Lumbermark: Resistant Clustering by Chopping Up Mutual Reachability Minimum Spanning Trees

2026-04-08

AI Summary

This study addresses the sensitivity of traditional clustering methods to noise and outliers when handling clusters of varying sizes, densities, and shapes. To overcome this limitation, the authors propose a robust divisive clustering algorithm that integrates mutual reachability distance with minimum spanning trees. The method iteratively identifies cluster structures by pruning large branches connected via prominent edges and allows users to specify the desired number of clusters, offering an effective alternative to HDBSCAN. Extensive experiments on multiple benchmark datasets demonstrate that the proposed algorithm achieves superior performance, balancing computational efficiency and usability. Open-source implementations in both Python and R are provided to facilitate adoption and reproducibility.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Distributed Search

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We introduce Lumbermark, a robust divisive clustering algorithm capable of detecting clusters of varying sizes, densities, and shapes. Lumbermark iteratively chops off large limbs connected by protruding segments of a dataset's mutual reachability minimum spanning tree. The use of mutual reachability distances smoothens the data distribution and decreases the influence of low-density objects, such as noise points between clusters or outliers at their peripheries. The algorithm can be viewed as an alternative to HDBSCAN that produces partitions with user-specified sizes. A fast, easy-to-use implementation of the new method is available in the open-source 'lumbermark' package for Python and R. We show that Lumbermark performs well on benchmark data and hope it will prove useful to data scientists and practitioners across different fields.

Problem

• clustering
• noise
• outliers
• varying densities
• cluster shapes

Innovation

• Lumbermark
• mutual reachability
• minimum spanning tree
• divisive clustering
• density-based clustering