Adaptive Density Level Set Clustering

Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We further show that this algorithm asymptotically recovers the corresponding connected components. Unlike previous work, our analysis does not require strong assumptions on the density such as continuity or even smoothness.