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arxiv: 2604.07143 · v1 · submitted 2026-04-08 · 💻 cs.LG · stat.AP· stat.ML

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

Marek Gagolewski This is my paper

Pith reviewed 2026-05-10 18:08 UTC · model grok-4.3

classification 💻 cs.LG stat.APstat.ML
keywords clusteringdivisive clusteringminimum spanning treemutual reachabilityrobust clusteringdensity-based clusteringHDBSCAN
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The pith

Lumbermark detects clusters of varying sizes, densities, and shapes by iteratively chopping protruding segments from a mutual reachability minimum spanning tree.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Lumbermark as a divisive clustering algorithm that begins with the mutual reachability minimum spanning tree of a dataset and repeatedly severs large limbs at their narrow connecting segments. This process is designed to recover groups that differ in size, density, and geometry while limiting the distorting effect of scattered low-density points. Mutual reachability distances are used to smooth local variations, so that noise between clusters or outliers at edges exert less pull on the cuts. The resulting partitions allow direct user control over cluster sizes, offering a practical alternative when standard density-based methods leave the number or scale of groups unspecified. Practitioners would value such a tool for obtaining reliable groupings from irregular real data without extensive retuning.

Core claim

Lumbermark is a robust divisive clustering algorithm capable of detecting clusters of varying sizes, densities, and shapes. It works by iteratively chopping 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 produces partitions with user-specified sizes and serves as an alternative to HDBSCAN.

What carries the argument

The mutual reachability minimum spanning tree, which the algorithm repeatedly severs at protruding segments to isolate clusters while reducing the effect of density variations and noise.

If this is right

  • The method separates clusters even when they differ substantially in size, density, and shape.
  • Low-density noise and peripheral outliers exert reduced influence on the final partition.
  • Users obtain direct control over the sizes of the clusters in the output.
  • A fast implementation exists that can serve as a drop-in alternative when HDBSCAN output sizes are not controllable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The tree-chopping view may connect to other graph-based clustering techniques that operate on minimum spanning trees.
  • The user-specified size control suggests utility in applications where balanced or constrained group sizes are required.
  • Benchmark performance indicates the approach could extend to domains with high-dimensional or irregularly shaped data groups.

Load-bearing premise

Mutual reachability distances smooth the data distribution enough for the chopping process to separate clusters accurately despite the presence of noise and outliers.

What would settle it

Running the algorithm on benchmark datasets with known ground-truth partitions and user-specified sizes, then checking whether the recovered clusters match the true structure in cases with added noise bridges or density gradients.

Figures

Figures reproduced from arXiv: 2604.07143 by Marek Gagolewski.

Figure 1
Figure 1. Figure 1: Three copies of an example dataset with four clusters: two horizontal segments and two Gaussian blobs connected by a point chain. Additionally, its Euclidean minimum spanning tree (left) as well as two 25-mutual reachability minimum spanning trees (centre, right) are depicted. Edge colour intensities correspond to the underlying distances with the darkest edge being the longest in each case. By increasing … view at source ↗
Figure 2
Figure 2. Figure 2: Proportion of datasets with AR ≥ 0.95 and < 0.8 and the average AR as a function of min_cluster_factor 𝑓 and smoothing parameter 𝑀 in the case of the Lumbermark algorithm on 47 datasets. Datasets with imbalanced and balanced reference cluster counts are studied separately. M. Gagolewski: Preprint; Last updated on 9 April 2026 Page 11 of 13 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Proportion of datasets with AR ≥ 0.95 and < 0.8 and the average AR as a function of the Gini index threshold 𝐺 and smoothing parameter 𝑀 in the case of the Genie algorithm on 47 datasets. Datasets with imbalanced and balanced reference cluster counts are studied separately. M. Gagolewski: Preprint; Last updated on 9 April 2026 Page 12 of 13 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Lumbermark, a divisive clustering algorithm that iteratively chops large limbs from the mutual reachability minimum spanning tree (MR-MST) of a dataset to identify clusters of varying sizes, densities, and shapes. It claims that mutual reachability distances smooth the distribution and reduce the effect of noise/outliers, positioning the method as a user-specified-size alternative to HDBSCAN. An open-source Python/R implementation is provided, with claims of good performance on benchmarks.

Significance. If the robustness claims hold, Lumbermark would offer a practical, interpretable alternative for noisy clustering tasks where cluster-size control is desired, extending MST-based ideas from HDBSCAN with a chopping heuristic. The open-source package supports reproducibility and adoption by practitioners.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (Method description): The central robustness claim—that mutual reachability distances 'smoothens the data distribution and decreases the influence of low-density objects' enabling accurate limb separation—lacks any theoretical analysis, bounds, or controlled failure-mode tests (e.g., for bridge noise, density gradients, or high dimensions), leaving the key assumption unverified despite being load-bearing for the 'resistant' guarantee.
  2. [§4] §4 (Experiments): Benchmark results are asserted without reported details on datasets, baselines (including HDBSCAN variants), metrics, or ablation tests isolating the mutual-reachability smoothing effect, so the performance claims cannot be assessed for support.
minor comments (2)
  1. [§3] The manuscript would benefit from pseudocode or a clear algorithmic listing of the chopping procedure (limb identification and cut criteria) to aid implementation and understanding.
  2. [§4] Figure captions and axis labels in the experimental plots should explicitly state the evaluation metrics and number of runs for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and outline revisions to improve clarity and support for the claims.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (Method description): The central robustness claim—that mutual reachability distances 'smoothens the data distribution and decreases the influence of low-density objects' enabling accurate limb separation—lacks any theoretical analysis, bounds, or controlled failure-mode tests (e.g., for bridge noise, density gradients, or high dimensions), leaving the key assumption unverified despite being load-bearing for the 'resistant' guarantee.

    Authors: We agree that the manuscript provides no formal theoretical analysis or bounds on the smoothing effect of mutual reachability distances. This property is drawn from the established use in HDBSCAN, where it reduces outlier influence via core-distance augmentation. In revision, we will expand §3 with additional intuition and controlled synthetic experiments (e.g., datasets with bridge noise, varying density gradients, and moderate dimensions) to demonstrate limb separation behavior empirically. Deriving general theoretical guarantees for the full heuristic procedure is beyond the current scope and noted as future work. revision: partial

  2. Referee: [§4] §4 (Experiments): Benchmark results are asserted without reported details on datasets, baselines (including HDBSCAN variants), metrics, or ablation tests isolating the mutual-reachability smoothing effect, so the performance claims cannot be assessed for support.

    Authors: The experimental section uses standard clustering benchmarks and compares against HDBSCAN, but we acknowledge the details may not have been presented with sufficient explicitness. In the revised manuscript, we will expand §4 to include: (i) a table of all datasets with sizes and characteristics, (ii) precise baseline configurations (HDBSCAN with multiple min_cluster_size settings), (iii) the full set of metrics (adjusted Rand index, normalized mutual information, etc.), and (iv) an ablation comparing results with and without mutual reachability distances. The open-source package already enables full reproduction of the reported runs. revision: yes

Circularity Check

0 steps flagged

No circularity; algorithm is a direct procedural description built on external MST concepts

full rationale

The paper presents Lumbermark as an iterative chopping procedure on a mutual reachability MST, stating its properties (smoothing low-density points) as a direct consequence of the established mutual reachability distance definition from prior literature. No equations, parameters, or steps are defined in terms of the target outputs; no predictions are fitted then renamed; no uniqueness theorems or ansatzes are smuggled via self-citation; the central claim does not reduce to its inputs by construction. The derivation chain is self-contained as a new algorithmic recipe rather than a tautological re-expression of fitted data or prior self-references.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim relies on the effectiveness of the chopping procedure on the mutual reachability MST, which is a new application of these concepts. No new entities are invented. Assessment is limited to abstract description.

free parameters (1)
  • user-specified cluster sizes
    The algorithm produces partitions with user-specified sizes, making the target cluster size a key input parameter.
axioms (1)
  • domain assumption Mutual reachability distances smoothen the data distribution and decrease the influence of low-density objects
    Directly stated in the abstract as a property of the approach.

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