Improving hyperplane based density clustering solutions with applications in image processing

[摘要] 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 andscalable way using projection pursuit. The main limitation of MDH is that it defines clusters using a linear hyperplane. In recent research, MDH was appliedto data which was non-linearly embedded in a high-dimensional feature spaceusing Kernel Principal Component Analysis. While this method has shown tobe an effective approach that extends the linear plane to a non-linear form, itdoes not scale well. A procedure is needed that can improve the hyperplanesolution in an efficient way. We pose a novel approach to improve upon MDHby 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 objectsbecomes prohibitive as the size of the dataset increases. To reduce computation,a single step gradient heuristic is proposed whereby observations arereassigned based on the initial gradient evaluated at each point in relation tothe hyperplane. This study critically reviews the validity of these approachesthrough applications with simulated and real-world datasets, with a focus onapplications in image segmentation. We show that these approaches have thepotential to improve hyperplane solutions.

[发布机构] Stellenbosch University