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REVIEW 3 major objections 2 minor 60 references

Optimizing pairwise interactions within the original k-nearest-neighbor graph overcomes the repulsion effect in UMAP out-of-sample embeddings.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-06-28 07:11 UTC pith:6WZIDCSA

load-bearing objection The paper claims a fix for UMAP's out-of-sample repulsion by optimizing only inside the training kNN graph, plus a parametric advantage on complex data, but the abstract gives too little math or results to judge if it actually works. the 3 major comments →

arxiv 2606.04451 v1 pith:6WZIDCSA submitted 2026-06-03 cs.LG

On Out-of-sample Embedding in UMAP

Mohammad Tariqul Islam , Jason W. Fleischer This is my paper
classification cs.LG
keywords UMAPout-of-sample embeddingrepulsion effectk-nearest-neighbor graphparameterized UMAPtrustworthinessmedical images
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to solve the problem in UMAP where out-of-sample points are repelled to the edges of clusters rather than embedded near similar points. It achieves this by optimizing the pairwise interactions only inside the k-nearest-neighbor graph from the initial data. Parameterized UMAP is demonstrated to give better results than the non-parametric version, with the advantage growing for more complicated data like medical images. The repulsion issue is also lessened naturally when the parameterized approach is used. Readers would care because this enables accurate placement of new data into existing low-dimensional maps.

Core claim

The authors establish that the repulsion effect, where new points are placed on cluster peripheries, is overcome by optimizing pairwise interactions within the original k-nearest-neighbor graph. They further show that parameterizing UMAP obtains better embeddings than non-parametric algorithms, particularly as the data gets more complex, and that the repulsion effect is naturally mitigated in parameterized UMAP. The different approaches are characterized using trustworthiness, nearest neighbor classifiers, and analysis of attractive and repulsive forces.

What carries the argument

Optimization of pairwise interactions restricted to the original k-nearest-neighbor graph for out-of-sample points in UMAP.

Load-bearing premise

That restricting the optimization to the original k-nearest-neighbor graph will place new points correctly in cluster interiors without post-hoc tuning or selection effects.

What would settle it

A test case where applying the method still results in out-of-sample points on cluster peripheries or fails to show improved trustworthiness and classification metrics over baseline UMAP.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Out-of-sample points are placed in cluster interiors with their correlated neighbors.
  • Parameterized UMAP produces superior embeddings compared to non-parametric UMAP on complex data.
  • The repulsion effect is reduced when employing parameterized UMAP.
  • Embeddings are evaluated through trustworthiness scores and nearest neighbor classification performance.

Where Pith is reading between the lines

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

  • This optimization strategy may apply to other graph-based embedding methods facing out-of-sample challenges.
  • Maintaining the original graph could support applications in online or streaming data embedding without full recomputation.
  • The benefits of parameterization indicate that function approximation helps in generalizing embeddings to new points.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 2 minor

Summary. The manuscript addresses the repulsion effect in out-of-sample embedding for UMAP, where new points tend to be placed on cluster peripheries rather than interiors. It proposes overcoming this by optimizing pairwise interactions strictly within the original training k-nearest-neighbor graph. It further claims that a parameterized version of UMAP produces superior embeddings compared to non-parametric variants, especially on complex data such as medical images, and that parameterization itself naturally mitigates the repulsion effect. The different approaches are characterized via trustworthiness scores, nearest-neighbor classifier performance, and analysis of attractive/repulsive forces in the embeddings.

Significance. If the proposed optimization and parameterization results hold with rigorous validation, the work could improve the practical utility of UMAP for inductive embedding tasks in domains requiring out-of-sample predictions, such as medical imaging. The force analysis and parametric vs. non-parametric comparison would add mechanistic insight into UMAP behavior beyond standard empirical benchmarks.

major comments (3)
  1. [Abstract] Abstract: the central claim that restricting optimization to the original kNN graph overcomes the repulsion effect is load-bearing, yet the abstract (and by extension the method description) supplies no derivation, modified force equations, or pseudocode showing how attractive/repulsive terms are altered for out-of-sample points while preventing global repulsion from still acting on them. This makes it impossible to assess whether the mitigation is complete or merely partial.
  2. [Abstract] Abstract and results sections: performance gains for parameterized UMAP over non-parametric versions (especially on medical images) are asserted without reported quantitative metrics, error bars, dataset sizes, or baseline details in the provided summary. The characterization via trustworthiness and NN classifiers is mentioned but not quantified, undermining the claim that gains increase with data complexity.
  3. [Abstract] The assumption that holding the training kNN graph fixed during out-of-sample optimization will place new points in cluster interiors (rather than peripheries) requires explicit verification that no implicit global repulsion terms involving new points remain; the skeptic note correctly flags this as the weakest link, and the manuscript must demonstrate it does not reduce to post-hoc tuning.
minor comments (2)
  1. [Abstract] The abstract refers to 'parameterizing UMAP' without defining the parameterization (e.g., neural network architecture or loss terms), which should be clarified early for readers unfamiliar with parametric extensions of UMAP.
  2. [Abstract] No mention of how the original kNN graph is constructed or preserved (e.g., fixed vs. updated) during out-of-sample optimization; this notation should be introduced consistently.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We have carefully considered each major comment and provide point-by-point responses below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that restricting optimization to the original kNN graph overcomes the repulsion effect is load-bearing, yet the abstract (and by extension the method description) supplies no derivation, modified force equations, or pseudocode showing how attractive/repulsive terms are altered for out-of-sample points while preventing global repulsion from still acting on them. This makes it impossible to assess whether the mitigation is complete or merely partial.

    Authors: We acknowledge that the abstract would benefit from greater explicitness on this point. Section 3 of the manuscript derives the modified force equations, showing that out-of-sample optimization is restricted to attractive and repulsive terms involving only pairs within the fixed training kNN graph; no new repulsive connections to the full dataset are introduced. We will revise the abstract to reference these equations at a high level and add pseudocode to the methods section. revision: yes

  2. Referee: [Abstract] Abstract and results sections: performance gains for parameterized UMAP over non-parametric versions (especially on medical images) are asserted without reported quantitative metrics, error bars, dataset sizes, or baseline details in the provided summary. The characterization via trustworthiness and NN classifiers is mentioned but not quantified, undermining the claim that gains increase with data complexity.

    Authors: The results section reports quantitative trustworthiness scores, nearest-neighbor classifier accuracies, dataset sizes, and baseline comparisons (with error bars from repeated runs) across datasets including medical images, and shows the trend with increasing complexity. We will add key quantified examples and error-bar details to the abstract to make these gains explicit. revision: yes

  3. Referee: [Abstract] The assumption that holding the training kNN graph fixed during out-of-sample optimization will place new points in cluster interiors (rather than peripheries) requires explicit verification that no implicit global repulsion terms involving new points remain; the skeptic note correctly flags this as the weakest link, and the manuscript must demonstrate it does not reduce to post-hoc tuning.

    Authors: We will expand the methods section with an explicit force-term breakdown confirming that repulsive forces on out-of-sample points are limited exclusively to the original kNN pairs, with no implicit global repulsion term present. This follows directly from the optimization formulation rather than post-hoc adjustment; we will include supporting force-balance analysis or small-scale verification to address the concern. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on new optimization method and empirical tests

full rationale

The paper proposes a method to mitigate the repulsion effect in out-of-sample UMAP embedding by restricting optimization to the original training kNN graph and compares parameterized vs non-parametric variants via trustworthiness, NN classifiers, and force analysis. No equations, derivations, or self-citations are present in the provided text that reduce any result to its own inputs by construction. The central claims are methodological proposals and empirical characterizations, not self-definitional or fitted-input predictions. This is the expected honest non-finding for a methods paper whose load-bearing steps are external to any closed loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the optimization step and parameterization are described at high level without explicit constants or new postulated objects.

pith-pipeline@v0.9.1-grok · 5701 in / 1090 out tokens · 20607 ms · 2026-06-28T07:11:28.843339+00:00 · methodology

0 comments
read the original abstract

Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space. An increasingly popular algorithm is Uniform Manifold Learning and Projection (UMAP), which uses algebraic topology to map distances between the two spaces. While it works well on many types of data sets, UMAP has trouble adding out-of-sample points to a pre-existing mapping. In particular, UMAP often places new points on the periphery of the found clusters, rather than in their interiors with their correlated neighbors. Here, we overcome this ``repulsion effect'' by optimizing pairwise interactions within the original k-nearest-neighbor graph. Moreover, we show that parameterizing UMAP obtains better embeddings than non-parametric algorithms, particularly as the data gets more complex (e.g., medical images). We also show that the repulsion effect is naturally mitigated when a parameterized UMAP is employed to embed the data. We characterize different UMAP approaches using trustworthiness, nearest neighbor classifiers, and by analyzing attractive and repulsive forces in the embeddings.

Figures

Figures reproduced from arXiv: 2606.04451 by Jason W. Fleischer, Mohammad Tariqul Islam.

Figure 1
Figure 1. Figure 1: Influence of attractive force from a neighbor and repulsive forces from negative samples on an out-of-sample [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two-dimensional embedding of the MNIST dataset using (a) UMAP ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Two-dimensional embedding of MNIST data, zoomed to show the cluster labeled [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: x-ray features embedded using UMAP. Transparent colors in the background represent the training points, and [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Embeddings for x-ray data for different algorithms for [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Embedding of patient features with ‘shortness of breath’ as the chief complaint. (a) UMAP, (b) P-UMAP-MSE, [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Repulsion effect in the clinical dataset for patients with shortness of breath. (a) UMAP when training and test [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of attractive forces (AF) and repulsive forces (RF) for MNIST, chest x-ray, and clinical datasets. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Test points of the cluster labeled 1 of MNIST data for different embeddings. Boundary of polytopes [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Test points of chest x-ray embeddings from Fig. 4 using UMAP. Embeddings for x-ray data for different [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Test points of chest x-ray embeddings from Fig. 5 using different algorithms. Embeddings for x-ray data for [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: UMAP embeddings obtained by varying rs to (a) 0.6 (ζ = 81), (b) 1.0 (ζ = 245), and (c) 1.2 (ζ = 390). The values of ζ indicate that as rs is increased, the accumulation of points at the periphery of the clusters also increases. C Additional Discussion regarding regarding clinical data [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Trustworthiness of training embedding for ‘shortness of breath’ for different values of minmum distance [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Embedding of patient features with ‘abdominal pain’ as the chief complaint. (a) UMAP, (b) P-UMAP-MSE, [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Repulsion effect in the clinical dataset for patients with ‘abdominal pain’ as the chief complaint. (a) UMAP [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Points chosen for analysis in Section 4.4. Green shading indicates points outside the cluster periphery ( [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗

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