Fully adaptive density-based clustering
This addresses a fundamental limitation in density-based clustering for data analysis applications, though it appears incremental as it builds on existing level set estimation methods.
The paper tackles the problem of density-based clustering's dependence on user-specified density levels by proposing an algorithm that estimates the smallest level with multiple connected components, showing consistent estimation and convergence rates with a histogram-based estimator.
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components. In the case where this algorithm is fed with histogram-based level set estimates, we provide a finite sample analysis, which is then used to show that the algorithm consistently estimates both the smallest level and the corresponding connected components. We further establish rates of convergence for the two estimation problems, and last but not least, we present a simple, yet adaptive strategy for determining the width-parameter of the involved density estimator in a data-depending way.