Low-Noise Density Clustering

We study density-based clustering under low-noise conditions. Our framework allows for sharply defined clusters such as clusters on lower dimensional manifolds. We show that accurate clustering is possible even in high dimensions. We propose two data-based methods for choosing the bandwidth and we study the stability properties of density clusters. We show that a simple graph-based algorithm known as the ``friends-of-friends'' algorithm successfully approximates the high density clusters.