Clustering with Uniformity- and Neighbor-Based Random Geometric Graphs

TL;DR

This paper introduces UN-CCDs, a graph-based clustering method that improves performance in moderate-dimensional data with complex clusters and noise by using a new spatial randomness test based on nearest neighbors.

Contribution

The paper develops UN-CCDs, a novel clustering approach that extends CCDs to moderate dimensions using a nearest-neighbor-distance Monte Carlo test, enhancing stability and reducing parameters.

Findings

UN-CCDs perform competitively on benchmark datasets.

The method is stable across various regimes with complex cluster geometries.

It remains largely parameter-free, simplifying practical use.

Abstract

We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on Ripley's K function, which exhibit performance degradation as dimensionality increases. To address this limitation, we introduce a nearest-neighbor-distance (NND) based Monte Carlo spatial randomness test (MC-SRT) for determining covering radii, resulting in the proposed Uniformity- and Neighbor-based CCDs (UN-CCDs). The proposed method is designed for datasets of moderate size and dimension, particularly in settings with complex cluster geometry and uniformly distributed background noise. Through Monte Carlo simulations and experiments on benchmark datasets, we show that UN-CCDs provide stable and competitive performance relative to several established clustering methods within the evaluated regimes, while remaining largely parameter-free. We also discuss computational trade-offs and identify the practical regimes in which the method is most effective. -- Keywords: Graph-based clustering; Cluster catch digraphs; Moderate-dimensional data; the nearest neighbor distance; Spatial randomness test.