Antibodies with Adaptive Radius as Prototypes of High-Dimensional Datasets

An adaptive radius immune algorithm proposed in the literature, denoted as ARIA, is claimed to preserve the density distribution of the original dataset when generating prototypes. Density-preserving prototypes may correspond to high-quality compact representations for clustering applications. The original samples in the dataset are interpreted as antigens, and the prototypes are interpreted as antibodies. In this paper, some theoretical results are provided to demonstrate that the original version of ARIA is not capable of generating density-preserving prototypes when high-dimensional datasets are considered. Further, the same theoretical results are explored to conceive a new version of ARIA, now capable of exhibiting the announced density-preserving attribute. The main innovation is in the way the algorithm estimates local densities.