Browsing by Author "Kenyon, Jacob Bradley"

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    Improving hyperplane based density clustering solutions with applications in image processing
    (Stellenbosch : Stellenbosch University, 2019-04) Kenyon, Jacob Bradley; Hofmeyr, David; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : Minimum Density Hyperplane (MDH) clustering is a recently proposed method that seeks the location of an optimal low-density separator by directly minimising the integral of the empirical density function on the separating surface. This approach learns underlying clusters within the data in an efficient and scalable way using projection pursuit. The main limitation of MDH is that it defines clusters using a linear hyperplane. In recent research, MDH was applied to data which was non-linearly embedded in a high-dimensional feature space using Kernel Principal Component Analysis. While this method has shown to be an effective approach that extends the linear plane to a non-linear form, it does not scale well. A procedure is needed that can improve the hyperplane solution in an efficient way. We pose a novel approach to improve upon MDH by reassigning observations in a neighbourhood around a hyperplane solution using a gradient ascent procedure, Mean Shift. While Mean Shift is shown to provide promising results, the computation required to reassign objects becomes prohibitive as the size of the dataset increases. To reduce computation, a single step gradient heuristic is proposed whereby observations are reassigned based on the initial gradient evaluated at each point in relation to the hyperplane. This study critically reviews the validity of these approaches through applications with simulated and real-world datasets, with a focus on applications in image segmentation. We show that these approaches have the potential to improve hyperplane solutions.