Isotropy criteria and algorithms for data clustering
Sanketh Shetty · 2011
Given a set of points, the goal of data clustering is to group them into clusters, such that the internal homogeneity of points within each cluster contrasts to inter-cluster heterogeneity. Over the last fifty years, many methods for data clustering have been developed in diverse scientific communities. However, many of these methods suffer from several shortcomings, and are unable to handle the rich diversity of cluster structures that are usually present in data. We develop an unsupervised, nonparametric approach to data clustering that addresses these shortcomings. Our goal is to build on the strengths of these methods, while simultaneously offering innovative solutions to their limitations. In our cluster model, clusters are seen as groups of points, with overlapping neighborhoods, that have similar spatial structures that are in contrast with their surroundings. We use the isotropy of a point distribution to characterize spatial structure. We argue that identifying the isotropic density neighborhoods of a point, helps in the detection of a diversity of cluster structures that are challenging to many other methods. We develop three different criteria for identifying neighborhoods with isotropic density. The first criterion is based on examining properties of one-dimensional projections in a hyperspherical neighborhood with uniform point distribution. The second and third criteria are based on the analysis of the force