Adaptive Clustering Using Kernel Density Estimators
This work addresses the challenge of robust and adaptive clustering for data analysis, offering a method that is less reliant on restrictive assumptions, though it appears incremental in its approach.
The authors tackled the problem of adaptive clustering by developing a recursive algorithm that estimates cluster trees using kernel density estimators, achieving finite sample guarantees and convergence rates without requiring strong continuity assumptions on the underlying density.
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as Hölder continuity, but only require intuitive geometric assumptions of non-parametric nature.