A methodology for automatic parameter-tuning and center selection in density-peak clustering methods

The density-peak clustering algorithm, which we refer to as DPC, is a novel and efficient density-based clustering approach. The method has the advantage of allowing non-convex clusters, and clusters of variable size and density, to be grouped together, but it also has some limitations, such as the visual location of centers and the parameter tuning. This paper describes an optimization-based methodology for automatic parameter/center selection applicable both to the DPC and to other algorithms derived from it. The objective function is an internal/external cluster validity index, and the decisions are the parameterization of the algorithm and the choice of centers. The internal validation measures lead to an automatic parameter-tuning process, and the external validation measures lead to the so-called optimal rules, which are a tool to bound the performance of a given algorithm from above on the set of parameterizations. A numerical experiment with real data was performed for the DPC and for the fuzzy weighted k-nearest neighbor (FKNN-DPC) which validates the automatic parameter-tuning methodology and demonstrates its efficiency compared to the state of the art.