Adaptive Clustering Using Kernel Density Estimators

We investigate statistical properties of a clustering algorithm that receives level set estimates from a kernel density estimator and then estimates the first split in the density level cluster tree if such a split is present or detects the absence of such a split. Key aspects of our analysis include finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for chosing the kernel bandwidth. For the rates and the adaptivity we do not need continuity assumptions on the density such as H\"older continuity, but only require intuitive geometric assumptions of non-parametric nature.