An efficient unsupervised method for obtaining low-density hyperplane separators is proposed. The method is based on a modified stochastic gradient descent applied on a convolution of the empirical distribution function with a smoothing kernel. Low-density hyperplanes are motivated by the fact that they avoid intersecting high density regions, and so tend to pass between high density clusters, thus separating them from one another, while keeping the individual clusters intact. Multiple hyperplanes can be combined in a hierarchical model to obtain a complete clustering solution. A simple post-processing of solutions induced by large collections of hyperplanes yields an efficient and accurate clustering method, capable of automatically selecting the number of clusters. Experiments show that the proposed method is highly competitive in terms of both speed and accuracy when compared with relevant benchmarks. Code is available in the form of an R package at
https://github.com/DavidHofmeyr/iMDH