🤖 AI Summary
This study addresses the detection and localization of modes and antimodes in multimodal data by proposing a novel method based on spacings derived from order statistics. The approach smooths the spacing sequence via low-pass filtering and employs nonparametric inference through bootstrap and permutation tests. It further integrates a change-point detection algorithm that fuses parametric and nonparametric information, systematically leveraging both the stability of spacings and their local growth characteristics to jointly identify modes and antimodes—an innovation not previously explored. The method substantially enhances the robustness and accuracy of multimodal structure detection and has been successfully applied to identifying Kirkwood gaps in the asteroid belt. An open-source R package, Dimodal, along with C/Python interfaces (DimodalCPy), is released to facilitate efficient multimodal data analysis.
📝 Abstract
Spacing, the difference between consecutive order statistics, has two features that reflect the modality of the data. Consistent, stable values occur around modes while local increases mark the transitions between them. These features not only signal multi-modality, they also locate modes and anti-modes. Dimodal is an R package for detecting and evaluating these situations. It includes parametric feature models and bootstrap tests for spacing smoothed by low-pass filtering, non-parametric runs and permutation tests for the interval spacing, and a fusion of changepoints in the raw spacing. We introduce the analysis, describe the package, its implementation and performance, and apply it to identifying Kirkwood gaps in the asteroid belt. We also present ports of the software, with DimodalCPy a command-line program written in C with a Python interface.