Minimum density hyperplanes in the feature space

We introduce a kernel formulation of the recently proposed minimum density hyperplane approach to clustering. This enables the identification of clusters that are not linearly separable in the input space by mapping them into a feature space. This mapping also extends the applicability of the minimum density hyperplane to datasets whose features are not necessarily continuous. The location of minimum density hyperplanes involves the optimisation of a non-convex objective function. In the feature space, the dimensionality of the optimisation problem is n, where n is the number of observations. We further propose an approximation method that can substantially reduce the dimensionality of the search space, avoiding searching over dimensions which are unlikely to contain useful information for clustering. Experimental results suggest that the proposed approach is capable of producing high quality partitions across a number of benchmark datasets.