performance in exploration target prediction. At this point, the exploration targets predicted by the CG-LR model occupy 14.39% of the study area and contain 93% of the known mineral deposits. The exploration targets predicted by the model are consistent with the metallogenic geological characteristics of the study area. Therefore, the CG-LR model can effectively integrate geological, remote sensing, and geochemical data for the study area to predict targets for mineral exploration.

     

The use of predictive analysis in spatiotemporal crime forecasting: Building and testing a model in an urban context

Police databases hold a large amount of crime data that could be used to inform us about current and future crime trends and patterns. Predictive analysis aims to optimize the use of these data to anticipate criminal events. It utilizes specific statistical methods to predict the likelihood of new crime events at small spatiotemporal units of analysis. The aim of this study is to investigate the potential of applying predictive analysis in an urban context. To this end, the available crime data for three types of crime (home burglary, street robbery, and battery) are spatially aggregated to grids of 200 by 200 m and retrospectively analyzed. An ensemble model is applied, synthesizing the results of a logistic regression and neural network model, resulting in bi-weekly predictions for 2014, based on crime data from the previous three years. Temporally disaggregated (day versus night predictions) monthly predictions are also made. The quality of the predictions is evaluated based on the following criteria: direct hit rate (proportion of incidents correctly predicted), precision (proportion of correct predictions versus the total number of predictions), and prediction index (ratio of direct hit rate versus proportion of total area predicted as high risk). Results indicate that it is possible to attain functional predictions by applying predictive analysis to grid-level crime data. The monthly predictions with a distinction between day and night produce better results overall than the bi-weekly predictions, indicating that the temporal resolution can have an important impact on the prediction performance.     

Incorporating Spatial Dependence in Predictive Vegetation Models: Residual Interpolation Methods*

Predictive vegetation modeling can be used statistically to relate the distribution of vegetation across a landscape as a function of important environmental variables. Often these models are developed without considering the spatial pattern that is inherent in biogeographical data, resulting from either biotic processes or missing or misspecified environmental variables. Including spatial dependence explicitly in a predictive model can be an efficient way to improve model accuracy with the available data. In this study, model residuals were interpolated and added to model predictions, and the resulting prediction accuracies were assessed. Adding kriged residuals improved model accuracy more often than adding simulated residuals, although some alliances showed no improvement or worse accuracy when residuals were added. In general, the prediction accuracies that were not increased by adding kriged residuals were either rare in the sample or had high nonspatial model accuracy. Regression interpolation methods can be an important addition to current tools used in predictive vegetation models as they allow observations that are predicted well by environmental variables to be left alone, while adjusting over‐ and underpredicted observations based on local factors.     

Spatial crime distribution and prediction for sporting events using social media

ABSTRACT

Sporting events attract high volumes of people, which in turn leads to increased use of social media. In addition, research shows that sporting events may trigger violent behavior that can lead to crime. This study analyses the spatial relationships between crime occurrences, demographic, socio-economic and environmental variables, together with geo-located Twitter messages and their ‘violent’ subsets. The analysis compares basketball and hockey game days and non-game days. Moreover, this research aims to analyze crime prediction models using historical crime data as a basis and then introducing tweets and additional variables in their role as covariates of crime. First, this study investigates the spatial distribution of and correlation between crime and tweets during the same temporal periods. Feature selection models are applied in order to identify the best explanatory variables. Then, we apply localized kernel density estimation model for crime prediction during basketball and hockey games, and on non-game days. Findings from this study show that Twitter data, and a subset of violent tweets, are useful in building prediction models for the seven investigated crime types for home and away sporting events, and non-game days, with different levels of improvement.     

Boosting for Mineral Prospectivity Modeling: A New GIS Toolbox

With an increasing demand for raw materials, predictive models that support successful mineral exploration targeting are of great importance. We evaluated different machine learning techniques with an emphasis on boosting algorithms and implemented them in an ArcGIS toolbox. Performance was tested on an exploration dataset from the Iberian Pyrite Belt (IPB) with respect to accuracy, performance, stability, and robustness. Boosting algorithms are ensemble methods used in supervised learning for regression and classification. They combine weak classifiers, i.e., classifiers that perform slightly better than random guessing to obtain robust classifiers. Each time a weak learner is added; the learning set is reweighted to give more importance to misclassified samples. Our test area, the IPB, is one of the oldest mining districts in the world and hosts giant volcanic-hosted massive sulfide (VMS) deposits. The spatial density of ore deposits, as well as the size and tonnage, makes the area unique, and due to the high data availability and number of known deposits, well-suited for testing machine learning algorithms. We combined several geophysical datasets, as well as layers derived from geological maps as predictors of the presence or absence of VMS deposits. Boosting algorithms such as BrownBoost and Adaboost were tested and compared to Logistic Regression (LR), Random Forests (RF) and Support Vector machines (SVM) in several experiments. We found performance results relatively similar, especially to BrownBoost, which slightly outperformed LR and SVM with respective accuracies of 0.96 compared to 0.89 and 0.93. Data augmentation by perturbing deposit location led to a 7% improvement in results. Variations in the split ratio of training and test data led to a reduction in the accuracy of the prediction result with relative stability occurring at a critical point at around 26 training samples out of 130 total samples. When lower numbers of training data were introduced accuracy dropped significantly. In comparison with other machine learning methods, Adaboost is user-friendly due to relatively short training and prediction times, the low likelihood of overfitting and the reduced number of hyperparameters for optimization. Boosting algorithms gave high predictive accuracies, making them a potential data-driven alternative for regional scale and/or brownfields mineral exploration.

     

Lithodiversity and Its Spatial Association with Metallic Mineral Sites,Great Basin of Nevada

Geographical information system (GIS) techniques were used to investigate the spatial association between metallic mineral sites and lithodiversity in Nevada. Mineral site data sets include various size and type subsets of about 5,500 metal-bearing occurrences and deposits. Lithodiversity was calculated by counting the number of unique geological map units within four sizes of square-shaped sample neighborhoods (2.5-by-2.5, 5-by-5, 10-by-10, and 20-by-20 km) on three different scales of geological maps (national, 1:2,500,000; state, 1:500,000; county, 1:250,000). The spatial association between mineral sites and lithodiversity was observed to increase with increasing lithodiversity. This relationship is consistent for (1) both basin-range and range-only regions, (2) four sizes of sample neighborhoods, (3) various mineral site subsets, (4) the three scales of geological maps, and (5) areas not covered by large-scale maps. A map scale of 1:500,000 and lithodiversity sampling neighborhood of 5-by-5 km was determined to best describe the association. Positive associations occurred for areas having >3 geological map units per neighborhood, with the strongest observed at approximately >7 units. Areas in Nevada with more than three geological map units per 5-by-5 km neighborhood contain more mineral sites than would be expected resulting from chance. High lithodiversity likely reflects the occurrence of complex structural, stratigraphic, and intrusive relationships that are thought to control, focus, localize, or expose mineralization. The application of lithodiversity measurements to areas that are not well explored may help delineate regional-scale exploration targets and provide GIS-supported mineral resource assessment and exploration activity another method that makes use of widely available geological map data.     

Remotely sensed agricultural modification improves prediction of suitable habitat for a threatened lizard

The geographical distribution of a species is limited by factors such as climate, resources, disturbances and species interactions. Environmental niche models attempt to encapsulate these limits and represent them spatially but do not always incorporate disturbance factors. We constructed MaxEnt models derived from a remotely sensed vegetation classification with, and without, an agricultural modification variable. Including agricultural modification improved model performance and led to more sites with native vegetation and fewer sites with exotic or degraded native vegetation being predicted suitable for A. parapulchella. Analysis of a relatively well-surveyed sub-area indicated that including agricultural modification led to slightly higher omission rates but markedly fewer likely false positives. Expert assessment of the model based on mapped habitat also suggested that including agricultural modification improved predictions. We estimate that agricultural modification has led to the destruction or decline of approximately 30–35% of the most suitable habitat in the sub-area studied and approximately 20–25% of suitable habitat across the entire study area, located in the Australian Capital Territory, Australia. Environmental niche models for a range of species, particularly habitat specialists, are likely to benefit from incorporating agricultural modification. Our findings are therefore relevant to threatened species planning and management, particularly at finer spatial scales.     

Radial Basis Functional Link Nets Used as a Prospectivity Mapping Tool for Orogenic Gold Deposits Within the Central Lapland Greenstone Belt, Northern Fennoscandian Shield

Among the more popular spatial modeling techniques, artificial neural networks (ANN) are tools that can deal with non-linear relationships, can classify unknown data into categories by using known examples for training, and can deal with uncertainty; characteristics that provide new possibilities for data exploration. Radial basis functional link nets (RBFLN), a form of ANN, are applied to generate a series of prospectivity maps for orogenic gold deposits within the Paleoproterozoic Central Lapland Greenstone Belt, Northern Fennoscandian Shield, Finland, which is considered highly prospective yet clearly under explored. The supervised RBFLN performs better than previously applied statistical weights-of-evidence or conceptual fuzzy logic methods, and equal to logistic regression method, when applied to the same geophysical and geochemical data layers that are proxies for conceptual geological controls. By weighting the training feature vectors in terms of the size of the gold deposits, the classification of the neural network results provides an improved prediction of the distribution of the more important deposits/occurrences. Thus, ANN, more specifically RBFLN, potentially provide a better tool to other methodologies in the development of prospectivity maps for mineral deposits, hence aiding conceptual exploration.     

Additive models in mining and exploration

In this paper we present the use of additive models (AMs) for geostatistical applications. AMs are generalizations of linear regression models which hold the central place in the toolbox of applied statisticians. Generally speaking, the linear relationship between response and predictors is replaced with a general functional form. Recently such models were introduced in geostatistics. Especially, we give an approach for binary data. In this case we get generalized additive models (GAMs). Logistic regression is quite popular in medical and biological research. Using logit links also in GAMs we get so called additive logistic models. An application for geostatistical data is introduced. In a second approach we use AMs for spatial prediction and surface modelling. In both cases an advantage of multivariate data can be taken. The proposed applications can be used in the development of exploration strategies, especially in the early stage of exploration     

Map Scale Effects on Estimating the Number of Undiscovered Mineral Deposits

Estimates of numbers of undiscovered mineral deposits, fundamental to assessing mineral resources, are affected by map scale. Where consistently defined deposits of a particular type are estimated, spatial and frequency distributions of deposits are linked in that some frequency distributions can be generated by processes randomly in space whereas others are generated by processes suggesting clustering in space. Possible spatial distributions of mineral deposits and their related frequency distributions are affected by map scale and associated inclusions of non-permissive or covered geological settings. More generalized map scales are more likely to cause inclusion of geologic settings that are not really permissive for the deposit type, or that include unreported cover over permissive areas, resulting in the appearance of deposit clustering. Thus, overly generalized map scales can cause deposits to appear clustered. We propose a model that captures the effects of map scale and the related inclusion of non-permissive geologic settings on numbers of deposits estimates, the zero-inflated Poisson distribution. Effects of map scale as represented by the zero-inflated Poisson distribution suggest that the appearance of deposit clustering should diminish as mapping becomes more detailed because the number of inflated zeros would decrease with more detailed maps. Based on observed worldwide relationships between map scale and areas permissive for deposit types, mapping at a scale with twice the detail should cut permissive area size of a porphyry copper tract to 29% and a volcanic-hosted massive sulfide tract to 50% of their original sizes. Thus some direct benefits of mapping an area at a more detailed scale are indicated by significant reductions in areas permissive for deposit types, increased deposit density and, as a consequence, reduced uncertainty in the estimate of number of undiscovered deposits. Exploration enterprises benefit from reduced areas requiring detailed and expensive exploration, and land-use planners benefit from reduced areas of concern.     

Data structures for three-dimensional spatial information systems in geology

Abstract

The accumulation of geological information in digital form, due to modern exploration methods, has introduced the possibility of applying geographical information system technology to the field of geology. To achieve the benefits in information management and in data analysis and interpretation, however, it will be necessary to develop spatial models and associated data structures which are specifically designed for working in three dimensions. Some progress in this direction has already been demonstrated, with the application of octree spatial subdivision techniques to the storage of uniform volume elements representing mineral properties. By imposing octree tessellations on more precisely-defined geometric data, such as triangulated surfaces and polygon line segments, it may now be possible to combine efficient spatial addressing with topologically-coded boundary representations of geological strata. The development of storage schemes capable of representing such geological boundary models at different scales poses a particular problem, a possible solution to which may be by means of hierarchical classification of the vertices of triangulated surfaces according to shape contribution.     

河南省火灾影响因素的空间分析

科学揭示火灾及其影响因素间的空间关系可为防火管理提供决策支持和有益启示。以往研究多在“空间平稳”的框架下进行火灾影响因素分析,但火灾和其可量化的影响因素往往自身均表现为“空间异质”,基于非空间的全局模型模拟可能会得出误导性甚至错误的结论。地理加权回归(GWR)可解释火灾及其影响因素间空间关系的局部变异。本文选取影响火灾分布的高程、坡度、居民地可达性、道路可达性、地表温度、归一化差植被指数和全球植被湿度指数作为解释变量,以是否火烧作为二元因变量,应用logistic GWR对河南省2002-2012年火季(9-10月)火灾的影响因素进行探索性分析。以多时态空间抽样取得训练样本,利用GWR 4.0软件开发一个logistic GWR火烧概率模型,从可靠性和区分能力两方面对模型性能分别进行内部检验和独立检验,以确保火灾影响因素分析的可靠和合理性。结果表明:①坡度、居民地可达性、温度、植被长势和植被湿度对河南省火灾的影响呈现显著空间变化,高程、道路可达性的影响空间变化不显著,低海拔、道路可达性差的区域更易发生火灾。②温度和植被长势对火灾影响省内全局显著,坡度、居民地可达性和植被湿度对火灾影响在省内仅部分区域显著。③河南省可划分为7种类型区,不同类型区的火灾影响因素相对重要性存在差异,应因地制宜制定防火策略和确定防火重点。④logistic GWR模型可用于分析火灾影响因素的局部空间变异,作为火险研究的一种有效工具。     

Soil-landscape modelling and spatial prediction of soil attributes

Abstract

Explicit and quantitative models for the spatial prediction of soil and landscape attributes are required for environmental modelling and management. In this study, advances in the spatial representation of hydrological and geomorphological processes using terrain analysis techniques are integrated with the development of a field sampling and soil-landscape model building strategy. Statistical models are developed using relationships between terrain attributes (plan curvature, compound topographic index, upslope mean plan curvature) and soil attributes (A horizon depth, Solum depth, E horizon presence/absence) in an area with uniform geology and geomorphic history. These techniques seem to provide appropriate methodologies for spatial prediction and understanding soil landscape processes.