Proximity Alert: Ipelets for Neighborhood Graphs and Clustering

TL;DR

This paper introduces a collection of Lua-based Ipelets for visualizing various neighborhood graphs and clustering algorithms to aid understanding in computational geometry and data analysis.

Contribution

It presents a set of freely available Ipelets for visualizing neighborhood graphs and clustering algorithms, enhancing insight into their behavior and properties.

Findings

Includes visualization tools for multiple neighborhood graphs.

Supports various clustering algorithms like DBSCAN, k-means, and hierarchical methods.

All Ipelets are programmed in Lua and freely accessible.

Abstract

Neighborhood graphs and clustering algorithms are fundamental structures in both computational geometry and data analysis. Visualizing them can help build insight into their behavior and properties. The Ipe extensible drawing editor, developed by Otfried Cheong, is a widely used software system for generating figures. One particular aspect of Ipe is the ability to add Ipelets, which extend its functionality. Here we showcase a set of Ipelets designed to help visualize neighborhood graphs and clustering algorithms. These include: $\eps$-neighbor graphs, furthest-neighbor graphs, Gabriel graphs, $k$-nearest neighbor graphs, $k^{th}$-nearest neighbor graphs, $k$-mutual neighbor graphs, $k^{th}$-mutual neighbor graphs, asymmetric $k$-nearest neighbor graphs, asymmetric $k^{th}$-nearest neighbor graphs, relative-neighbor graphs, sphere-of-influence graphs, Urquhart graphs, Yao graphs, and clustering algorithms including complete-linkage, DBSCAN, HDBSCAN, $k$-means, $k$-means++, $k$-medoids, mean shift, and single-linkage. Our Ipelets are all programmed in Lua and are freely available.