Informal unpaved roads in developing countries arise naturally through human movement and informal housing setups. These roads are not authorised nor maintained by council, nor recorded in official databases or online maps. Mapping such roads from satellite images is a common problem, as information on these roads is critical for sustainable city growth. Information on their location and extent may be gleaned from spatial big data, however, no automatic or semi-automatic approach is freely available. This research develops a novel algorithm for extracting informal roads from multispectral satellite images, using physical road characteristics. These include near-infrared reflectance, addressed via the NDVI index, shape, addressed via measures of compactness and elongation, and grey-value intensity. The crux of the algorithm is the Discrete Pulse Transform, implemented via the Roadmaker's Pavage. The algorithm provides a classification of road objects, along with an associated uncertainty measure for each road object. Accuracy is assessed using per-pixel assessment metrics and metrics based on road characteristics, including completeness, correctness, and Pratt's Figure of Merit, which is applied to road extraction accuracy for the first time. The algorithm is applied to areas in Gauteng and North West Provinces, South Africa. Sources of uncertainty and error are discussed, such as indefinite boundaries, surface type heterogeneity, trees and shadows. / Mini Dissertation (MSc)--University of Pretoria, 2019. / Acknowledgement of the National Research Foundation for the funding provided through the NRF-SASA Crisis in Academic Statistics grant. / Statistics / MSc / Unrestricted

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The purpose of the present dissertation is to study model selection techniques which are specifically designed for classification of high-dimensional data with a large number of classes. To the best of our knowledge, this problem has never been studied in depth previously. We assume that the number of components p is much larger than the number of samples n, and that only few of those p components are useful for subsequent classification. In what follows, we introduce two Bayesian models which use two different approaches to the problem: one which discards components which have “almost constant” values (Model 1) and another which retains the components for which between-group variations are larger than withingroup variation (Model 2). We show that particular cases of the above two models recover familiar variance or ANOVA-based component selection. When one has only two classes and features are a priori independent, Model 2 reduces to the Feature Annealed Independence Rule (FAIR) introduced by Fan and Fan (2008) and can be viewed as a natural generalization to the case of L > 2 classes. A nontrivial result of the dissertation is that the precision of feature selection using Model 2 improves when the number of classes grows. Subsequently, we examine the rate of misclassification with and without feature selection on the basis of Model 2.

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