Spatial clustering algorithms for areal data

[摘要] The main aim of this thesis is to develop new spatial clustering approaches which can simultaneously identify different areal clusters and guarantee their geographical contiguity. The second aim is to adjust the finite mixture model in order to cope with the issues caused by outliers or singletons (clusters with only one object). In addition, the thesis also aims to extend the applications of these newly proposed spatial clustering techniques from univariate to multivariate space.In Chapter 1, I will review some available clustering techniques in grouping spatial data and will also introduce different types of clustering data and the Glasgow housing market data which will be used in the thesis’s application. At the end of this chapter, I will outline the structure of this thesis. In Chapter 2, I will give the general statistical theory and inference methodologies used across this thesis, including frequentist and Bayesian statistical inferences, multidimensional scaling and the Procrustes transformation. In Chapter 3, I will introduce techniques that could be used in transforming between two types of clustering data introduced in Chapter 1. Chapter 4 will define some cluster and graph terminology and will also introduce different clustering techniques, such as hierarchical clustering, Chameleon hierarchical clustering and model-based clustering. In this chapter, I will also cover some techniques used in cluster comparisons, methods for number of clusters decisions and number of dimensions decisions. Chapter 6 will introduce more detail about spatial hierarchical clustering. The simulation results from spatial hierarchical clustering will be used as the reference results for comparison with the results from the proposed novel spatial clustering techniques in later chapters.The newly proposed clustering techniques, Chameleon spatial hierarchical clustering, spatially constrained finite mixture model with noise component or with priors and spatially constrained Bayesian model-based clustering with dissimilarities, in clustering areal data will be introduced in Chapters 7, 8 and 9 respectively. Also, the simulations and the application in Glasgow housing market will be given at the end of each of these three chapters. Chameleon spatial hierarchical clustering combined the spatial contiguity with Chameleon hierarchical clustering, so areas grouped together are spatially contiguous. Spatially constrained finite mixture models incorporate the spatial prior distribution into the classical finite mixture model to deal with the spatial contiguity issue. Also, I will make the spatially constrained finite mixture model more robust by incorporating a uniform distribution to model the noise points or adding prior distributions to the model. In Chapter 9, I will add a spatial prior to the model-based clustering with dissimilarities model and then will use a Bayesian approach to obtain a spatial contiguous clustering. Chapter 10 will be conclusions and discussion about the newly proposed clustering methods.

[发布机构] University:University of Glasgow;Department:School of Mathematics and Statistics

[关键词] QA Mathematics