Maximum Clusterability Divisive Clustering

The notion of cluster ability is often used to determine how strong the cluster structure within a set of data is, as well as to assess the quality of a clustering model. In multivariate applications, however, the cluster ability of a data set can be obscured by irrelevant or noisy features. We study the problem of finding low dimensional projections which maximise the cluster ability of a data set. In particular, we seek low dimensional representations of the data which maximise the quality of a binary partition. We use this bi-partitioning recursively to generate high quality clustering models. We illustrate the improvement over standard dimension reduction and clustering techniques, and evaluate our method in experiments on real and simulated data sets.