Towards geostatistical learning for the geosciences: A case study in improving the spatial awareness of spectral clustering

The particularities of geosystems and geoscience data must be understood before any development or implementation of statistical learning algorithms. Without such knowledge, the predictions and inferences may not be accurate and physically consistent. Accuracy, transparency and interpretability, credibility, and physical realism are minimum criteria for statistical learning algorithms when applied to the geosciences. This study briefly reviews several characteristics of geoscience data and challenges for novel statistical learning algorithms. A novel spatial spectral clustering approach is introduced to illustrate how statistical learners can be adapted for modelling geoscience data. The spatial awareness and physical realism of the spectral clustering are improved by utilising a dissimilarity matrix based on nonparametric higher-order spatial statistics. The proposed model-free technique can identify meaningful spatial clusters (i.e. meaningful geographical subregions) from multivariate spatial data at different scales without the need to define a model of co-dependence. Several mixed (e.g. continuous and categorical) variables can be used as inputs to the proposed clustering technique. The proposed technique is illustrated using synthetic and real mining datasets. The results of the case studies confirm the usefulness of the proposed method for modelling spatial data

Quantification of uncertainty of geometallurgical variables for mine planning optimisation

Interest in geometallurgy has increased significantly over the past 15 years or so because of the benefits it brings to mine planning and operation. Its use and integration into design, planning and operation is becoming increasingly critical especially in the context of declining ore grades and increasing mining and processing costs. This thesis, comprising four papers, offers methodologies and methods to quantify geometallurgical uncertainty and enrich the block model with geometallurgical variables, which contribute to improved optimisation of mining operations. This enhanced block model is termed a geometallurgical block model. Bootstrapped non-linear regression models by projection pursuit were built to predict grindability indices and recovery, and quantify model uncertainty. These models are useful for populating the geometallurgical block model with response attributes. New multi-objective optimisation formulations for block caving mining were formulated and solved by a meta-heuristics solver focussing on maximising the project revenue and, at the same time, minimising several risk measures. A novel clustering method, which is able to use both continuous and categorical attributes and incorporate expert knowledge, was also developed for geometallurgical domaining which characterises the deposit according to its metallurgical response. The concept of geometallurgical dilution was formulated and used for optimising production scheduling in an open-pit case study.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Quantitative Optimisation of Drilling for Brownfields Mineral Exploration

This research presents a novel optimisation framework for brownfields exploration drilling. The proposed optimisation methodology has been developed applying geostatistical methods and modern portfolio theory. The use of conditional simulations ensures that geological uncertainty is taken into account, and the application of Markowitz portfolio theory makes drilling funds allocation optimal. The proposed method closes the gap in current research by incorporating the inherent geological uncertainty of an exploration target and mineral economics

Fuzzy clustering with spatial correction and its application to geometallurgical domaining

Published online: 25 July 2018This paper describes a proposed method for clustering attributes on the basis of their spatial variability and the uncertainty of cluster member- ship. The method is applied to geometallurgical domaining in mining ap- plications. The main objective of geometallurgical clustering is to ensure consistent feed to a processing plant by minimising transitions between di erent types of feed coming from di erent domains (clusters). For this purpose, clusters should contain not only similar geometallurgical char- acteristics but also be located in as few contiguous and compact spatial locations as possible so as to maximise the homogeneity of ore delivered to the plant. Most existing clustering methods applied to geometallurgy have two problems. Firstly, they are unable to di erentiate subsets of attributes at the cluster level and therefore cluster membership can only be assigned on the basis of exactly identical attributes, which may not be the case in practice. Secondly, as they do not take account of the spatial relationships they can produce clusters which may be spatially dispersed and/or overlapped. In the work described in this paper a new clustering method is introduced that integrates three distinct steps to ensure qual- ity clustering. In the rst step, fuzzy membership information is used to minimise compactness and maximise separation. In the second step, the best subsets of attributes are de ned and applied for domaining purposes. These two steps are iterated to convergence. In the nal step a graph- based labelling method, which takes spatial constraints into account, is used to produce the nal clusters. Three examples are presented to illus- trate the application of the proposed method. These examples demon- strate that the proposed method can reveal useful relationships among geometallurgical attributes within a clear and compact spatial structure. The resulting clusters can be used directly in mine planning to optimise the ore feed to be delivered to the processing plant.E. Sepúlveda, P. A. Dowd, C. X

Mine evaluation optimisation

The definition of a mineral resource during exploration is a fundamental part of lease evaluation, which establishes the fair market value of the entire asset being explored in the open market. Since exact prediction of grades between sampled points is not currently possible by conventional methods, an exact agreement between predicted and actual grades will nearly always contain some error. These errors affect the evaluation of resources so impacting on characterisation of risks, financial projections and decisions about whether it is necessary to carry on with the further phases or not. The knowledge about minerals below the surface, even when it is based upon extensive geophysical analysis and drilling, is often too fragmentary to indicate with assurance where to drill, how deep to drill and what can be expected. Thus, the exploration team knows only the density of the rock and the grade along the core. The purpose of this study is to improve the process of resource evaluation in the exploration stage by increasing prediction accuracy and making an alternative assessment about the spatial characteristics of gold mineralisation. There is significant industrial interest in finding alternatives which may speed up the drilling phase, identify anomalies, worthwhile targets and help in establishing fair market value. Recent developments in nonconvex optimisation and high-dimensional statistics have led to the idea that some engineering problems such as predicting gold variability at the exploration stage can be solved with the application of clusterwise linear and penalised maximum likelihood regression techniques. This thesis attempts to solve the distribution of the mineralisation in the underlying geology using clusterwise linear regression and convex Least Absolute Shrinkage and Selection Operator (LASSO) techniques. The two presented optimisation techniques compute predictive solutions within a domain using physical data provided directly from drillholes. The decision-support techniques attempt a useful compromise between the traditional and recently introduced methods in optimisation and regression analysis that are developed to improve exploration targeting and to predict the gold occurrences at previously unsampled locations.Doctor of Philosoph

A review of clustering techniques and developments

© 2017 Elsevier B.V. This paper presents a comprehensive study on clustering: exiting methods and developments made at various times. Clustering is defined as an unsupervised learning where the objects are grouped on the basis of some similarity inherent among them. There are different methods for clustering the objects such as hierarchical, partitional, grid, density based and model based. The approaches used in these methods are discussed with their respective states of art and applicability. The measures of similarity as well as the evaluation criteria, which are the central components of clustering, are also presented in the paper. The applications of clustering in some fields like image segmentation, object and character recognition and data mining are highlighted

Spatial analysis for the distribution of cells in tissue sections

Spatial analysis, playing an essential role in data mining, is applied in a considerable number of fields. It is because of its broad applicability that dealing with the interdisciplinary issues is becoming more prevalent. It aims at exploring the underlying patterns of the data. In this project, we will employ the methodology that we utilize to tackle spatial problems to investigate how the cells distribute in the infected tissue sections and if there are clusters existing among the cells. The cells that are neighboring to the viruses are of interest. The data were provided by the Medetect Company in the form of 2-dimensional point data. We firstly adopted two common spatial analysis methods, clustering methods and proximity methods. In addition, a method for constructing a 2-dimensional hull was developed in order to delineate the compartments in tissue sections. A binomial test was conducted to evaluate the results. It is detectable that the clusters do exist among cells. The immune cells would accumulate around the viruses. We also found different patterns near and far away from viruses. This study implicates that the cells are interactive with each other and thus present the spatial patterns. However, our analyses are restricted in a planar circumstance instead of treating them in 3-dimensional space. For the further study, the spatial analysis could be carried out in three dimensions.It has been popular to utilize the heuristic methods or the existing methods to discover new findings and explain the mysterious phenomena in other subjects. And it is known that everything in nature relates to each other. In this sense, we could assume that the entire distribution of objects is relative to the locations of individuals. The idea of my work is attempting to explore this spatial relationship existing among cells. In my project, the relationships between individual cells or groups of cells are interesting. Our data is presented like the point cloud. It is doubted that if there are any groups existing among these points and if the viruses have neighbors. The methods are mainly categorized into three parts. The first method is to integrate the similar objects into groups. Here the similar objects could be the ones that are close to each other. The second method analyzes the degree of closeness between objects and looks for the neighbors of viruses. The last method can be used to draw the border of a point cloud, which seems like constructing the boundary of districts. Within each method, we carried out the corresponding case studies. Since similar objects can be grouped together, it is interesting to look into the details of each group. Thus we can know which two objects are similar in the same group. Basically, different types of cells in the same group can be checked and studied. In the closeness analysis, we found that some cells are indeed closer to each other. The constructed border could help us know the shape of point clouds. It can be concluded that the spatial relationship does exist among the cells. Groups of cells can be identified at a large extent. And one certain type of cells could be more attracted by some cells from a local level. However, this study is carried out in a 2D space. Actually, we neglect the real shape of cells which have heights. This could be a more interesting topic in the future

Subsurface Characterization by Means of Geovisual Analytics

This Thesis is concerned with one of the major problems in subsurface characterizations emerging from ever-increasing loads of data in the last decades: What kind of technologies suit well for extracting novel, valid and useful knowledge from persistent data repositories for the characterization of subsurface regions and how can such technologies be implemented in an integrated, community-open software platform? In order to address those questions, an interactive, open-source software platform for geoscientific knowledge discovery has been developed, which enables domain experts to generate, optimize and validate prognostic models of the subsurface domain. Such a free tool has been missing in the geoscientific community so far. The extensible software platform GeoReVi (Geological Reservoir Virtualization) implements selected aspects of geovisual analytics with special attention being paid to an implementation of the knowledge discovery in databases process. With GeoReVi the human expert can model and visualize static and dynamic systems in the subsurface in a feedback cycle. The created models can be analyzed and parameterized by means of modern approaches from geostatistics and data mining. Hence, knowledge that is useful to both the assessment of subsurface potentials and to support decision-making during the utilization process of the subsurface regions can be extracted and exchanged in a formalized manner. The modular software application is composed of both integrated and centralized databases, a graphical user interface and a business logic. In order to fulfill the needs of low computing time in accordance with high computational complexity of spatial problems, the software system makes intense use of parallelism and asynchronous programming. The competitiveness of industry branches, which are aimed at utilizing the subsurface in unknown regions, such as the geothermal energy production or carbon capture and storage, are especially dependent on the quality of spatial forecasts for relevant rock and fluid properties. Thus, the focus of this work has been laid upon the implementation of algorithms, which enhance the predictability of properties in space under consideration of uncertainty. The software system was therefore evaluated in ample real-world scenarios by solving problems from scientific, educational and industrial projects. The implemented software system shows an excellent suitability to generically address spatial problems such as interpolation or stochastic simulation under consideration of numerical uncertainty. In this context, GeoReVi served as a tool for discovering new knowledge with special regard to investigating the heterogeneity of rock media on multiple scales of investigation. Among others, it could be demonstrated that the three-dimensional scalar fields of different petrophysical and geochemical properties in sandstone media may diverge significantly at small-scales. In fact, if the small-scale variability is not considered in field-scale projects, in which the sampling density is usually low, statistical correlations and thus empirical relationships might be feigned. Furthermore, it could be demonstrated that the simple kriging variance, which is used to simulate the natural variability in sequential simulations, systematically underestimates the intrinsic variability of the investigated sandstone media. If the small-scale variability can be determined by high-resolution sampling, it can be used to enhance conditional simulations at the scale of depositional environments

ADCN: An Anisotropic Density-Based Clustering Algorithm for Discovering Spatial Point Patterns with Noise

Density-based clustering algorithms such as DBSCAN have been widely used for spatial knowledge discovery as they offer several key advantages compared to other clustering algorithms. They can discover clusters with arbitrary shapes, are robust to noise and do not require prior knowledge (or estimation) of the number of clusters. The idea of using a scan circle centered at each point with a search radius Eps to find at least MinPts points as a criterion for deriving local density is easily understandable and sufficient for exploring isotropic spatial point patterns. However, there are many cases that cannot be adequately captured this way, particularly if they involve linear features or shapes with a continuously changing density such as a spiral. In such cases, DBSCAN tends to either create an increasing number of small clusters or add noise points into large clusters. Therefore, in this paper, we propose a novel anisotropic density-based clustering algorithm (ADCN). To motivate our work, we introduce synthetic and real-world cases that cannot be sufficiently handled by DBSCAN (and OPTICS). We then present our clustering algorithm and test it with a wide range of cases. We demonstrate that our algorithm can perform as equally well as DBSCAN in cases that do not explicitly benefit from an anisotropic perspective and that it outperforms DBSCAN in cases that do. We show that our approach has the same time complexity as DBSCAN and OPTICS, namely O(n log n) when using a spatial index and O(n 2 ) otherwise. We provide an implementation and test the runtime over multiple cases. Finally, we apply DBSCAN, OPTICS, and ADCN to the task of extracting urban areas of interest (AOI) from geotagged photos in six cities. Visual comparison shows that, comparing to DBSCAN and OPTICS, ADCN is inclined to extract AOIs with linear shapes which follow the underline road networks. ADCN also turns out to connect clusters when the spatial distribution of them shows similar directions